Whiteley, J. P.
2017-10-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.
2018-01-01
Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.
GPU-based acceleration of computations in nonlinear finite element deformation analysis.
Mafi, Ramin; Sirouspour, Shahin
2014-03-01
The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.
Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol
2010-12-01
Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 64; Issue 3 ... Keywords. Nonlinear dynamics; logistic map; -deformation; Tsallis statistics. ... As a specific example, a -deformation procedure is applied to the logistic map. Compared ...
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Gorb, Yuliya; Walton, Jay R.
2010-01-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Gorb, Yuliya
2010-11-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Nonlinear finite element analyses: advances and challenges in dental applications.
Wakabayashi, N; Ona, M; Suzuki, T; Igarashi, Y
2008-07-01
To discuss the development and current status of application of nonlinear finite element method (FEM) in dentistry. The literature was searched for original research articles with keywords such as nonlinear, finite element analysis, and tooth/dental/implant. References were selected manually or searched from the PUBMED and MEDLINE databases through November 2007. The nonlinear problems analyzed in FEM studies were reviewed and categorized into: (A) nonlinear simulations of the periodontal ligament (PDL), (B) plastic and viscoelastic behaviors of dental materials, (C) contact phenomena in tooth-to-tooth contact, (D) contact phenomena within prosthodontic structures, and (E) interfacial mechanics between the tooth and the restoration. The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress-strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model. The definition of contact area critically affects the reliability of the contact analyses, especially for implant-abutment complexes. To predict the failure risk of a bonded tooth-restoration interface, it is essential to assess the normal and shear stresses relative to the interface. The inclusion of viscoelasticity and plastic deformation to the program to account for the time-dependent, thermal sensitive, and largely deformable nature of dental materials would enhance its application. Further improvement of the nonlinear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
The Finite Deformation Dynamic Sphere Test Problem
Energy Technology Data Exchange (ETDEWEB)
Versino, Daniele [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Brock, Jerry Steven [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-02
In this manuscript we describe test cases for the dynamic sphere problem in presence of finite deformations. The spherical shell in exam is made of a homogeneous, isotropic or transverse isotropic material and elastic and elastic-plastic material behaviors are considered. Twenty cases, (a) to (t), are thus defined combining material types and boundary conditions. The inner surface radius, the outer surface radius and the material's density are kept constant for all the considered test cases and their values are r_{i} = 10mm, r_{o} = 20mm and p = 1000Kg/m^{3} respectively.
International Nuclear Information System (INIS)
Xiao Xuejian; Chen Ruxin
1995-02-01
Based on the R. Hills incremental virtual power principle and the elasto-plastic constitution equation for large deformation and by considering physical nonlinear, geometric nonlinear and thermal effects, a plane and axisymmetric finite element equation for thermal large elasto-plastic deformation has been established in the Euler description. The corresponding analysis program ATLEPD has been also complied for thermal large elasto-plastic deformation process of O-ring in RPV. The variations of stress, strain, contact specific pressure, mesh deformation and the aspects of spring back in upsetting and spring back process have been also investigated. Numerical results are fairly consistent with experimental ones. (5 figs., 4 tabs.)
International Nuclear Information System (INIS)
Jaganathan, Ramaswamy; Sinha, Sudeshna
2005-01-01
A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors-a phenomenon rare in one-dimensional maps
Linear and Nonlinear Finite Elements.
1983-12-01
Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y , (1-y)’ 1-y’ 2 - y" (6) that change eq. (5) to V) = , [yŖ(1 + y") - Qy
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel.
International Nuclear Information System (INIS)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel
Predictions of total deformations in Jebba main dam by finite ...
African Journals Online (AJOL)
This paper examined the deformations of the Jebba Main Dam, Jebba Nigeria using the finite element method. The study also evaluated the predicted deformations and compared them with the actual deformations in the dam to identify possible causes of the observed longitudinal crack at the dam crest. The Jebba dam is a ...
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
Partitioning of elastic energy in open-cell foams under finite deformations
International Nuclear Information System (INIS)
Harb, Rani; Taciroglu, Ertugrul; Ghoniem, Nasr
2013-01-01
The challenges associated with the computational modeling and simulation of solid foams are threefold—namely, the proper representation of an intricate geometry, the capability to accurately describe large deformations, and the extremely arduous numerical detection and enforcement of self-contact during crushing. The focus of this study is to assess and accurately quantify the effects of geometric nonlinearities (i.e. finite deformations, work produced under buckling-type motions) on the predicted mechanical response of open-cell foams of aluminum and polyurethane prior to the onset of plasticity and contact. Beam elements endowed with three-dimensional finite deformation kinematics are used to represent the foam ligaments. Ligament cross-sections are discretized through a fiber-based formulation that provides accurate information regarding the onset of plasticity, given the uniaxial yield stress–strain data for the bulk material. It is shown that the (hyper-) elastic energy partition within ligaments is significantly influenced by kinematic nonlinearities, which frequently cause strong coupling between the axial, bending, shear and torsional deformation modes. This deformation mode-coupling is uniquely obtained as a result of evaluating equilibrium in the deformed configuration, and is undetectable when small deformations are assumed. The relationship between the foam topology and energy partitioning at various stages of moderate deformation is also investigated. Coupled deformation modes are shown to play an important role, especially in perturbed Kelvin structures where over 70% of the energy is stored in coupled axial-shear and axial-bending modes. The results from this study indicate that it may not always be possible to accurately simulate the onset of plasticity (and the response beyond this regime) if finite deformation kinematics are neglected
Corrugated Membrane Nonlinear Deformation Process Calculation
Directory of Open Access Journals (Sweden)
A. S. Nikolaeva
2015-01-01
Full Text Available Elastic elements are widely used in instrumentation. They are used to create a particular interference between the parts, for accumulating mechanical energy, as the motion transmission elements, elastic supports, and sensing elements of measuring devices. Device reliability and quality depend on the calculation accuracy of the elastic elements. A corrugated membrane is rather common embodiment of the elastic element.The corrugated membrane properties depend largely on its profile i.e. a generatrix of the meridian surface.Unlike other types of pressure elastic members (bellows, tube spring, the elastic characteristics of which are close to linear, an elastic characteristic of the corrugated membrane (typical movement versus external load is nonlinear. Therefore, the corrugated membranes can be used to measure quantities, nonlinearly related to the pressure (e.g., aircraft air speed, its altitude, pipeline fluid or gas flow rate. Another feature of the corrugated membrane is that significant movements are possible within the elastic material state. However, a significant non-linearity of membrane characteristics leads to severe complicated calculation.This article is aimed at calculating the corrugated membrane to obtain the elastic characteristics and the deformed shape of the membrane meridian, as well as at investigating the processes of buckling. As the calculation model, a thin-walled axisymmetric shell rotation is assumed. The material properties are linearly elastic. We consider a corrugated membrane of sinusoidal profile. The membrane load is a uniform pressure.The algorithm for calculating the mathematical model of an axisymmetric corrugated membrane of constant thickness, based on the Reissner’s theory of elastic thin shells, was realized as the author's program in C language. To solve the nonlinear problem were used a method of changing the subspace of control parameters, developed by S.S., Gavriushin, and a parameter marching method
Finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials
Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.
Idkaidek, Ashraf; Jasiuk, Iwona
2015-12-01
We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Energy Technology Data Exchange (ETDEWEB)
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
International Nuclear Information System (INIS)
Volk, Brent L; Lagoudas, Dimitris C; Chen, Yi-Chao
2010-01-01
This study presents the analysis of the finite deformation response of a shape memory polymer (SMP). This two-part paper addresses the thermomechanical characterization of SMPs, the derivation of material parameters for a finite deformation phenomenological model, the numerical implementation of such a model, and the predictions from the model with comparisons to experimental data. Part II of this work presents the calibration of a previously developed thermoelastic constitutive model which is capable of handling finite deformations. The model is proposed in a general three-dimensional framework; however, this work focuses on reducing the model to one dimension and subsequently calibrating the model using experimental data obtained in part I. The one-dimensional numerical implementation of the model is presented, including the handling of the system of nonlinear equations and the integral term resulting from the constitutive model. The model is then used to predict the uniaxial shape memory effect. Results indicate good agreement between the model predictions and the experimental results, but the predictions do not capture the irrecoverable deformation present at the end of recovery
Relation of deformed nonlinear algebras with linear ones
International Nuclear Information System (INIS)
Nowicki, A; Tkachuk, V M
2014-01-01
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)
Nonlinear finite element analysis of concrete structures
International Nuclear Information System (INIS)
Ottosen, N.S.
1980-05-01
This report deals with nonlinear finite element analysis of concrete structures loaded in the short-term up until failure. A profound discussion of constitutive modelling on concrete is performed; a model, applicable for general stress states, is described and its predictions are compared with experimental data. This model is implemented in the AXIPLANE-program applicable for axisymmetrick and plane structures. The theoretical basis for this program is given. Using the AXIPLANE-program various concrete structures are analysed up until failure and compared with experimental evidence. These analyses include panels pressure vessel, beams failing in shear and finally a specific pull-out test, the Lok-Test, is considered. In these analyses, the influence of different failure criteria, aggregate interlock, dowel action, secondary cracking, magnitude of compressive strenght, magnitude of tensile strenght and of different post-failure behaviours of the concrete are evaluated. Moreover, it is shown that a suitable analysis of the theoretical data results in a clear insight into the physical behaviour of the considered structures. Finally, it is demonstrated that the AXISPLANE-program for widely different structures exhibiting very delicate structural aspects gives predictions that are in close agreement with experimental evidence. (author)
Geometry of finite deformations and time-incremental analysis
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2016-01-01
Roč. 81, May (2016), s. 230-244 ISSN 0020-7462 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * time-incremental analysis * Lagrangian system * evolution equation of Lie type Subject RIV: BE - Theoretical Physics Impact factor: 2.074, year: 2016 http://www.sciencedirect.com/science/article/pii/S0020746216000330
Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior
Directory of Open Access Journals (Sweden)
Jieqing Huang
2014-01-01
Full Text Available This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. On the basis of some assumptions about the secondary consolidation behavior, the continuity equation of pore water in Gibson’s consolidation theory is modified. Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. Afterwards, the calculation results of this new method and other two methods are compared. It can be found that Gibson’s method may underestimate the excess pore water pressure during primary consolidation. The new method which takes the secondary consolidation behavior, the nonlinear compressibility, and nonlinear permeability of soils into consideration can precisely estimate the settlement rate and the final settlement of Hangzhou soft clay sample.
Hosseini, Seyed Farhad; Hashemian, Ali; Moetakef-Imani, Behnam; Hadidimoud, Saied
2018-03-01
In the present paper, the isogeometric analysis (IGA) of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables (displacement and rotation) in a finite element analysis are considered to be the same as the non-uniform rational basis spline (NURBS) basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.
Lefèvre, Victor; Lopez-Pamies, Oscar
2017-02-01
This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi
Angela Mihai, L.; Goriely, Alain
2013-01-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects
Energy Technology Data Exchange (ETDEWEB)
Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)
2006-04-01
In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.
Frost heave modelling of buried pipelines using non-linear Fourier finite elements
International Nuclear Information System (INIS)
Wan, R. G.; You, R.
1998-01-01
Numerical analysis of the response of a three-dimensional soil-pipeline system in a freezing environment using non-linear Fourier finite elements was described as an illustration of the effectiveness of this technique in analyzing plasticity problems. Plastic deformations occur when buried pipeline is under the action of non-uniform frost heave. The three-dimensional frost heave which develops over time including elastoplastic deformations of the soil and pipe are computed. The soil heave profile obtained in the numerical analysis was consistent with experimental findings for similar configurations. 8 refs., 8 figs
Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field
International Nuclear Information System (INIS)
Deng Fengyan; He Xingsuo; Li Liang; Zhang Juan
2007-01-01
In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a 'stiffening beam' can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases
Optimization of deformation monitoring networks using finite element strain analysis
Alizadeh-Khameneh, M. Amin; Eshagh, Mehdi; Jensen, Anna B. O.
2018-04-01
An optimal design of a geodetic network can fulfill the requested precision and reliability of the network, and decrease the expenses of its execution by removing unnecessary observations. The role of an optimal design is highlighted in deformation monitoring network due to the repeatability of these networks. The core design problem is how to define precision and reliability criteria. This paper proposes a solution, where the precision criterion is defined based on the precision of deformation parameters, i. e. precision of strain and differential rotations. A strain analysis can be performed to obtain some information about the possible deformation of a deformable object. In this study, we split an area into a number of three-dimensional finite elements with the help of the Delaunay triangulation and performed the strain analysis on each element. According to the obtained precision of deformation parameters in each element, the precision criterion of displacement detection at each network point is then determined. The developed criterion is implemented to optimize the observations from the Global Positioning System (GPS) in Skåne monitoring network in Sweden. The network was established in 1989 and straddled the Tornquist zone, which is one of the most active faults in southern Sweden. The numerical results show that 17 out of all 21 possible GPS baseline observations are sufficient to detect minimum 3 mm displacement at each network point.
Finite element analysis of nonlinear creeping flows
International Nuclear Information System (INIS)
Loula, A.F.D.; Guerreiro, J.N.C.
1988-12-01
Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt
Advances in dynamic relaxation techniques for nonlinear finite element analysis
International Nuclear Information System (INIS)
Sauve, R.G.; Metzger, D.R.
1995-01-01
Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Nonlinear analysis of shear deformable beam-columns partially ...
African Journals Online (AJOL)
In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless Winkler foundation, undergoing moderate large deflections under general boundary ...
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.
Directory of Open Access Journals (Sweden)
Olga Kononova
2016-01-01
Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
A finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)
International Nuclear Information System (INIS)
Volk, Brent L; Lagoudas, Dimitris C; Chen, Yi-Chao; Whitley, Karen S
2010-01-01
This study presents the analysis of the finite deformation response of a shape memory polymer (SMP). This two-part paper addresses the thermomechanical characterization of SMPs, the derivation of material parameters for a finite deformation phenomenological model, the numerical implementation of such a model, and the predictions from the model with comparisons to experimental data. Part I of this work presents the thermomechanical characterization of the material behavior of a shape memory polymer. In this experimental investigation, the vision image correlation system, a visual–photographic apparatus, was used to measure displacements in the gauge area. A series of tensile tests, which included nominal values of the extension of 10%, 25%, 50%, and 100%, were performed on SMP specimens. The effects on the free recovery behavior of increasing the value of the applied deformation and temperature rate were considered. The stress–extension relationship was observed to be nonlinear for increasing values of the extension, and the shape recovery was observed to occur at higher temperatures upon increasing the temperature rate. The experimental results, aided by the advanced experimental apparatus, present components of the material behavior which are critical for the development and calibration of models to describe the response of SMPs
Hybrid High-Order methods for finite deformations of hyperelastic materials
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2018-01-01
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.
Dynamic visual cryptography on deformable finite element grids
Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.
2017-07-01
Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Energy Technology Data Exchange (ETDEWEB)
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Soft tissue deformation using a Hierarchical Finite Element Model.
Faraci, Alessandro; Bello, Fernando; Darzi, Ara
2004-01-01
Simulating soft tissue deformation in real-time has become increasingly important in order to provide a realistic virtual environment for training surgical skills. Several methods have been proposed with the aim of rendering in real-time the mechanical and physiological behaviour of human organs, one of the most popular being Finite Element Method (FEM). In this paper we present a new approach to the solution of the FEM problem introducing the concept of parent and child mesh within the development of a hierarchical FEM. The online selection of the child mesh is presented with the purpose to adapt the mesh hierarchy in real-time. This permits further refinement of the child mesh increasing the detail of the deformation without slowing down the simulation and giving the possibility of integrating force feedback. The results presented demonstrate the application of our proposed framework using a desktop virtual reality (VR) system that incorporates stereo vision with integrated haptics co-location via a desktop Phantom force feedback device.
A nonaffine network model for elastomers undergoing finite deformations
Davidson, Jacob D.; Goulbourne, N. C.
2013-08-01
In this work, we construct a new physics-based model of rubber elasticity to capture the strain softening, strain hardening, and deformation-state dependent response of rubber materials undergoing finite deformations. This model is unique in its ability to capture large-stretch mechanical behavior with parameters that are connected to the polymer chemistry and can also be easily identified with the important characteristics of the macroscopic stress-stretch response. The microscopic picture consists of two components: a crosslinked network of Langevin chains and an entangled network with chains confined to a nonaffine tube. These represent, respectively, changes in entropy due to thermally averaged chain conformations and changes in entropy due to the magnitude of these conformational fluctuations. A simple analytical form for the strain energy density is obtained using Rubinstein and Panyukov's single-chain description of network behavior. The model only depends on three parameters that together define the initial modulus, extent of strain softening, and the onset of strain hardening. Fits to large stretch data for natural rubber, silicone rubber, VHB 4905 (polyacrylate rubber), and b186 rubber (a carbon black-filled rubber) are presented, and a comparison is made with other similar constitutive models of large-stretch rubber elasticity. We demonstrate that the proposed model provides a complete description of elastomers undergoing large deformations for different applied loading configurations. Moreover, since the strain energy is obtained using a clear set of physical assumptions, this model may be tested and used to interpret the results of computer simulation and experiments on polymers of known microscopic structure.
A comparison of numerical methods used for finite element modelling of soft tissue deformation
Pathmanathan, P
2009-05-01
Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.
A comparison of numerical methods used for finite element modelling of soft tissue deformation
Pathmanathan, P; Gavaghan, D; Whiteley, J
2009-01-01
Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.
Nonlinear finite element formulation for analyzing shape memory alloy cylindrical panels
International Nuclear Information System (INIS)
Mirzaeifar, R; Shakeri, M; Sadighi, M
2009-01-01
In this paper, a general incremental displacement based finite element formulation capable of modeling material nonlinearities based on first-order shear deformation theory (FSDT) is developed for cylindrical shape memory alloy (SMA) shells. The Boyd–Lagoudas phenomenological model with polynomial hardening in conjunction with 3D incremental convex cutting plane explicit algorithm is implemented for preparing the SMA constitutive model in the finite element formulation. Several numerical examples are presented for demonstrating the performance of the proposed formulation in stress, deflection and phase transformation analysis of pseudoelastic behavior of shape memory cylindrical panels with various boundary conditions. Also, it is shown that the presented formulation can be implemented for studying plates and beams with rectangular cross section
Nonlinear magnetohydrodynamics simulation using high-order finite elements
International Nuclear Information System (INIS)
Plimpton, Steven James; Schnack, D.D.; Tarditi, A.; Chu, M.S.; Gianakon, T.A.; Kruger, S.E.; Nebel, R.A.; Barnes, D.C.; Sovinec, C.R.; Glasser, A.H.
2005-01-01
A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p (ge) 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x(parallel)/x(perpendicular)) is computed accurately with p (ge) 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.
Stupishin, L. U.; Nikitin, K. E.; Kolesnikov, A. G.
2018-02-01
The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin; Carrillo, José
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Finite element solution of quasistationary nonlinear magnetic field
International Nuclear Information System (INIS)
Zlamal, Milos
1982-01-01
The computation of quasistationary nonlinear two-dimensional magnetic field leads to the following problem. There is given a bounded domain OMEGA and an open nonempty set R included in OMEGA. We are looking for the magnetic vector potential u(x 1 , x 2 , t) which satisifies: 1) a certain nonlinear parabolic equation and an initial condition in R: 2) a nonlinear elliptic equation in S = OMEGA - R which is the stationary case of the above mentioned parabolic equation; 3) a boundary condition on delta OMEGA; 4) u as well as its conormal derivative are continuous accross the common boundary of R and S. This problem is formulated in two equivalent abstract ways. There is constructed an approximate solution completely discretized in space by a generalized Galerkin method (straight finite elements are a special case) and by backward A-stable differentiation methods in time. Existence and uniqueness of a weak solution is proved as well as a weak and strong convergence of the approximate solution to this solution. There are also derived error bounds for the solution of the two-dimensional nonlinear magnetic field equations under the assumption that the exact solution is sufficiently smooth
Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses
Agata, R.; Ichimura, T.; Hyodo, M.; Barbot, S.; Hori, T.
2017-12-01
To explain earthquake generation processes, simulation methods of earthquake cycles have been studied. For such simulations, the combination of the rate- and state-dependent friction law at the fault plane and the boundary integral method based on Green's function in an elastic half space is widely used (e.g. Hori 2009; Barbot et al. 2012). In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, while the effects of complex physics such as mantle rheology and gravity are generally not taken into account. To consider such effects, we seek to develop an earthquake cycle simulation combining crustal deformation computation based on the finite element (FE) method with the rate- and state-dependent friction law. Since the drawback of this approach is the computational cost associated with obtaining numerical solutions, we adopt a recently developed fast and scalable FE solver (Ichimura et al. 2016), which assumes use of supercomputers, to solve the problem in a realistic time. As in the previous approach, we solve the governing equations consisting of the rate- and state-dependent friction law. In solving the equations, we compute stress changes along the fault plane due to crustal deformation using FE simulation, instead of computing them by superimposing slip response function as in the previous approach. In stress change computation, we take into account nonlinear viscoelastic deformation in the asthenosphere. In the presentation, we will show simulation results in a normative three-dimensional problem, where a circular-shaped velocity-weakening area is set in a square-shaped fault plane. The results with and without nonlinear viscosity in the asthenosphere will be compared. We also plan to apply the developed code to simulate the post-earthquake deformation of a megathrust earthquake, such as the 2011 Tohoku earthquake. Acknowledgment: The results were obtained using the K computer at the RIKEN (Proposal number
Energy Technology Data Exchange (ETDEWEB)
Cai, X C; Marcinkowski, L; Vassilevski, P S
2005-02-10
This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
Ren Penghao; Wang Aimin; Wang Xiaolong; Zhang Yanlin
2017-01-01
After aluminum alloy sheet metal parts machining, the residual stress release will cause a large deformation. To solve this problem, this paper takes a aluminum alloy sheet aerospace workpiece as an example, establishes the theoretical model of elastic deformation and the finite element model, and places quantitative initial stress in each element of machining area, analyses stress release simulation and deformation. Through different initial stress release simulative analysis of deformation ...
On the all-order perturbative finiteness of the deformed N=4 SYM theory
International Nuclear Information System (INIS)
Rossi, G.C.; Sokatchev, E.; Stanev, Ya.S.
2006-01-01
We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6
Sun, W.; Na, S.
2017-12-01
A stabilized thermo-hydro-mechanical (THM) finite element model is introduced to investigate the freeze-thaw action of frozen porous media in the finite deformation range. By applying the mixture theory, frozen soil is idealized as a composite consisting of three phases, i.e., solid grain, unfrozen water and ice crystal. A generalized hardening rule at finite strain is adopted to replicate how the elasto-plastic responses and critical state evolve under the influence of phase transitions and heat transfer. The enhanced particle interlocking and ice strengthening during the freezing processes and the thawing-induced consolidation at the geometrical nonlinear regimes are both replicated in numerical examples. The numerical issues due to lack of two-fold inf-sup condition and ill-conditioning of the system of equations are addressed. Numerical examples for engineering applications at cold region are analyzed via the proposed model to predict the impacts of changing climate on infrastructure at cold regions.
Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames
Directory of Open Access Journals (Sweden)
R.S.B. STRAMANDINOLI
Full Text Available Abstract In this work, a two-dimensional finite element (FE model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model. It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.
Analysis of nonlinear deformations and damage in CFRP textile laminates
International Nuclear Information System (INIS)
Ullah, H; Harland, A R; Silberschmidt, V V; Lucas, T; Price, D
2011-01-01
Carbon fibre-reinforced polymer (CFRP) textile composites are widely used in aerospace, automotive and construction components and structures thanks to their relatively low production costs, higher delamination and impact strength. They can also be used in various products in sports industry. These products are usually exposed to different in-service conditions such as large bending deformation and multiple impacts. Composite materials usually demonstrate multiple modes of damage and fracture due to their heterogeneity and microstructure, in contrast to more traditional homogeneous structural materials like metals and alloys. Damage evolution affects both their in-service properties and performance that can deteriorate with time. These damage modes need adequate means of analysis and investigation, the major approaches being experimental characterisation, numerical simulations and microtomography analysis. This research deals with a deformation behaviour and damage in composite laminates linked to their quasi-static bending. Experimental tests are carried out to characterise the behaviour of woven CFRP material under large-deflection bending. Two-dimensional finite element (FE) models are implemented in the commercial code Abaqus/Explicit to study the deformation behaviour and damage in woven CFRP laminates. Multiple layers of bilinear cohesive-zone elements are employed to model the onset and progression of inter-ply delamination process. X-ray Micro-Computed Tomography (MicroCT) analysis is carried out to investigate internal damage mechanisms such as cracking and delaminations. The obtained results of simulations are in agreement with experimental data and MicroCT scans.
Analysis of nonlinear deformations and damage in CFRP textile laminates
Energy Technology Data Exchange (ETDEWEB)
Ullah, H; Harland, A R; Silberschmidt, V V [Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Leicester-shire, LE11 3TU (United Kingdom); Lucas, T; Price, D, E-mail: H.Ullah@lboro.ac.uk [Adidas AG, Herzogenaruch (Germany)
2011-07-19
Carbon fibre-reinforced polymer (CFRP) textile composites are widely used in aerospace, automotive and construction components and structures thanks to their relatively low production costs, higher delamination and impact strength. They can also be used in various products in sports industry. These products are usually exposed to different in-service conditions such as large bending deformation and multiple impacts. Composite materials usually demonstrate multiple modes of damage and fracture due to their heterogeneity and microstructure, in contrast to more traditional homogeneous structural materials like metals and alloys. Damage evolution affects both their in-service properties and performance that can deteriorate with time. These damage modes need adequate means of analysis and investigation, the major approaches being experimental characterisation, numerical simulations and microtomography analysis. This research deals with a deformation behaviour and damage in composite laminates linked to their quasi-static bending. Experimental tests are carried out to characterise the behaviour of woven CFRP material under large-deflection bending. Two-dimensional finite element (FE) models are implemented in the commercial code Abaqus/Explicit to study the deformation behaviour and damage in woven CFRP laminates. Multiple layers of bilinear cohesive-zone elements are employed to model the onset and progression of inter-ply delamination process. X-ray Micro-Computed Tomography (MicroCT) analysis is carried out to investigate internal damage mechanisms such as cracking and delaminations. The obtained results of simulations are in agreement with experimental data and MicroCT scans.
Analysis of nonlinear deformations and damage in CFRP textile laminates
Ullah, H.; Harland, A. R.; Lucas, T.; Price, D.; Silberschmidt, V. V.
2011-07-01
Carbon fibre-reinforced polymer (CFRP) textile composites are widely used in aerospace, automotive and construction components and structures thanks to their relatively low production costs, higher delamination and impact strength. They can also be used in various products in sports industry. These products are usually exposed to different in-service conditions such as large bending deformation and multiple impacts. Composite materials usually demonstrate multiple modes of damage and fracture due to their heterogeneity and microstructure, in contrast to more traditional homogeneous structural materials like metals and alloys. Damage evolution affects both their in-service properties and performance that can deteriorate with time. These damage modes need adequate means of analysis and investigation, the major approaches being experimental characterisation, numerical simulations and microtomography analysis. This research deals with a deformation behaviour and damage in composite laminates linked to their quasi-static bending. Experimental tests are carried out to characterise the behaviour of woven CFRP material under large-deflection bending. Two-dimensional finite element (FE) models are implemented in the commercial code Abaqus/Explicit to study the deformation behaviour and damage in woven CFRP laminates. Multiple layers of bilinear cohesive-zone elements are employed to model the onset and progression of inter-ply delamination process. X-ray Micro-Computed Tomography (MicroCT) analysis is carried out to investigate internal damage mechanisms such as cracking and delaminations. The obtained results of simulations are in agreement with experimental data and MicroCT scans.
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran
2012-05-01
This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro-macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation. © 2012 Elsevier Ltd.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Energy Technology Data Exchange (ETDEWEB)
Patra, Anirban [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wen, Wei [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Martinez Saez, Enrique [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tome, Carlos [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-31
This report describes the implementation of a crystal plasticity framework (VPSC) for irradiation hardening and plastic deformation in the finite element code, MOOSE. Constitutive models for irradiation hardening and the crystal plasticity framework are described in a previous report [1]. Here we describe these models briefly and then describe an algorithm for interfacing VPSC with finite elements. Example applications of tensile deformation of a dog bone specimen and a 3D pre-irradiated bar specimen performed using MOOSE are demonstrated.
Finite bandwidth, nonlinear convective flow in a mushy layer
Energy Technology Data Exchange (ETDEWEB)
Riahi, D N, E-mail: daniel.riahi@utrgv.edu [School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, One West University Boulevard, Brownsville, TX 78520 (United States)
2017-04-15
Finite amplitude convection with a continuous finite bandwidth of modes in a horizontal mushy layer during the solidification of binary alloys is investigated. We analyze the nonlinear convection for values of the Rayleigh number close to its critical value by using multiple scales and perturbation techniques. Applying a combined temporal and spatial evolution approach, we determine a set of three coupled differential equations for the amplitude functions of the convective modes. A large number of new subcritical or supercritical stable solutions to these equations in the form of steady rolls and hexagons with different horizontal length scales are detected. We find, in particular, that depending on the parameter values and on the magnitude and direction of the wave number vectors for the amplitude functions, hexagons with down-flow or up-flow at the cells’ centers or rolls can be stable. Rolls or hexagons with longer horizontal wave length can be stable at higher amplitudes, and there are cases where hexagons are unstable for any value of the Rayleigh number, while rolls are stable only for the values of the Rayleigh number beyond some value. We also detected new stable and irregular flow patterns with two different horizontal scales in the form of superposition of either two sets of hexagons or two sets of inclined rolls. (paper)
Directory of Open Access Journals (Sweden)
Ren Penghao
2017-01-01
Full Text Available After aluminum alloy sheet metal parts machining, the residual stress release will cause a large deformation. To solve this problem, this paper takes a aluminum alloy sheet aerospace workpiece as an example, establishes the theoretical model of elastic deformation and the finite element model, and places quantitative initial stress in each element of machining area, analyses stress release simulation and deformation. Through different initial stress release simulative analysis of deformation of the workpiece, a linear relationship between initial stress and deformation is found; Through simulative analysis of coupling direction-stress release, the superposing relationship between the deformation caused by coupling direction-stress and the deformation caused by single direction stress is found. The research results provide important theoretical support for the stress threshold setting and deformation controlling of the workpieces in the production practice.
Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Chowdury, A.R.; Naskar, M.
1986-01-01
Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli
Oden, J. T.; Becker, E. B.; Lin, T. L.; Hsieh, K. T.
1984-01-01
The formulation and numerical analysis of several problems related to the behavior of pneumatic tires are considered. These problems include the general rolling contact problem of a rubber-like viscoelastic cylinder undergoing finite deformations and the finite deformation of cord-reinforced rubber composites. New finite element models are developed for these problems. Numerical results obtained for several representative cases are presented.
Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.
2014-01-01
Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
Analysis of acoustic resonator with shape deformation using finite ...
Indian Academy of Sciences (India)
G M KALMSEa, AJAY CHAUDHARIb and P B PATILb a Science College, PB No. 62, Nanded 431603, India b Department of Physics, Dr B A M University, Aurangabad 431 004, India e-mail: bamuaur@bom4.vsnl.net.in. MS received 23 September 1999. Abstract. An acoustic resonator with shape deformation has been ...
Volume changes in hydrogels subjected to finite deformations
DEFF Research Database (Denmark)
Drozdov, Aleksey; Christiansen, Jesper de Claville
2013-01-01
Constitutive equations are derived for the elastic response of hydrogels under an arbitrary deformationwith finite strains. An expression is proposed for the free energy density of a hydrogel based on the Floryconcept of a network of flexible chains with constrained junctions whose reference conf...
A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure
International Nuclear Information System (INIS)
Bonatsos, D.; Daskaloyannis, C.; Kolokotronis, P.; Ludu, A.; Quesne, C.
1997-01-01
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J 0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as scr(A) q + (1). This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0,1,2,hor-ellipsis. To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su q (2) and scr(A) q + (1), is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su q (2) is carried over to scr(A) q + (1), thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and scr(R)-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-color quasitriangular Hopf algebra because the corresponding scr(R)-matrix is a solution of the colored Yang endash Baxter equation, where the open-quotes colorclose quotes parameters take two discrete values associated with the two series of finite-dimensional representations. copyright 1997 American Institute of Physics
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet
2012-02-01
Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
Moraleda, Joaquín; Segurado, Javier; LLorca, Javier
2009-09-01
The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.
Energy Technology Data Exchange (ETDEWEB)
Wang, X.; Xu, Z.; Kim, Y-S.; Lai, L.; Cheng, G.; Xu, S. [Atomic Energy of Canada Limited, Mississauga, Ontario (Canada)
2010-07-01
During normal operation, the collapsible CANDU® fuel sheath deforms, especially, it may deform into longitudinal ridges or collapse instantaneously into the axial gaps between the end pellet and endcap or between two neighbouring pellets. These phenomena occur under certain conditions, such as the coolant pressure exceeding critical pressures for longitudinal ridging or axial collapse. Both longitudinal ridging and axial collapse phenomena result from plastic instability in the sheath under coolant pressure. Longitudinal ridging features one or multiple lobes or 'ridges' (outward from the sheath surface) formed along the sheath in the longitudinal direction. Axial collapse features a 'valley' around the sheath circumference. Both phenomena can lead to sheath overstrain, which in turn potentially leads to sheath failure. The LONGER code, which contains empirical correlations, has been used to predict the critical pressures for these two sheath deformation phenomena. To study fuel behaviour outside of the application ranges of the LONGER empirical correlations, a mechanistic model is needed. FEAST (Finite Element Analysis for Stresses) is an AECL computer code used to assess the structural integrity of the CANDU fuel element. The FEAST code has recently been developed (to Version 3.1) to model processes occurring during longitudinal ridge formation and instantaneous collapse into the axial gap. The new models include those for geometric non-linearity (large deformation, large material rotation), non-linear stress-strain curve for plastic deformation, Zr-4 sheath creep law, and variable Young’s Modulus etc. This paper describes the mechanistic model (FEAST 3.1) development for analyses of longitudinal ridging and instantaneous collapse into axial gap, and the comparison with the results from empirical correlations in LONGER. (author)
International Nuclear Information System (INIS)
Wang, X.; Xu, Z.; Kim, Y-S.; Lai, L.; Cheng, G.; Xu, S.
2010-01-01
During normal operation, the collapsible CANDU® fuel sheath deforms, especially, it may deform into longitudinal ridges or collapse instantaneously into the axial gaps between the end pellet and endcap or between two neighbouring pellets. These phenomena occur under certain conditions, such as the coolant pressure exceeding critical pressures for longitudinal ridging or axial collapse. Both longitudinal ridging and axial collapse phenomena result from plastic instability in the sheath under coolant pressure. Longitudinal ridging features one or multiple lobes or 'ridges' (outward from the sheath surface) formed along the sheath in the longitudinal direction. Axial collapse features a 'valley' around the sheath circumference. Both phenomena can lead to sheath overstrain, which in turn potentially leads to sheath failure. The LONGER code, which contains empirical correlations, has been used to predict the critical pressures for these two sheath deformation phenomena. To study fuel behaviour outside of the application ranges of the LONGER empirical correlations, a mechanistic model is needed. FEAST (Finite Element Analysis for Stresses) is an AECL computer code used to assess the structural integrity of the CANDU fuel element. The FEAST code has recently been developed (to Version 3.1) to model processes occurring during longitudinal ridge formation and instantaneous collapse into the axial gap. The new models include those for geometric non-linearity (large deformation, large material rotation), non-linear stress-strain curve for plastic deformation, Zr-4 sheath creep law, and variable Young’s Modulus etc. This paper describes the mechanistic model (FEAST 3.1) development for analyses of longitudinal ridging and instantaneous collapse into axial gap, and the comparison with the results from empirical correlations in LONGER. (author)
Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation
International Nuclear Information System (INIS)
Goudreau, G.L.; Hallquist, J.O.
1979-08-01
Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications
A finite deformation theory of higher-order gradient crystal plasticity
DEFF Research Database (Denmark)
Kuroda, Mitsutoshi; Tvergaard, Viggo
2008-01-01
crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution......For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation...
Finite Deformation of Materials with an Ensemble of Defects
Energy Technology Data Exchange (ETDEWEB)
J.K. Dienes
2003-01-01
The theory of large deformations developed here is closely related to continuum mechanics but it differs in several major respects, especially in considering the deformation associated with various types of physical behavior, making it possible to synthesize a general approach to formulating constitutive laws. One goal is to derive general concepts of strain, strain rate, stress, and stress rate that are somewhat more physics-based than in most standard works on continuum mechanics, and to demonstrate some new relations between these quantities. With these concepts it is possible to develop a generalized principle of superposition of strain rates (GSSR) that accounts for damage as well as plastic flow. The traditional superposition of strain rates allows for addition of elastic and plastic strain rates and is commonly thought to be valid only for small strains. The GSSR allows us to compute deformations involving plastic flow and, in addition, brittle failure, fragmentation, high-pressure effects and other types of behavior as necessary, and the theory is valid for arbitrarily large deformations. In fact, GSSR is derived from more basic ideas and has broader application than the standard superposition of strain rates. The physical basis for calculations of complex material response is developed in a separate report. The implementation into the SCRAM computer program is documented separately. The polar decomposition theorem is taken as a starting point for the theory of large deformation, an approach somewhat different from that usually taken in continuum mechanics. Two sets of orthogonal axes are distinguished, space axes that are fixed in ambient space, and polar axes that are related to material deformation. This clarifies several concepts; for example, it is shown that the Signorini and Green-St. Venant strains are actually measures of the same physical entity, one in space axes and the other in polar axes. It follows that they are not competing measures, as is
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran; Muliana, Anastasia Hanifah
2012-01-01
This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i
International Nuclear Information System (INIS)
Biffle, J.H.
1991-01-01
1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory
Directory of Open Access Journals (Sweden)
Vladimir P. Agapov
2017-01-01
Full Text Available Abstract. Objectives Modern building codes prescribe the calculation of building structures taking into account the nonlinearity of deformation. To achieve this goal, the task is to develop a methodology for calculating prestressed reinforced concrete beams, taking into account physical and geometric nonlinearity. Methods The methodology is based on nonlinear calculation algorithms implemented and tested in the computation complex PRINS (a program for calculating engineering constructions for other types of construction. As a tool for solving this problem, the finite element method is used. Non-linear calculation of constructions is carried out by the PRINS computational complex using the stepwise iterative method. In this case, an equation is constructed and solved at the loading step, using modified Lagrangian coordinates. Results The basic formulas necessary for both the formation and the solution of a system of nonlinear algebraic equations by the stepwise iteration method are given, taking into account the loading, unloading and possible additional loading. A method for simulating prestressing is described by setting the temperature action on the reinforcement and stressing steel rod. Different approaches to accounting for physical and geometric nonlinearity of reinforced concrete beam rods are considered. A calculation example of a flat beam is given, in which the behaviour of the beam is analysed at various stages of its loading up to destruction. Conclusion A program is developed for the calculation of flat and spatially reinforced concrete beams taking into account the nonlinearity of deformation. The program is adapted to the computational complex PRINS and as part of this complex is available to a wide range of engineering, scientific and technical specialists.
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Verschoor, M.; Jalba, A.C.
2012-01-01
Elastically deformable models have found applications in various areas ranging from mechanical sciences and engineering to computer graphics. The method of Finite Elements has been the tool of choice for solving the underlying PDE, when accuracy and stability of the computations are more important
Material model for non-linear finite element analyses of large concrete structures
Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.
2016-01-01
A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu
2011-01-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes
A modal method for finite amplitude, nonlinear sloshing
Indian Academy of Sciences (India)
A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefﬁcients in the expansions of the interface and the potential. The effects ...
A modal method for finite amplitude, nonlinear sloshing
Indian Academy of Sciences (India)
Abstract. A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
A work-hardening rule for finite elastic-plastic deformation of metals at elevated temperatures
International Nuclear Information System (INIS)
Lee, L.H.N.; Horng, J.T.
1975-01-01
The paper is concerned with an extension of Prager-Ziegler's kinematic work-hardening rule for infinitesimal elastic-plastic deformation to a work-hardening rule for finite elastic-plastic deformation of a polycrystalline metal. It is shown that the finite work-hardening rule, which accounts for the Bauschinger and temperature effects within certain pressure and temperature ranges, satisfies certain invariant, continuity and thermodynamic requirements. A description of the kinematics of an elastic-plastic body is employed with reference to three separate configurations: initial, current and an intermediate configuration. The intermediate configuration is a conceptual, local configuration obtained by removing the stress and temperature changes in the neighborhood of an element. A rigid body rotation of the intermediate configuration is allowed. Piola-Kirchhoff stresses and Green deformation tensors referred to the initial and intermediate configurations are employed as stress and strain measures. The plastic deformation has been associated with the motion and production of dislocations. It has been observed that the motion of mobile dislocations usually occur in the narrow slip bands in each grain, leaving the basic lattice structure practically intact, so that the macroscopic elastic properties of the material are essentially independent of plastic deformation. Employing this fact and the thermodynamic laws, a simplified elastic stress-strain relationship of the plastically deformed material, which agrees with the results of Naghdi and Trapp, is obtained
Boyko, Evgeniy; Gat, Amir; Bercovici, Moran
2017-11-01
We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.
Nonlinear quantum fluid equations for a finite temperature Fermi plasma
International Nuclear Information System (INIS)
Eliasson, Bengt; Shukla, Padma K
2008-01-01
Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi-Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma
Experimental and finite element analyses of plastic deformation behavior in vortex extrusion
International Nuclear Information System (INIS)
Shahbaz, M.; Pardis, N.; Kim, J.G.; Ebrahimi, R.; Kim, H.S.
2016-01-01
Vortex extrusion (VE) is a single pass severe plastic deformation (SPD) technique which can impose high strain values with almost uniform distribution within cross section of the processed material. This technique needs no additional facilities for installation on any conventional extrusion equipment. In this study the deformation behavior of material during VE is investigated and the results are compared with those of conventional extrusion (CE). These investigations include finite element analysis, visioplasticity, and microstructural characterization of the processed samples. The results indicate that the VE process can accumulate a higher strain value by applying an additional torsional deformation. The role of this additional deformation mode on the microstructural evolution of the VE sample is discussed and compared with the results obtained on the CE samples.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.; Langer, U.
2010-01-01
of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
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Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
International Nuclear Information System (INIS)
Cook, W.A.
1978-10-01
Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented
Comparative Analysis of Bulge Deformation between 2D and 3D Finite Element Models
Directory of Open Access Journals (Sweden)
Qin Qin
2014-02-01
Full Text Available Bulge deformation of the slab is one of the main factors that affect slab quality in continuous casting. This paper describes an investigation into bulge deformation using ABAQUS to model the solidification process. A three-dimensional finite element analysis model of the slab solidification process has been first established because the bulge deformation is closely related to slab temperature distributions. Based on slab temperature distributions, a three-dimensional thermomechanical coupling model including the slab, the rollers, and the dynamic contact between them has also been constructed and applied to a case study. The thermomechanical coupling model produces outputs such as the rules of bulge deformation. Moreover, the three-dimensional model has been compared with a two-dimensional model to discuss the differences between the two models in calculating the bulge deformation. The results show that the platform zone exists in the wide side of the slab and the bulge deformation is affected strongly by the ratio of width-to-thickness. The indications are also that the difference of the bulge deformation for the two modeling ways is little when the ratio of width-to-thickness is larger than six.
Fluid boundary of a viscoplastic Bingham flow for finite solid deformations
Thual , Olivier; Lacaze , Laurent
2010-01-01
International audience; The modelling of viscoplastic Bingham fluids often relies on a rheological constitutive law based on a "plastic rule function" often identical to the yield criterion of the solid state. It is also often assumed that this plastic rule function vanishes at the boundary between the solid and fluid states, based on the fact that it is true in the limit of small deformations of the solid state or for simple yield criteria. We show that this is not the case for finite deform...
Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent
2011-05-01
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society
Nonlinear tension-bending deformation of a shape memory alloy rod
International Nuclear Information System (INIS)
Shang, Zejin; Wang, Zhongmin
2012-01-01
Based on the measured shape memory alloy (SMA) stress–strain curve and the nonlinear large deformation theory of extensible beams (or rods), the first-order nonlinear governing equations of a SMA cantilever straight rod are established. They consist of a boundary-value problem of ordinary differential equations with a strong nonlinearity, in which seven unknown functions are contained and the arc length of the deformed axis is considered as one of the basic unknown functions. The shooting method combining with the Newton–Raphson iteration method is applied to solve the equations numerically. For a SMA cantilever rod subjected to a transverse uniformly distributed force, the deformation characteristics curves, the maximum strain and the maximum stress distribution curves along the longitudinal direction of rod, and the relation curves between deformation characteristic parameters and transverse uniformly force under different slenderness ratios are obtained. The effects of material nonlinearity, geometrical nonlinearity and slenderness ratio on the tension-bending deformation of the SMA cantilever rod are investigated. The numerical simulation results are in good agreement with the experimental data from the literature, verifying the soundness of the entire numerical simulation scheme. (paper)
q Breathers in Finite Lattices: Nonlinearity and Weak Disorder
Ivanchenko, M. V.
2009-05-01
Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.
Nonlinear frequency shift of finite-amplitude electrostatic surface waves
International Nuclear Information System (INIS)
Stenflo, L.
1989-01-01
The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov, I. Proceedings International Conference on Plasma Physics, Kiev, 1987, Vol. 2, p. 694, who assumed a linear exponential attenuation behaviour. (author)
Nonlinear Finite Element Analysis of Pull-Out Test
DEFF Research Database (Denmark)
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region...
Nonlinear nonstationary analysis with the finite element method
International Nuclear Information System (INIS)
Vaz, L.E.
1981-01-01
In this paper, after some introductory remarks on numerical methods for the integration of initial value problems, the applicability of the finite element method for transient diffusion analysis as well as dynamic and inelastic analysis is discussed, and some examples are presented. (RW) [de
Finite element modeling of nanotube structures linear and non-linear models
Awang, Mokhtar; Muhammad, Ibrahim Dauda
2016-01-01
This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2015-01-01
Roč. 226, č. 1 (2015), s. 17-35 ISSN 0001-5970 R&D Projects: GA ČR(CZ) GA103/09/2101 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * evolution equation of Lie-type * time-discrete integration Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.694, year: 2015 http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1
Nonlinear Finite Element Analysis of Reinforced Concrete Shells
Directory of Open Access Journals (Sweden)
Mustafa K. Ahmed
2013-05-01
Full Text Available This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1 with enhanced shear interpolation will be used in this study. Table (1 describes shape functions and their derivatives of this element.An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10 have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiation. Attention is given to the tension stiffening phenomenon and the degrading effect of cracking on the compressive and shear strength of concrete. Perfect bond between concrete and steel is assumed. Attention is given also to geometric nonlinearities. An example have been chosen in order to demonstrate the suitability of the models by comparing the predicted behaviour with the experimental results for shell exhibiting various modes of failure.
FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH
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Q. A. HASAN
2017-11-01
Full Text Available The paper presents Finite Element Analysis to determine the ultimate shear capacity of tapered composite plate girder. The effect of degree of taper on the ultimate shear capacity of tapered steel-concrete composite plate girder with a nonlinear varying web depth, effect of slenderness ratio on the ultimate shear capacity, and effect of flange stiffness on the ductility were considered as the parametric studies. Effect of concrete slab on the ultimate shear capacity of tapered plate girders was also considered and it was found to be so effective on the ultimate shear capacity of the tapered plate girder compared with the steel one. The accuracy of the finite element method is established by comparing the finite element with the results existing in the literature. The study was conducted using nonlinear finite element modelling with computer software LUSAS 14.7.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
A non-linear elastic constitutive framework for replicating plastic deformation in solids.
Energy Technology Data Exchange (ETDEWEB)
Roberts, Scott Alan; Schunk, Peter Randall
2014-02-01
Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.
International Nuclear Information System (INIS)
Hussein, Bassam A.; Weed, David; Shabana, Ahmed A.
2009-01-01
In the finite element absolute nodal coordinate formulation (ANCF), the elimination of the relative translations and rotations at a point does not necessarily define a fully clamped joint, particularly in the case of fully parameterized ANCF finite elements that allow for the deformation of the cross section. In this investigation, the formulations and results of two different sets of clamped end conditions that define two different joints are compared. The first joint, called the partially clamped joint, eliminates only the translations and rotations at a point on the cross section. The second joint, called the fully clamped joint, eliminates all the translation, rotation and deformation degrees of freedom at a point on the cross section. The kinematic equations that define the partially and fully clamped joints are developed, and the dynamic equations used in the comparative numerical study presented in this paper are shown. As discussed in this investigation, the fully clamped joint does not allow for the deformation of the cross section at the joint node since the gradient vectors remain orthogonal unit vectors. The partially clamped joint, on the other hand, allows for the deformation of the cross section. Nanson's formula is used as a measure of the deformation of the cross section in the case of the partially clamped joint. A very flexible pendulum that has a rigid body attached to its free end is used to compare the results of the partially and fully clamped joints. The numerical results obtained using this very flexible pendulum example show that, while the type of joint (partially or fully clamped) does not significantly affect the gross reference motion of the system, there are fundamental differences between the two joints since the partially clamped joint allows for the cross section deformations at the joint node
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
International Nuclear Information System (INIS)
Andrianov, I.V.; Danishevsky, V.V.
1994-01-01
Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions
Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells
Directory of Open Access Journals (Sweden)
Humberto Breves Coda
2009-01-01
Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.
International Nuclear Information System (INIS)
Esfandiar, Habib; KoraYem, Moharam Habibnejad
2015-01-01
In this study, the researchers try to examine nonlinear dynamic analysis and determine Dynamic load carrying capacity (DLCC) in flexible manipulators. Manipulator modeling is based on Timoshenko beam theory (TBT) considering the effects of shear and rotational inertia. To get rid of the risk of shear locking, a new procedure is presented based on mixed finite element formulation. In the method proposed, shear deformation is free from the risk of shear locking and independent of the number of integration points along the element axis. Dynamic modeling of manipulators will be done by taking into account small and large deformation models and using extended Hamilton method. System motion equations are obtained by using nonlinear relationship between displacements-strain and 2nd PiolaKirchoff stress tensor. In addition, a comprehensive formulation will be developed to calculate DLCC of the flexible manipulators during the path determined considering the constraints end effector accuracy, maximum torque in motors and maximum stress in manipulators. Simulation studies are conducted to evaluate the efficiency of the method proposed taking two-link flexible and fixed base manipulators for linear and circular paths into consideration. Experimental results are also provided to validate the theoretical model. The findings represent the efficiency and appropriate performance of the method proposed.
Energy Technology Data Exchange (ETDEWEB)
Esfandiar, Habib; KoraYem, Moharam Habibnejad [Islamic Azad University, Tehran (Iran, Islamic Republic of)
2015-09-15
In this study, the researchers try to examine nonlinear dynamic analysis and determine Dynamic load carrying capacity (DLCC) in flexible manipulators. Manipulator modeling is based on Timoshenko beam theory (TBT) considering the effects of shear and rotational inertia. To get rid of the risk of shear locking, a new procedure is presented based on mixed finite element formulation. In the method proposed, shear deformation is free from the risk of shear locking and independent of the number of integration points along the element axis. Dynamic modeling of manipulators will be done by taking into account small and large deformation models and using extended Hamilton method. System motion equations are obtained by using nonlinear relationship between displacements-strain and 2nd PiolaKirchoff stress tensor. In addition, a comprehensive formulation will be developed to calculate DLCC of the flexible manipulators during the path determined considering the constraints end effector accuracy, maximum torque in motors and maximum stress in manipulators. Simulation studies are conducted to evaluate the efficiency of the method proposed taking two-link flexible and fixed base manipulators for linear and circular paths into consideration. Experimental results are also provided to validate the theoretical model. The findings represent the efficiency and appropriate performance of the method proposed.
Optimum Control for Nonlinear Dynamic Radial Deformation of Turbine Casing with Time-Varying LSSVM
Directory of Open Access Journals (Sweden)
Cheng-Wei Fei
2015-01-01
Full Text Available With the development of the high performance and high reliability of aeroengine, the blade-tip radial running clearance (BTRRC of high pressure turbine seriously influences the reliability and performance of aeroengine, wherein the radial deformation control of turbine casing has to be concerned in BTRRC design. To improve BTRRC design, the optimum control-based probabilistic optimization of turbine casing radial deformation was implemented using time-varying least square support vector machine (T-LSSVM by considering nonlinear material properties and dynamic thermal load. First the T-LSSVM method was proposed and its mathematical model was established. And then the nonlinear dynamic optimal control model of casing radial deformation was constructed with T-LSSVM. Thirdly, through the numerical experiments, the T-LSSVM method is demonstrated to be a promising approach in reducing additional design samples and improving computational efficiency with acceptable computational precision. Through the optimum control-based probabilistic optimization for nonlinear dynamic radial turbine casing deformation, the optimum radial deformation is 7.865 × 10−4 m with acceptable reliability degree 0.995 6, which is reduced by 7.86 × 10−5 m relative to that before optimization. These results validate the effectiveness and feasibility of the proposed T-LSSVM method, which provides a useful insight into casing radial deformation, BTRRC control, and the development of gas turbine with high performance and high reliability.
Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio
Chang, T. Y.; Sawamiphakdi, K.
1984-01-01
A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Finite elements for non-linear analysis of pipelines
International Nuclear Information System (INIS)
Benjamim, A.C.; Ebecken, N.F.F.
1982-01-01
The application of a three-dimensional lagrangian formulation for the great dislocations analysis and great rotation of pipelines systems is studied. This formulation is derived from the soil mechanics and take into account the shear stress effects. Two finite element models are implemented. The first, of right axis, uses as interpolation functions the conventional gantry functions, defined in relation to mobile coordinates. The second, of curve axis and variable cross sections, is obtained from the degeneration of the three-dimensional isoparametric element, and uses as interpolation functions third degree polynomials. (E.G.) [pt
Nonlinear Finite Element Analysis of a General Composite Shell
1988-12-01
for (t) in Equation (B.15) (Appendix B) and writes it as a function of displacements for I the nonlinear problem one obtains [8] 3 29 (*(a)) - [K(a...linked to the main program before execution. Isubroutine upress(t,pa,pb,iunit, ielt ,x,y,z,live,press) c c Pressure distribution subroutine for c...then compiled and linked to the main program before execution. I SUBROUTINE UPRESS(T,PA,PB,IUNIT, IELT ,X,Y,Z,LIVE,PRESS) C c Pressure distribution
Li, S; Lu, M; Kim, J; Glide-Hurst, C; Chetty, I; Zhong, H
2012-06-01
Purpose Clinical implementation of adaptive treatment planning is limited by the lack of quantitative tools to assess deformable image registration errors (R-ERR). The purpose of this study was to develop a method, using finite element modeling (FEM), to estimate registration errors based on mechanical changes resulting from them. Methods An experimental platform to quantify the correlation between registration errors and their mechanical consequences was developed as follows: diaphragm deformation was simulated on the CT images in patients with lung cancer using a finite element method (FEM). The simulated displacement vector fields (F-DVF) were used to warp each CT image to generate a FEM image. B-Spline based (Elastix) registrations were performed from reference to FEM images to generate a registration DVF (R-DVF). The F- DVF was subtracted from R-DVF. The magnitude of the difference vector was defined as the registration error, which is a consequence of mechanically unbalanced energy (UE), computed using 'in-house-developed' FEM software. A nonlinear regression model was used based on imaging voxel data and the analysis considered clustered voxel data within images. Results A regression model analysis showed that UE was significantly correlated with registration error, DVF and the product of registration error and DVF respectively with R̂2=0.73 (R=0.854). The association was verified independently using 40 tracked landmarks. A linear function between the means of UE values and R- DVF*R-ERR has been established. The mean registration error (N=8) was 0.9 mm. 85.4% of voxels fit this model within one standard deviation. Conclusions An encouraging relationship between UE and registration error has been found. These experimental results suggest the feasibility of UE as a valuable tool for evaluating registration errors, thus supporting 4D and adaptive radiotherapy. The research was supported by NIH/NCI R01CA140341. © 2012 American Association of Physicists in
Directory of Open Access Journals (Sweden)
Xiaohui Mo
2017-01-01
Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
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Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Li, Xiaomin; Guo, Xueli; Guo, Haiyan
2018-06-01
Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.
Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications
Kuehl, Joseph J.
2017-02-01
A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.
Non-linear finite element analyses applicable for the design of large reinforced concrete structures
Engen, M; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik
2017-01-01
In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises
Modal representation of geometrically nonlinear behavior by the finite element method
International Nuclear Information System (INIS)
Nagy, D.A.
1977-01-01
A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. (Auth.)
Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine
DEFF Research Database (Denmark)
Wong, Christian; Gehrchen, P Martin; Darvann, Tron
2003-01-01
A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompressible nucleus surrounded by nonlinear annulus fibe...
Nonlinear finite element analysis of reinforced and prestressed concrete shells with edge beams
International Nuclear Information System (INIS)
Srinivasa Rao, P.; Duraiswamy, S.
1994-01-01
The structural design of reinforced and prestressed concrete shells demands the application of nonlinear finite element analysis (NFEM) procedures to ensure safety and serviceability. In this paper the details of a comprehensive NFEM program developed are presented. The application of the program is highlighted by solving two numerical problems and comparing the results with experimental results. (author). 20 refs., 15 figs
COYOTE: a finite element computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Gartling, D.K.
1978-06-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...
Laursen, Tod A
2003-01-01
This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.
A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking
Institute of Scientific and Technical Information of China (English)
ZHANG ZuTao; ZHANG JiaShu
2009-01-01
Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.
Directory of Open Access Journals (Sweden)
Alexander M. Chernysh
2018-01-01
Full Text Available Modifiers of membranes cause local defects on the cell surface. Measurement of the rigidity at the sites of local defects can provide further information about the structure of defects and mechanical properties of altered membranes.The purpose of the study: a step-by-step study of the process of a nonlinear deformation of red blood cells membranes under the effect of modifiers of different physico-chemical nature.Materials and methods. The membrane deformation of a viscoelastic composite erythrocyte construction inside a cell was studied by the atomic force spectroscopy. Nonlinear deformations formed under the effect of hemin, Zn2+ ions, and verapamil were studied.Results. The process of elastic deformation of the membrane with the indentation of a probe at the sites of local defects caused by modifiers was demonstrated. The probe was inserted during the same step of the piezo scanner z displacement; the probe indentation occured at the different discrete values of h, which are the functions of the membrane structure. At the sites of domains, under the effect of the hemin, tension areas and plasticity areas appeared. A mathematical model of probe indentation at the site of membrane defects is presented.Conclusion. The molecular mechanisms of various types of nonlinear deformations occurring under the effect of toxins are discussed. The results of the study may be of interest both for fundamental researchers of the blood cell properties and for practical reanimatology and rehabilitology.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
International Nuclear Information System (INIS)
Upadrashta, Deepesh; Yang, Yaowen
2015-01-01
Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)
Finite Element Method in the Three Dimensions Deformation Computation ofKartini Reactor Stack
International Nuclear Information System (INIS)
Supriyono; Syarip; Wibisono, I
2000-01-01
The calculation of the Kartini reactor stack i.e. one of the nuclearinstallations in P3TM-BATAN Yogyakarta by using SAP 90 software have beendone. The calculation is done as a safety review of building towards theearthquake style in Yogyakarta. The 3-dimension deformation calculation isperformed by the numeric method i.e. finite element method with the form ofelements is the shell. The result obtained showed that the construction oftower safe to the existing earthquake, where the moment exerted as a resultof earthquake style was different under the moment having been kept by thebuilding structure. By knowing the deformation on the stack it is expectedcould be used for concluding the strength of the whole reactor building.(author)
Nagata, Keitro; Nishimura, Jun; Shimasaki, Shinji
2018-03-01
We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and intro-duce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a 43 × 8 lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.
Effect of Punch Stroke on Deformation During Sheet Forming Through Finite Element
Akinlabi, Stephen; Akinlabi, Esther
2017-08-01
Forming is one of the traditional methods of making shapes, bends and curvature in metallic components during a fabrication process. Mechanical forming, in particular, employs the use of a punch, which is pressed against the sheet material to be deformed into a die by the application of an external force. This study reports on the finite element analysis of the effects of punch stroke on the resulting sheet deformation, which is directly a function of the structural integrity of the formed components for possible application in the automotive industry. The results show that punch stroke is directly proportional to the resulting bend angle of the formed components. It was further revealed that the developed plastic strain increases as the punch stroke increases.
Finite element modeling of ground deformation and gravity field at Mt. Etna
Directory of Open Access Journals (Sweden)
G. Ganci
2008-06-01
Full Text Available An elastic 3-D axi-symmetric model based on Finite Element Method (FEM is proposed to compute ground deformation and gravity changes caused by overpressure sources in volcanic areas. The numerical computations are focused on the modeling of a complex description of Mt Etna in order to evaluate the effect of topography, medium heterogeneities and source geometries. Both ground deformation and gravity changes are investigated by solving a coupled numerical problem considering a simplified ground surface profile and a multi-layered crustal structure inferred from seismic tomography. The role of the source geometry is also explored taking into account spherical and ellipsoidal volumetric sources. The comparison between numerical results and those predicted by analytical solutions disclosed significant discrepancies. These differences constrain the applicability of simple spherical source and homogeneous half-space hypotheses, which are usually implicitly assumed when analytical solutions are applied.
Research of carbon composite material for nonlinear finite element method
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Finite element modelling of the creep deformation of T91 steel weldments at 600 C
Energy Technology Data Exchange (ETDEWEB)
Bhadrui, A.K. [Indira Gandhi Centre for Atomic Research, Kalpakkam (India); Gaudig, W. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt; Theofel, H. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt; Maile, K. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt
1996-05-01
Finite element modelling of the creep deformation of T91 steel weldments, welded using the manual metal arc (MMA) and submerged arc (SA) welding processes, was carried out to predict creep curves for both of the weldments under different stresses and compared with the experimental data. The stress and strain redistribution across the length of the transverse-weld specimens has also been predicted. Data of creep tests at 600 C at stresses between 90-130 MPa for the base metal, the MMA and SA weld metals, and the simulated heat-affected zone were used to determine Garofalo`s equation for creep strain. Finite element meshes for both of the weldments were constructed after calculating the HAZ locations using Rosenthal`s heat flow equation. (orig.)
Shutova, M. N.; Skibin, G. M.; Evtushenko, S. I.
2017-11-01
The paper is devoted to the problem of definition of availability index of deforming building construction in atypical cases. The authors revealed a real applicability of the finite-elements analyses package, such as ANSYS, for engineering testing calculations of building constructions and determination of the sites of increased stresses. It was determined that stresses increased up to 7.75 times in the sites with mechanical defects (for steel crane girder); also, the authors revealed the convergence of the calculation results between the finite element method and a usual decision using the strength of materials (in the limits 2-14% for steel truss frame). The equivalent stresses don’t exceed the maximum permissible tension for this type of steel. The building constructions have a limited availability index.
On the stress calculation within phase-field approaches: a model for finite deformations
Schneider, Daniel; Schwab, Felix; Schoof, Ephraim; Reiter, Andreas; Herrmann, Christoph; Selzer, Michael; Böhlke, Thomas; Nestler, Britta
2017-08-01
Numerical simulations based on phase-field methods are indispensable in order to investigate interesting and important phenomena in the evolution of microstructures. Microscopic phase transitions are highly affected by mechanical driving forces and therefore the accurate calculation of the stresses in the transition region is essential. We present a method for stress calculations within the phase-field framework, which satisfies the mechanical jump conditions corresponding to sharp interfaces, although the sharp interface is represented as a volumetric region using the phase-field approach. This model is formulated for finite deformations, is independent of constitutive laws, and allows using any type of phase inherent inelastic strains.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.
Shang, Xituan; Yen, Michael R T; Gaber, M Waleed
2010-06-01
The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.
Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model
Directory of Open Access Journals (Sweden)
Yue-bao Deng
2016-01-01
Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Modal representation of geometrically nonlinear behavior by the finite element method
International Nuclear Information System (INIS)
Nagy, D.A.
1977-01-01
A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. Formulation of the finite element displacement method for material linearity but retaining the full, nonlinear strain-displacement relations (geometric nonlinearity) leads to highly nonlinear equations relating the unknown nodal generalized displacements r to the applied loading R. Restriction to small strains alone does not linearize these equations for thin-type structural configurations; only explicitly requiring that all products of displacement gadients be much smaller than the gadients themselves reduces the equations to the familiar linear form Ksub(e)r=R, where Ksub(e) is the elastic stiffness. Assuming then that the solutions r of the linear equations also satisfies the full nonlinear equations (i.e., that the above explicit requirement is satisfied), a second solution to the full equations can be sought for a one-parameter loading path lambdaR, leading to the well-known linear (bifurcation) buckling eigenvalue problem Ksub(e)X=-Ksub(g)XΛ where Ksub(g) is the geometric stiffness, X the matrix whose columns are the eigenvectors (so-called buckling mode shapes) and Λ is a diagonal matrix of eigenvalues lambda(i) (so-called load scale factors). From the viewpoint of the practising structural analyst using finite element software, the method presented here gives broader and deeper significance to an existing linear (bifurcation) buckling analysis capability, in that the additional computations are minimal beyond those already required for a linear static and buckling analysis, and should be easily performable within any well-designed general purpose finite element system
International Nuclear Information System (INIS)
Walter, H.; Mang, H.A.
1991-01-01
A procedure for combining nonlinear short-time behavior of concrete with nonlinear creep compliance functions is presented. It is an important ingredient of a computer code for nonlinear finite element (FE) analysis of prestressed concrete shells, considering creep, shrinkage and ageing of concrete, and relaxation of the prestressing steel. The program was developed at the Institute for Strength of Materials of Technical University of Vienna, Austria. The procedure has resulted from efforts to extend the range of application of a Finite Element program, abbreviated as FESIA, which originally was capable of modeling reinforeced concrete in the context of thin-shell analysis, using nonlinear constitutive relations for both, conrete and steel. The extension encompasses the time-dependent behavior of concrete: Creep, shrinkage and ageing. Creep is modeled with the help of creep compliance functions which may be nonlinear to conform with the short-time constitutive relations. Ageing causes an interdependence between long-time and short-time deformations. The paper contains a description of the physical background of the procedure and hints on the implementation of the algorithm. The focus is on general aspects. Details of the aforementioned computer program are considered only where this is inevitable. (orig.)
SU-F-I-50: Finite Element-Based Deformable Image Registration of Lung and Heart
Energy Technology Data Exchange (ETDEWEB)
Penjweini, R [University of Pennsylvania, Philadelphia, Pennsylvania (United States); Kim, M [University of Pennsylvania, Philadelphia, PA (United States); Zhu, T [University Pennsylvania, Philadelphia, PA (United States)
2016-06-15
Purpose: Photodynamic therapy (PDT) is used after surgical resection to treat the microscopic disease for malignant pleural mesothelioma and to increase survival rates. Although accurate light delivery is imperative to PDT efficacy, the deformation of the pleural volume during the surgery impacts the delivered light dose. To facilitate treatment planning, we use a finite-element-based (FEM) deformable image registration to quantify the anatomical variation of lung and heart volumes between CT pre-(or post-) surgery and surface contours obtained during PDT using an infrared camera-based navigation system (NDI). Methods: NDI is used during PDT to obtain the information of the cumulative light fluence on every cavity surface point that is being treated. A wand, comprised of a modified endotrachial tube filled with Intralipid and an optical fiber inside the tube, is used to deliver the light during PDT. The position of the treatment is tracked using an attachment with nine reflective passive markers that are seen by the NDI system. Then, the position points are plotted as three-dimensional volume of the pleural cavity using Matlab and Meshlab. A series of computed tomography (CT) scans of the lungs and heart, in the same patient, are also acquired before and after the surgery. The NDI and CT contours are imported into COMSOL Multiphysics, where the FEM-based deformable image registration is obtained. The NDI and CT contours acquired during and post-PDT are considered as the reference, and the Pre-PDT CT contours are used as the target, which will be deformed. Results: Anatomical variation of the lung and heart volumes, taken at different times from different imaging devices, was determined by using our model. The resulting three-dimensional deformation map along x, y and z-axes was obtained. Conclusion: Our model fuses images acquired by different modalities and provides insights into the variation in anatomical structures over time.
Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method.
Yarahmadian, Mehran; Zhong, Yongmin; Gu, Chengfan; Shin, Jaehyun
2018-01-01
Soft tissue modeling plays an important role in the development of surgical training simulators as well as in robot-assisted minimally invasive surgeries. It has been known that while the traditional Finite Element Method (FEM) promises the accurate modeling of soft tissue deformation, it still suffers from a slow computational process. This paper presents a Kalman filter finite element method to model soft tissue deformation in real time without sacrificing the traditional FEM accuracy. The proposed method employs the FEM equilibrium equation and formulates it as a filtering process to estimate soft tissue behavior using real-time measurement data. The model is temporally discretized using the Newmark method and further formulated as the system state equation. Simulation results demonstrate that the computational time of KF-FEM is approximately 10 times shorter than the traditional FEM and it is still as accurate as the traditional FEM. The normalized root-mean-square error of the proposed KF-FEM in reference to the traditional FEM is computed as 0.0116. It is concluded that the proposed method significantly improves the computational performance of the traditional FEM without sacrificing FEM accuracy. The proposed method also filters noises involved in system state and measurement data.
Institute of Scientific and Technical Information of China (English)
Wei LIU; Zhenyuan JIA; Fuji WANG; Yongshun ZHANG; Dongming GUO
2008-01-01
The geometrical nonlinearity of a giant magne-tostrictive thin film (GMF) can be clearly detected under the magnetostriction effect. Thus, using geometrical linear elastic theory to describe the strain, stress, and constitutive relationship of GMF is inaccurate. According to nonlinear elastic theory, a nonlinear deformation model of the bimorph GMF is established based on assumptions that the magnetostriction effect is equivalent to the effect of body force loaded on the GMF. With Taylor series method, the numerical solution is deduced. Experiments on TbDyFe/Polyimide (PI)/SmFe and TbDyFe/Cu/SmFe are then conducted to verify the proposed model, respectively. Results indicate that the nonlinear deflection curve model is in good conformity with the experimental data.
Non-linear actions of physiological agents: Finite disarrangements elicit fitness benefits.
Sedlic, Filip; Kovac, Zdenko
2017-10-01
Finite disarrangements of important (vital) physiological agents and nutrients can induce plethora of beneficial effects, exceeding mere attenuation of the specific stress. Such response to disrupted homeostasis appears to be universally conserved among species. The underlying mechanism of improved fitness and longevity, when physiological agents act outside their normal range is similar to hormesis, a phenomenon whereby toxins elicit beneficial effects at low doses. Due to similarity with such non-linear response to toxins described with J-shaped curve, we have coined a new term "mirror J-shaped curves" for non-linear response to finite disarrangement of physiological agents. Examples from the clinical trials and basic research are provided, along with the unifying mechanisms that tie classical non-linear response to toxins with the non-linear response to physiological agents (glucose, oxygen, osmolarity, thermal energy, calcium, body mass, calorie intake and exercise). Reactive oxygen species and cytosolic calcium seem to be common triggers of signaling pathways that result in these beneficial effects. Awareness of such phenomena and exploring underlying mechanisms can help physicians in their everyday practice. It can also benefit researchers when designing studies and interpreting growing number of scientific data showing non-linear responses to physiological agents. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.
Non-linear actions of physiological agents: Finite disarrangements elicit fitness benefits
Directory of Open Access Journals (Sweden)
Filip Sedlic
2017-10-01
Full Text Available Finite disarrangements of important (vital physiological agents and nutrients can induce plethora of beneficial effects, exceeding mere attenuation of the specific stress. Such response to disrupted homeostasis appears to be universally conserved among species. The underlying mechanism of improved fitness and longevity, when physiological agents act outside their normal range is similar to hormesis, a phenomenon whereby toxins elicit beneficial effects at low doses. Due to similarity with such non-linear response to toxins described with J-shaped curve, we have coined a new term “mirror J-shaped curves” for non-linear response to finite disarrangement of physiological agents. Examples from the clinical trials and basic research are provided, along with the unifying mechanisms that tie classical non-linear response to toxins with the non-linear response to physiological agents (glucose, oxygen, osmolarity, thermal energy, calcium, body mass, calorie intake and exercise. Reactive oxygen species and cytosolic calcium seem to be common triggers of signaling pathways that result in these beneficial effects. Awareness of such phenomena and exploring underlying mechanisms can help physicians in their everyday practice. It can also benefit researchers when designing studies and interpreting growing number of scientific data showing non-linear responses to physiological agents.
Finite-time stabilisation of a class of switched nonlinear systems with state constraints
Huang, Shipei; Xiang, Zhengrong
2018-06-01
This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.
Finite-time output feedback stabilization of high-order uncertain nonlinear systems
Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei
2018-06-01
This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.
Finiteness of Ricci flat supersymmetric non-linear sigma-models
International Nuclear Information System (INIS)
Alvarez-Gaume, L.; Ginsparg, P.
1985-01-01
Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.)
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
DEFF Research Database (Denmark)
Clausen, Johan; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...
Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.
Basafa, Ehsan; Farahmand, Farzam
2011-05-01
Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.
Spaans, K.; Auriac, A.; Sigmundsson, F.; Hooper, A. J.; Bjornsson, H.; Pálsson, F.; Pinel, V.; Feigl, K. L.
2014-12-01
Icelandic ice caps, covering ~11% of the country, are known to be surging glaciers. Such process implies an important local crustal subsidence due to the large ice mass being transported to the ice edge during the surge in a few months only. In 1993-1995, a glacial surge occurred at four neighboring outlet glaciers in the southwestern part of Vatnajökull ice cap, the largest ice cap in Iceland. We estimated that ~16±1 km3 of ice have been moved during this event while the fronts of some of the outlet glaciers advanced by ~1 km.Surface deformation associated with this surge has been surveyed using Interferometric Synthetic Aperture Radar (InSAR) acquisitions from 1992-2002, providing high resolution ground observations of the study area. The data show about 75 mm subsidence at the ice edge of the outlet glaciers following the transport of the large volume of ice during the surge (Fig. 1). The long time span covered by the InSAR images enabled us to remove ~12 mm/yr of uplift occurring in this area due to glacial isostatic adjustment from the retreat of Vatnajökull ice cap since the end of the Little Ice Age in Iceland. We then used finite element modeling to investigate the elastic Earth response to the surge, as well as confirm that no significant viscoelastic deformation occurred as a consequence of the surge. A statistical approach based on Bayes' rule was used to compare the models to the observations and obtain an estimate of the Young's modulus (E) and Poisson's ratio (v) in Iceland. The best-fitting models are those using a one-kilometer thick top layer with v=0.17 and E between 12.9-15.3 GPa underlain by a layer with v=0.25 and E from 67.3 to 81.9 GPa. Results demonstrate that InSAR data and finite element models can be used successfully to reproduce crustal deformation induced by ice mass variations at Icelandic ice caps.Fig. 1: Interferograms spanning 1993 July 31 to 1995 June 19, showing the surge at Tungnaárjökull (Tu.), Skaftárjökull (Sk.) and S
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Jin; Lee, Hong Pyo; Seo, Jeong Moon [Korea Atomic Energy Research Institute, Taejeon (Korea)
2002-03-01
The maim goal of this research is to develop a nonlinear finite element analysis program NUCAS to accurately predict global and local failure modes of containment building subjected to internal pressure. In this report, we describe the techniques we developed throught this research. An adequate model to the analysis of containment building such as microscopic material model is adopted and it applied into the development Reissner-Mindlin degenerated shell element. To avoid finite element deficiencies, the substitute strains based on the assumed strain method is used in the shell formulation. Arc-length control method is also adopted to fully trace the peak load-displacement path due to crack formation. In addition, a benchmark test suite is developed to investigate the performance of NUCAS and proposed as the future benchmark tests for nonlinear analysis of reinforced concrete. Finally, the input format of NUCAS and the examples of input/output file are described. 39 refs., 65 figs., 8 tabs. (Author)
International Nuclear Information System (INIS)
Lee, Tae Hee; Yoo, Jung Hun; Choi, Hyeong Cheol
2002-01-01
A finite element package is often used as a daily design tool for engineering designers in order to analyze and improve the design. The finite element analysis can provide the responses of a system for given design variables. Although finite element analysis can quite well provide the structural behaviors for given design variables, it cannot provide enough information to improve the design such as design sensitivity coefficients. Design sensitivity analysis is an essential step to predict the change in responses due to a change in design variables and to optimize a system with the aid of the gradient-based optimization techniques. To develop a numerical method of design sensitivity analysis, analytical derivatives that are based on analytical differentiation of the continuous or discrete finite element equations are effective but analytical derivatives are difficult because of the lack of internal information of the commercial finite element package such as shape functions. Therefore, design sensitivity analysis outside of the finite element package is necessary for practical application in an industrial setting. In this paper, the semi-analytic method for design sensitivity analysis is used for the development of the design sensitivity module outside of a commercial finite element package of ANSYS. The direct differentiation method is employed to compute the design derivatives of the response and the pseudo-load for design sensitivity analysis is effectively evaluated by using the design variation of the related internal nodal forces. Especially, we suggest an effective method for stress and nonlinear design sensitivity analyses that is independent of the commercial finite element package is also discussed. Numerical examples are illustrated to show the accuracy and efficiency of the developed method and to provide insights for implementation of the suggested method into other commercial finite element packages
Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir
2017-12-01
FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.
Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent
2016-04-01
Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.
International Nuclear Information System (INIS)
Rensch, H.J.; Wunderlich, W.
1981-01-01
The governing partial differential equations used are valid for small strains and moderate rotations. Plasticity relations are based on J 2 -flow theory. In order to eliminate the circumferential coordinate, the loading as well as the unkown quantities are expanded in Fourier series in the circumferential direction. The nonlinear terms due to moderate rotations and plastic deformations are treated as pseudo load quantities. In this way, the governing equations can be reduced to uncoupled systems of first-order ordinary differential equations in the meridional direction. They are then integrated over a shell segment via a matrix series expansion. The resulting element transfer matrices are transformed into stiffness matrices, and for the analysis of the total structure the finite element method is employed. Thus, arbitrary branching of the shell geometry is possible. Compared to two-dimensional approximations, the major advantage of the semi-analytical procedure is that the structural stiffness matrix usually has a small handwidth, resulting in shorter computer run times. Moreover, its assemblage and triangularization has to be carried out only once bacause all nonlinear effects are treated as initial loads. (orig./HP)
TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1984-02-01
Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)
Non-linear shape functions over time in the space-time finite element method
Directory of Open Access Journals (Sweden)
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
International Nuclear Information System (INIS)
Ruas, V.
1982-09-01
A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt
Charco, María; González, Pablo J.; Galán del Sastre, Pedro
2017-04-01
The Kilauea volcano (Hawaii, USA) is one of the most active volcanoes world-wide and therefore one of the better monitored volcanoes around the world. Its complex system provides a unique opportunity to investigate the dynamics of magma transport and supply. Geodetic techniques, as Interferometric Synthetic Aperture Radar (InSAR) are being extensively used to monitor ground deformation at volcanic areas. The quantitative interpretation of such surface ground deformation measurements using geodetic data requires both, physical modelling to simulate the observed signals and inversion approaches to estimate the magmatic source parameters. Here, we use synthetic aperture radar data from Sentinel-1 radar interferometry satellite mission to image volcano deformation sources during the inflation along Kilauea's Southwest Rift Zone in April-May 2015. We propose a Finite Element Model (FEM) for the calculation of Green functions in a mechanically heterogeneous domain. The key aspect of the methodology lies in applying the reciprocity relationship of the Green functions between the station and the source for efficient numerical inversions. The search for the best-fitting magmatic (point) source(s) is generally conducted for an array of 3-D locations extending below a predefined volume region. However, our approach allows to reduce the total number of Green functions to the number of the observation points by using the, above mentioned, reciprocity relationship. This new methodology is able to accurately represent magmatic processes using physical models capable of simulating volcano deformation in non-uniform material properties distribution domains, which eventually will lead to better description of the status of the volcano.
Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures
Directory of Open Access Journals (Sweden)
O. Kohnehpooshi
Full Text Available Abstract The current investigation focused on the development of effective and suitable modelling of reinforced concrete component with and without strengthening. The modelling includes physical and constitutive models. New interface elements have been developed, while modified constitutive law have been applied and new computational algorithm is utilised. The new elements are the Truss-link element to model the interaction between concrete and reinforcement bars, the interface element between two plate bending elements and the interface element to represent the interfacial behaviour between FRP, steel plates and concrete. Nonlinear finite-element (FE codes were developed with pre-processing. The programme was written using FORTRAN language. The accuracy and efficiency of the finite element programme were achieved by analyzing several examples from the literature. The application of the 3D FE code was further enhanced by carrying out the numerical analysis of the three dimensional finite element analysis of FRP strengthened RC beams, as well as the 3D non-linear finite element analysis of girder bridge. Acceptable distributions of slip, deflection, stresses in the concrete and FRP plate have also been found. These results show that the new elements are effective and appropriate to be used for structural component modelling.
Angela Mihai, L.
2013-03-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.
International Nuclear Information System (INIS)
Kapuria, S; Yaqoob Yasin, M
2013-01-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)
Diverse Geological Applications For Basil: A 2d Finite-deformation Computational Algorithm
Houseman, Gregory A.; Barr, Terence D.; Evans, Lynn
Geological processes are often characterised by large finite-deformation continuum strains, on the order of 100% or greater. Microstructural processes cause deformation that may be represented by a viscous constitutive mechanism, with viscosity that may depend on temperature, pressure, or strain-rate. We have developed an effective com- putational algorithm for the evaluation of 2D deformation fields produced by Newto- nian or non-Newtonian viscous flow. With the implementation of this algorithm as a computer program, Basil, we have applied it to a range of diverse applications in Earth Sciences. Viscous flow fields in 2D may be defined for the thin-sheet case or, using a velocity-pressure formulation, for the plane-strain case. Flow fields are represented using 2D triangular elements with quadratic interpolation for velocity components and linear for pressure. The main matrix equation is solved by an efficient and compact conjugate gradient algorithm with iteration for non-Newtonian viscosity. Regular grids may be used, or grids based on a random distribution of points. Definition of the prob- lem requires that velocities, tractions, or some combination of the two, are specified on all external boundary nodes. Compliant boundaries may also be defined, based on the idea that traction is opposed to and proportional to boundary displacement rate. In- ternal boundary segments, allowing fault-like displacements within a viscous medium have also been developed, and we find that the computed displacement field around the fault tip is accurately represented for Newtonian and non-Newtonian viscosities, in spite of the stress singularity at the fault tip. Basil has been applied by us and colleagues to problems that include: thin sheet calculations of continental collision, Rayleigh-Taylor instability of the continental mantle lithosphere, deformation fields around fault terminations at the outcrop scale, stress and deformation fields in and around porphyroblasts, and
An axisymmetrical non-linear finite element model for induction heating in injection molding tools
DEFF Research Database (Denmark)
Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano
2016-01-01
To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed......, including the non-linear temperature dependent magnetic data described by a three-parameter modified Frohlich equation fitted to the magnetic saturation curve, and solved with an iterative procedure. The numerical calculations are compared with experiments conducted with two types of induction coils, built...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...
Afifi, Ahmed; Nakaguchi, Toshiya; Tsumura, Norimichi
2010-03-01
In many medical applications, the automatic segmentation of deformable organs from medical images is indispensable and its accuracy is of a special interest. However, the automatic segmentation of these organs is a challenging task according to its complex shape. Moreover, the medical images usually have noise, clutter, or occlusion and considering the image information only often leads to meager image segmentation. In this paper, we propose a fully automated technique for the segmentation of deformable organs from medical images. In this technique, the segmentation is performed by fitting a nonlinear shape model with pre-segmented images. The kernel principle component analysis (KPCA) is utilized to capture the complex organs deformation and to construct the nonlinear shape model. The presegmentation is carried out by labeling each pixel according to its high level texture features extracted using the overcomplete wavelet packet decomposition. Furthermore, to guarantee an accurate fitting between the nonlinear model and the pre-segmented images, the particle swarm optimization (PSO) algorithm is employed to adapt the model parameters for the novel images. In this paper, we demonstrate the competence of proposed technique by implementing it to the liver segmentation from computed tomography (CT) scans of different patients.
Wu, Tsai-Chin; Anderson, Rae
We use active microrheology coupled to single-molecule fluorescence imaging to elucidate the microscale dynamics of entangled DNA. DNA naturally exists in a wide range of lengths and topologies, and is often confined in cell nucleui, forming highly concentrated and entangled biopolymer networks. Thus, DNA is the model polymer for understanding entangled polymer dynamics as well as the crowded environment of cells. These networks display complex viscoelastic properties that are not well understood, especially at the molecular-level and in response to nonlinear perturbations. Specifically, how microscopic stresses and strains propagate through entangled networks, and what molecular deformations lead to the network stress responses are unknown. To answer these important questions, we optically drive a microsphere through entangled DNA, perturbing the system far from equilibrium, while measuring the resistive force the DNA exerts on the bead during and after bead motion. We simultaneously image single fluorescent-labeled DNA molecules throughout the network to directly link the microscale stress response to molecular deformations. We characterize the deformation of the network from the molecular-level to the mesoscale, and map the stress propagation throughout the network. We further study the impact of DNA length (11 - 115 kbp) and topology (linear vs ring DNA) on deformation and propagation dynamics, exploring key nonlinear features such as tube dilation and power-law relaxation.
Finite element analysis of a finite-strain plasticity problem
International Nuclear Information System (INIS)
Crose, J.G.; Fong, H.H.
1984-01-01
A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)
Toward transient finite element simulation of thermal deformation of machine tools in real-time
Naumann, Andreas; Ruprecht, Daniel; Wensch, Joerg
2018-01-01
Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit-explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand.
International Nuclear Information System (INIS)
Manach, P.Y.; Favier, D.; Rio, G.
1996-01-01
The aim of this paper is to analyse the generation of internal stresses during the predeformation of NiTi shape memory alloys in the martensitic state. This allows to determine the initial stress state in which the material will transform during the shape memory effect due to heating consecutively to this prestrain. In that way a three-dimensional finite element model of the deformation of shape memory alloys has been developed, the constitutive law being defined using an elastohysteresis tensor model. The influence of behavioural and geometrical factors are illustrated considering the numerical simulation of different cases of practical importance for industrial applications : the study of the bending behaviour of a NiTi cantilever beam as well as the study of the swelling of a pipe connection under both uniform and non uniform internal displacement fields. (orig.)
Understanding compressive deformation behavior of porous Ti using finite element analysis
Energy Technology Data Exchange (ETDEWEB)
Roy, Sandipan; Khutia, Niloy [Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur (India); Das, Debdulal [Department of Metallurgy and Materials Engineering, Indian Institute of Engineering Science and Technology, Shibpur (India); Das, Mitun, E-mail: mitun@cgcri.res.in [Bioceramics and Coating Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata (India); Balla, Vamsi Krishna [Bioceramics and Coating Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata (India); Bandyopadhyay, Amit [W. M. Keck Biomedical Materials Research Laboratory, School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164 (United States); Chowdhury, Amit Roy, E-mail: arcbesu@gmail.com [Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur (India)
2016-07-01
In the present study, porous commercially pure (CP) Ti samples with different volume fraction of porosities were fabricated using a commercial additive manufacturing technique namely laser engineered net shaping (LENS™). Mechanical behavior of solid and porous samples was evaluated at room temperature under quasi-static compressive loading. Fracture surfaces of the failed samples were analyzed to determine the failure modes. Finite Element (FE) analysis using representative volume element (RVE) model and micro-computed tomography (CT) based model have been performed to understand the deformation behavior of laser deposited solid and porous CP-Ti samples. In vitro cell culture on laser processed porous CP-Ti surfaces showed normal cell proliferation with time, and confirmed non-toxic nature of these samples. - Highlights: • Porous CP-Ti samples fabricated using additive manufacturing technique • Compressive deformation behavior of porous samples closely matches with micro-CT and RVE based analysis • In vitro studies showed better cell proliferation with time on porous CP-Ti surfaces.
Understanding compressive deformation behavior of porous Ti using finite element analysis
International Nuclear Information System (INIS)
Roy, Sandipan; Khutia, Niloy; Das, Debdulal; Das, Mitun; Balla, Vamsi Krishna; Bandyopadhyay, Amit; Chowdhury, Amit Roy
2016-01-01
In the present study, porous commercially pure (CP) Ti samples with different volume fraction of porosities were fabricated using a commercial additive manufacturing technique namely laser engineered net shaping (LENS™). Mechanical behavior of solid and porous samples was evaluated at room temperature under quasi-static compressive loading. Fracture surfaces of the failed samples were analyzed to determine the failure modes. Finite Element (FE) analysis using representative volume element (RVE) model and micro-computed tomography (CT) based model have been performed to understand the deformation behavior of laser deposited solid and porous CP-Ti samples. In vitro cell culture on laser processed porous CP-Ti surfaces showed normal cell proliferation with time, and confirmed non-toxic nature of these samples. - Highlights: • Porous CP-Ti samples fabricated using additive manufacturing technique • Compressive deformation behavior of porous samples closely matches with micro-CT and RVE based analysis • In vitro studies showed better cell proliferation with time on porous CP-Ti surfaces
The Application Research of Inverse Finite Element Method for Frame Deformation Estimation
Directory of Open Access Journals (Sweden)
Yong Zhao
2017-01-01
Full Text Available A frame deformation estimation algorithm is investigated for the purpose of real-time control and health monitoring of flexible lightweight aerospace structures. The inverse finite element method (iFEM for beam deformation estimation was recently proposed by Gherlone and his collaborators. The methodology uses a least squares principle involving section strains of Timoshenko theory for stretching, torsion, bending, and transverse shearing. The proposed methodology is based on stain-displacement relations only, without invoking force equilibrium. Thus, the displacement fields can be reconstructed without the knowledge of structural mode shapes, material properties, and applied loading. In this paper, the number of the locations where the section strains are evaluated in the iFEM is discussed firstly, and the algorithm is subsequently investigated through a simple supplied beam and an experimental aluminum wing-like frame model in the loading case of end-node force. The estimation results from the iFEM are compared with reference displacements from optical measurement and computational analysis, and the accuracy of the algorithm estimation is quantified by the root-mean-square error and percentage difference error.
INSAR AND FINITE ELEMENT ANALYSIS OF GROUND DEFORMATION AT LAKE URMIA CAUSEWAY (LUC, NORTHWEST IRAN
Directory of Open Access Journals (Sweden)
R. Shamshiri
2013-09-01
Full Text Available Precise long-term deformation monitoring of causeways and bridges is of vital task for maintenance and management work related to transportation safety. In this study, we analyse the settlement of Lake Urmia Causeway (LUC, northwest Iran, using observations from InSAR and Finite Element Model (FEM simulation. For InSAR processing, we analyse 58 SAR images of ENVISAT, ALOS and TerraSAR-X (TSX using the SBAS technique to assess the settlement of embankments in the years 2003–2013. The InSAR results show deflation on both embankments with a peak velocity of > 5 cm/year in the satellite Line Of Sight (LOS direction. The InSAR observations are then used to construct a settlement compaction model for the cross section at the distance of 4 km from the most western edge of the causeway, using a 2D Finite Element Model. Our FEM results suggest that settlement of the embankments will continue in the future due to consolidation phenomenon.
Hindle, D.; Malz, A.; Donndorf, S.; Kley, J.; Kopp, H.
2012-04-01
We develop a coupled numerical model for fluid flow in deforming sedimentary basins. We combine a distinct element method for large deformations of crustal materials, with a finite element method for fluid flow according to a diffusion type equation. The key question in such a model is how to simulate evolving permeabilities due to upper and possibly middle crustal deformation, and the coupled issue of how localisation of deformation in faults and shear zones is itself influenced by fluid flow and fluid pressure and vice versa. Currently our knowledge of these issues is restricted, even sketchy. There are a number of hypotheses, based partly on geological and isotope geochemical observations, such as "seismic pumping" models, and fluid induced weak décollement models for thrust sheet transport which have gained quite wide acceptance. Observations around thrusts at the present day have also often been interpreted as showing deformation induced permeability. However, combining all the physics of these processes into a numerical simulation is a complicated task given the ranges of, in particular time scales of the processes we infer to be operating based on our various observations. We start this task by using an elastic fracture relationship between normal stresses across distinct element contacts (which we consider to be the equivalent of discrete, sliding fractures) and their openness and hence their transmissivity. This relates the mechanical state of the distinct element system to a discrete permeability field. Further than that, the geometry of the mechanical system is used to provide boundary conditions for fluid flow in a diffusion equation which also incorporates the permeability field. The next question we address is how to achieve a feedback between fluid pressures and deformation. We try two approaches: one treats pore space in the DEM as real, and calculates the force exerted locally by fluids and adds this to the force balance of the model; another
Crystal plasticity finite element analysis of deformation behaviour in SAC305 solder joint
Darbandi, Payam
Due to the awareness of the potential health hazards associated with the toxicity of lead (Pb), actions have been taken to eliminate or reduce the use of Pb in consumer products. Among those, tin (Sn) solders have been used for the assembly of electronic systems. Anisotropy is of significant importance in all structural metals, but this characteristic is unusually strong in Sn, making Sn based solder joints one of the best examples of the influence of anisotropy. The effect of anisotropy arising from the crystal structure of tin and large grain microstructure on the microstructure and the evolution of constitutive responses of microscale SAC305 solder joints is investigated. Insights into the effects of key microstructural features and dominant plastic deformation mechanisms influencing the measured relative activity of slip systems in SAC305 are obtained from a combination of optical microscopy, orientation imaging microscopy (OIM), slip plane trace analysis and crystal plasticity finite element (CPFE) modeling. Package level SAC305 specimens were subjected to shear deformation in sequential steps and characterized using optical microscopy and OIM to identify the activity of slip systems. X-ray micro Laue diffraction and high energy monochromatic X-ray beam were employed to characterize the joint scale tensile samples to provide necessary information to be able to compare and validate the CPFE model. A CPFE model was developed that can account for relative ease of activating slip systems in SAC305 solder based upon the statistical estimation based on correlation between the critical resolved shear stress and the probability of activating various slip systems. The results from simulations show that the CPFE model developed using the statistical analysis of activity of slip system not only can satisfy the requirements associated with kinematic of plastic deformation in crystal coordinate systems (activity of slip systems) and global coordinate system (shape changes
Non-linear analysis of skew thin plate by finite difference method
International Nuclear Information System (INIS)
Kim, Chi Kyung; Hwang, Myung Hwan
2012-01-01
This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
Jokhio, G. A.; Izzuddin, B. A.
2015-05-01
This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
International Nuclear Information System (INIS)
Banks, J.W.; Hittinger, J.A.
2010-01-01
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
FEAST: a two-dimensional non-linear finite element code for calculating stresses
International Nuclear Information System (INIS)
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
Directory of Open Access Journals (Sweden)
Husain M. Husain
2013-05-01
Full Text Available In this work a program is developed to carry out the nonlinear analysis (material nonlinearity of prestressed concrete beams using tendons of carbon fiber reinforced polymer (CFRP instead of steel. The properties of this material include high strength, light weight, and insusceptibility to corrosion and magnetism. This material is still under investigation, therefore it needs continuous work to make it beneficial in concrete design. Four beams which are tested experimentally by Yan et al. are examined by the developed computer program to reach a certain analytical approach of the design and analysis of such beams because there is no available restrictions or recommendations covering this material in the codes. The program uses the finite element analysis by dividing the beams into isoparametric 20-noded brick elements. The results obtained are good in comparison with experimental results.
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated...... as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis
International Nuclear Information System (INIS)
Chang, T.Y.; Prachuktam, S.; Reich, M.
1976-11-01
An assessment on a nonlinear structural analysis finite element program called NONSAP is given with respect to its inelastic analysis capability for pressure vessels and components. The assessment was made from the review of its theoretical basis and bench mark problem runs. It was found that NONSAP has only limited capability for inelastic analysis. However, the program was written flexible enough that it can be easily extended or modified to suit the user's need. Moreover, some of the numerical difficulties in using NONSAP are pointed out
ABAQUS/EPGEN - a general purpose finite element code with emphasis on nonlinear applications
International Nuclear Information System (INIS)
Hibbitt, H.D.
1984-01-01
The article contains a summary description of ABAQUS, a finite element program designed for general use in nonlinear as well as linear structural problems, in the context of its application to nuclear structural integrity analysis. The article begins with a discussion of the design criteria and methods upon which the code development has been based. The engineering modelling capabilities, currently implemented in the program - elements, constitutive models and analysis procedures - are then described. Finally, a few demonstration examples are presented, to illustrate some of the program's features that are of interest in structural integrity analysis associated with nuclear power plants. (orig.)
Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory
International Nuclear Information System (INIS)
Cook, W.A.
1981-01-01
Extensions to shell analysis not usually associated with shell theory are described in this paper. These extensions involve thick shells, nonlinear materials, a linear normal stress approximation, and a changing shell thickness. A finite element shell-of-revolution model has been developed to analyze nuclear material shipping containers under severe impact conditions. To establish the limits for this shell model, the basic assumptions used in its development were studied; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress
Compatible-strain mixed finite element methods for incompressible nonlinear elasticity
Faghih Shojaei, Mostafa; Yavari, Arash
2018-05-01
We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.
Extension of non-linear beam models with deformable cross sections
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
Hamim, Salah Uddin Ahmed
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.
Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.
Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen
2008-08-01
Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.
A voxel-based finite element model for the prediction of bladder deformation
Energy Technology Data Exchange (ETDEWEB)
Xiangfei, Chai; Herk, Marcel van; Hulshof, Maarten C. C. M.; Bel, Arjan [Radiation Oncology Department, Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam (Netherlands); Radiation Oncology Department, Netherlands Cancer Institute, 1066 CX Amsterdam (Netherlands); Radiation Oncology Department, Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam (Netherlands)
2012-01-15
Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classical FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to
A voxel-based finite element model for the prediction of bladder deformation
International Nuclear Information System (INIS)
Chai Xiangfei; Herk, Marcel van; Hulshof, Maarten C. C. M.; Bel, Arjan
2012-01-01
Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classical FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
Influence of first proximal phalanx geometry on hallux valgus deformity: a finite element analysis.
Morales-Orcajo, Enrique; Bayod, Javier; Becerro-de-Bengoa-Vallejo, Ricardo; Losa-Iglesias, Marta; Doblare, Manuel
2015-07-01
Hallux abducto valgus (HAV), one of the most common forefoot deformities, occurs primarily in elderly women. HAV is a complex disease without a clearly identifiable cause for its higher prevalence in women compared with men. Several studies have reported various skeletal parameters related to HAV. This study examined the geometry of the proximal phalanx of the hallux (PPH) as a potential etiologic factor in this deformity. A total of 43 cadaver feet (22 males and 21 females) were examined by means of cadaveric dissection. From these data, ten representative PPHs for both genders were selected, corresponding to five percentiles for males (0, 25, 50, 75, and 100%) and five for females. These ten different PPHs were modeled and inserted in ten foot models. Stress distribution patterns within these ten PPH models were qualitatively compared using finite element analysis. In the ten cases analyzed, tensile stresses were larger on the lateral side, whereas compressive stresses were larger on the medial side. The bones of males were larger than female bones for each of the parameters examined; however, the mean difference between lateral and medial sides of the PPH (mean ± SD) was larger in women. Also the shallower the concavity at the base of the PPH, the larger the compressive stresses predicted. Internal forces on the PPH, due to differences in length between its medial and lateral sides, may force the PPH into a less-stressful position. The geometry of the PPH is a significant factor in HAV development influencing the other reported skeletal parameters and, thus, should be considered during preoperative evaluation. Clinical assessment should evaluate the first ray as a whole and not as isolated factors.
International Nuclear Information System (INIS)
Peng, Han Min; Ding, Qing Jun; Hui, Yao; Li, Hua Feng; Zhao, Chun Sheng
2010-01-01
Ionic polymer–metal composites (IPMC) are a class of electroactive polymers (EAP), and they currently attract numerous researchers to study their performance characteristics and applications. However, research on its start-up characteristics still requires more attention. In the IPMC start-up state (the moment of applying an actuation voltage at the very beginning), its mechanical performance is different in the stable working state (working for at least 10 min). Therefore, this paper focuses on three performance relationships of an IPMC strip between its maximal tip deformation and voltage, its maximal stress and voltage, as well as its maximal strain and voltage, both in the two states. Different from other reports, we found that they present nonlinear tendencies in the start-up state rather than linear ones. Therefore, based on the equivalent bimorph beam model, a finite element electromechanical coupling calculation module in the ANSYS software was utilized to simulate these characteristics. Furthermore, a test system is introduced to validate the phenomena. As a whole, these three relationships and the FEA method may be beneficial for providing control strategies effectively to IPMC actuators, especially in their start-up states
Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids
Svendsen, Bob; Shanthraj, Pratheek; Raabe, Dierk
2018-03-01
The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To this end, basic balance and constitutive relations from non-equilibrium thermodynamics and continuum mixture theory are combined with a phase-field-based description of multicomponent solid phases and their interfaces. Solid phase modeling is based in particular on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields (e.g., related to chemical ordering, structural ordering, or defects), and local internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables. In this context, various phase interface models are considered. In the equilibrium limit, phase contrasts in composition and local deformation in the phase interface region are determined via bulk energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multicomponent, multiphase, generalization of existing two-phase binary alloy interface equilibrium conditions (e.g., KKS). On the mechanical side, the equilibrium limit of one interface model considered represents a multiphase generalization of Reuss-Sachs conditions from mechanical homogenization theory. Analogously, other interface models considered represent generalizations of interface equilibrium conditions consistent with laminate and sharp-interface theory. In the last part of the work, selected existing models are formulated within the current framework as special cases and discussed in detail.
Hamilton, Mark F.
1989-08-01
Four projects are discussed in this annual summary report, all of which involve basic research in nonlinear acoustics: Scattering of Sound by Sound, a theoretical study of two nonconlinear Gaussian beams which interact to produce sum and difference frequency sound; Parametric Receiving Arrays, a theoretical study of parametric reception in a reverberant environment; Nonlinear Effects in Asymmetric Sound Beams, a numerical study of two dimensional finite amplitude sound fields; and Pulsed Finite Amplitude Sound Beams, a numerical time domain solution of the KZK equation.
DeBenedictis, Andrew; Atherton, Timothy J.; Rodarte, Andrea L.; Hirst, Linda S.
2018-03-01
A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus
2014-01-01
In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.
A nonlinear finite element model of a piezoelectric tube actuator with hysteresis and creep
International Nuclear Information System (INIS)
Chung, S H; Fung, Eric H K
2010-01-01
Piezoelectric tube actuators are commonly used for nanopositioning in atomic force microscopes (AFMs). However, piezoelectric tube actuators exhibit hysteresis and creep which significantly limit the accuracy of nanopositioning. A finite element model of a piezoelectric tube actuator with hysteresis and creep is important for control purposes, but so far one has not been developed. The purpose of this paper is to present a nonlinear finite element (FE) model with hysteresis and creep for design purposes. Prandtl–Ishlinskii (PI) hysteresis operators and creep operators are adopted into constitutive equations. The nonlinear FE model is formulated using energy approach and Hamilton's principle. The parameters of the PI hysteresis operators and the creep operators are identified by comparing the simulation results and experimental results of other researchers. The working operation of the piezoelectric tube actuator is simulated by the reduced order FE model, and the displacement error due to hysteresis, creep and coupling effect is investigated. An output feedback controller is implemented into the reduced order FE model to show that this model is controllable
A study of gradient strengthening based on a finite-deformation gradient crystal-plasticity model
Pouriayevali, Habib; Xu, Bai-Xiang
2017-11-01
A comprehensive study on a finite-deformation gradient crystal-plasticity model which has been derived based on Gurtin's framework (Int J Plast 24:702-725, 2008) is carried out here. This systematic investigation on the different roles of governing components of the model represents the strength of this framework in the prediction of a wide range of hardening behaviors as well as rate-dependent and scale-variation responses in a single crystal. The model is represented in the reference configuration for the purpose of numerical implementation and then implemented in the FEM software ABAQUS via a user-defined subroutine (UEL). Furthermore, a function of accumulation rates of dislocations is employed and viewed as a measure of formation of short-range interactions. Our simulation results reveal that the dissipative gradient strengthening can be identified as a source of isotropic-hardening behavior, which may represent the effect of irrecoverable work introduced by Gurtin and Ohno (J Mech Phys Solids 59:320-343, 2011). Here, the variation of size dependency at different magnitude of a rate-sensitivity parameter is also discussed. Moreover, an observation of effect of a distinctive feature in the model which explains the effect of distortion of crystal lattice in the reference configuration is reported in this study for the first time. In addition, plastic flows in predefined slip systems and expansion of accumulation of GNDs are distinctly observed in varying scales and under different loading conditions.
Calculation model of non-linear dynamic deformation of composite multiphase rods
Directory of Open Access Journals (Sweden)
Mishchenko Andrey Viktorovich
2014-05-01
Full Text Available The method of formulating non-linear physical equations for multiphase rods is suggested in the article. Composite multiphase rods possess various structures, include shear, polar, radial and axial inhomogeneity. The Timoshenko’s hypothesis with the large rotation angles is used. The method is based on the approximation of longitudinal normal stress low by basic functions expansions regarding the linear viscosity low. The shear stresses are calculated with the equilibrium equation using the subsidiary function of the longitudinal shift force. The system of differential equations connecting the internal forces and temperature with abstract deformations are offered by the basic functions. The application of power functions with arbitrary index allows presenting the compact form equations. The functional coefficients in this system are the highest order rigidity characteristics. The whole multiphase cross-section rigidity characteristics are offered the sums of the rigidity characteristics of the same phases individually. The obtained system allows formulating the well-known particular cases. Among them: hard plasticity and linear elastic deformation, different module deformation and quadratic Gerstner’s low elastic deformation. The reform of differential equations system to the quasilinear is suggested. This system contains the secant variable rigidity characteristics depending on abstract deformations. This system includes the sum of the same uniform blocks of different order. The rods phases defined the various set of uniform blocks phase materials. The integration of dynamic, kinematic and physical equations taking into account initial and edge condition defines the full dynamical multiphase rods problem. The quasilinear physical equations allow getting the variable flexibility matrix of multiphase rod and rods system.
Zeqiri, Bajram; Cook, Ashley; Rétat, Lise; Civale, John; ter Haar, Gail
2015-04-01
The acoustic nonlinearity parameter, B/A, is an important parameter which defines the way a propagating finite amplitude acoustic wave progressively distorts when travelling through any medium. One measurement technique used to determine its value is the finite amplitude insertion substitution (FAIS) method which has been applied to a range of liquid, tissue and tissue-like media. Importantly, in terms of the achievable measurement uncertainties, it is a relative technique. This paper presents a detailed study of the method, employing a number of novel features. The first of these is the use of a large area membrane hydrophone (30 mm aperture) which is used to record the plane-wave component of the acoustic field. This reduces the influence of diffraction on measurements, enabling studies to be carried out within the transducer near-field, with the interrogating transducer, test cell and detector positioned close to one another, an attribute which assists in controlling errors arising from nonlinear distortion in any intervening water path. The second feature is the development of a model which estimates the influence of finite-amplitude distortion as the acoustic wave travels from the rear surface of the test cell to the detector. It is demonstrated that this can lead to a significant systematic error in B/A measurement whose magnitude and direction depends on the acoustic property contrast between the test material and the water-filled equivalent cell. Good qualitative agreement between the model and experiment is reported. B/A measurements are reported undertaken at (20 ± 0.5) °C for two fluids commonly employed as reference materials within the technical literature: Corn Oil and Ethylene Glycol. Samples of an IEC standardised agar-based tissue-mimicking material were also measured. A systematic assessment of measurement uncertainties is presented giving expanded uncertainties in the range ±7% to ±14%, expressed at a confidence level close to 95
Solving nonlinear nonstationary problem of heat-conductivity by finite element method
Directory of Open Access Journals (Sweden)
Антон Янович Карвацький
2016-11-01
Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions
A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems
Directory of Open Access Journals (Sweden)
Antônio Marcos Gonçalves de Lima
Full Text Available AbstractMany authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency- and temperature-dependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency- and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.
International Nuclear Information System (INIS)
Hawileh, Rami A.; El-Maaddawy, Tamer A.; Naser, Mohannad Z.
2012-01-01
Highlights: ► A 3D nonlinear FE model is developed of RC deep beams with web openings. ► We used cohesion elements to simulate bond. ► The developed FE model is suitable for analysis of such complex structures. -- Abstract: This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.
Finite-size effect of η-deformed AdS5×S5 at strong coupling
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Changrim Ahn
2017-04-01
Full Text Available We compute Lüscher corrections for a giant magnon in the η-deformed (AdS5×S5η using the su(2|2q-invariant S-matrix at strong coupling and compare with the finite-size effect of the corresponding string state, derived previously. We find that these two results match and confirm that the su(2|2q-invariant S-matrix is describing world-sheet excitations of the η-deformed background.
Finite-size giant magnons on η-deformed AdS{sub 5}×S{sup 5}
Energy Technology Data Exchange (ETDEWEB)
Ahn, Changrim, E-mail: ahn@ewha.ac.kr; Bozhilov, Plamen, E-mail: bozhilov@inrne.bas.bg
2014-10-07
We consider strings moving in the R{sub t}×S{sub η}{sup 3} subspace of the η-deformed AdS{sub 5}×S{sup 5} and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation.
Finite-size giant magnons on η-deformed AdS5×S5
Directory of Open Access Journals (Sweden)
Changrim Ahn
2014-10-01
Full Text Available We consider strings moving in the Rt×Sη3 subspace of the η-deformed AdS5×S5 and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation.
Magesh, Varadaraju; Harikrishnan, Pandurangan; Kingsly Jeba Singh, Devadhas
2018-04-01
Torque applied on anterior teeth is vital for root positioning and stability. The aim of this study was to evaluate the detailed slot wall deformation in stainless steel (SS) and titanium (Ti) edgewise brackets during palatal root torque using finite element analysis. A finite element model was developed from a maxillary central incisor SS bracket (0.022 in). The generated torque values from an SS rectangular archwire (0.019 × 0.025 in) while twisting from 5° to 40° were obtained experimentally by a spine tester, and the calculated torque force was applied in the bracket slot. The deformations of the slot walls in both SS and Ti brackets were measured at various locations. There were gradual increases in the deformations of both bracket slot walls from the bottom to top locations. In the SS bracket slot for the 40° twist, the deformations were 9.28, 36.8, and 44.8 μm in the bottom, middle, and top slot wall locations, respectively. Similarly, in the Ti bracket slot for the 40° twist, the deformations were 39.2, 62.4, and 76.2 μm in the bottom, middle, and top slot wall locations, respectively. The elastic limits were reached at 28° for SS and at 37° for Ti. Both SS and Ti bracket slots underwent deformation during torque application. There are variations in the deformations at different locations in the slot walls and between the materials. Copyright © 2017 American Association of Orthodontists. Published by Elsevier Inc. All rights reserved.
Nonlinearly deformed W∞ algebra and second hamiltonian structure of KP hierarchy
International Nuclear Information System (INIS)
Yu Feng; Wu Yongshi
1992-01-01
The characteristic nonlinearity of W N algebras, appropriate for their many applications in two-dimensional quantum physics, is lost in the usual large-N limits. In this paper we search for nonlinear extensions of the Virasoro algebra that incorporate all higher-spin currents with spin s≥2. We show that under certain natural homogeneity requirements, the Jacobi identities lead to a unique nonlinear, centerless deformation of classical w ∞ and W ∞ . The latter, which we call dW/dt ∞ , constitutes a universal W-algebra which is very likely to contain all W N algebras by reduction. Also it is closely related to the linear W 1+∞ by a set of interesting recursion relations, which suggests the isomorphism of dW/dt ∞ to the second hamiltonian structure of the KP hierarchy proposed by Dickey. The implications for the symmetries in two-dimensional quantum gravity and noncritical c≤1 strings in the context of the KP approach are discussed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Stone, C.M.
1997-07-01
SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. 43 refs., 22 figs.
International Nuclear Information System (INIS)
Frija, M.; Hassine, T.; Fathallah, R.; Bouraoui, C.; Dogui, A.
2006-01-01
This paper presents a numerical simulation of the shot peening process using finite element method. The majority of the controlling parameters of the process have been taken into account. The shot peening loading has been characterised by using energy equivalence between the dynamic impact and a static indentation of a peening shot in the treated surface. The behaviour of the subjected material is supposed to be elastic plastic with damage. An integrated law of the damage proposed by Lemaitre and Chaboche has been used. The proposed model leads to obtain the residual stress, the plastic deformation profiles and the surface damage. An application on a shot peened Ni-based super alloy Waspaloy has been carried out. The comparison of the residual stresses, obtained by X-ray diffraction method and by finite element calculation, shows a good correlation. The in-depth profile of the plastic deformations and the superficial damage values are in good agreement with the experimental observations
Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K
2014-06-01
Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently
Energy Technology Data Exchange (ETDEWEB)
Del Coz Diaz, J.J.; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown. [Author].
Energy Technology Data Exchange (ETDEWEB)
Diaz del Coz, J.J. [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)]. E-mail: juanjo@constru.uniovi.es; Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Rodriguez, A. Martin [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Martinez-Luengas, A. Lozano [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.
International Nuclear Information System (INIS)
Diaz del Coz, J.J.; Nieto, P.J. Garcia; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon
2006-01-01
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown
DEFF Research Database (Denmark)
Lu, Kaiyuan; Rasmussen, Peter Omand; Ritchie, Ewen
2011-01-01
This paper presents a new method for computation of the nonlinear flux linkage in 3-D finite-element models (FEMs) of electrical machines. Accurate computation of the nonlinear flux linkage in 3-D FEM is not an easy task. Compared to the existing energy-perturbation method, the new technique......-perturbation method. The new method proposed is validated using experimental results on two different permanent magnet machines....
Reed, K. W.; Atluri, S. N.
1983-01-01
A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.
Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E
2013-12-01
In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
De Donato, O.; Parisi, M.A.
1977-01-01
When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)
A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems
Gambolati, Giuseppe; Teatini, Pietro
1996-01-01
A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.
CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1988-12-01
A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)
Performance analysis for minimally nonlinear irreversible refrigerators at finite cooling power
Long, Rui; Liu, Zhichun; Liu, Wei
2018-04-01
The coefficient of performance (COP) for general refrigerators at finite cooling power have been systematically researched through the minimally nonlinear irreversible model, and its lower and upper bounds in different operating regions have been proposed. Under the tight coupling conditions, we have calculated the universal COP bounds under the χ figure of merit in different operating regions. When the refrigerator operates in the region with lower external flux, we obtained the general bounds (0 present large values, compared to a relative small loss from the maximum cooling power. If the cooling power is the main objective, it is desirable to operate the refrigerator at a slightly lower cooling power than at the maximum one, where a small loss in the cooling power induces a much larger COP enhancement.
International Nuclear Information System (INIS)
Kulak, R.F.; Belytschko, T.B.
1975-09-01
The formulation of a finite-element procedure for the implicit transient and static analysis of plate/shell type structures in three-dimensional space is described. The triangular plate/shell element can sustain both membrane and bending stresses. Both geometric and material nonlinearities can be treated, and an elastic-plastic material law has been incorporated. The formulation permits the element to undergo arbitrarily large rotations and translations; but, in its present form it is restricted to small strains. The discretized equations of motion are obtained by a stiffness method. An implicit integration algorithm based on trapezoidal integration formulas is used to integrate the discretized equations of motion in time. To ensure numerical stability, an iterative solution procedure with equilibrium checks is used
Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping
Smith, Timothy; Pantano, Carlos
2017-11-01
We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.
Nonlinear deformation of skeletal muscles in a passive state and in isotonic contraction
Shil'ko, S. V.; Chernous, D. A.; Pleskachevskii, Yu. M.
2012-07-01
A procedure for a two-level modeling of deformation of skeletal muscles is offered. Based on a phenomenological model of an individual muscle fiber, consisting of a viscous, a contractive, and two nonlinearly elastic elements (the first level), various means for describing a skeletal muscle as a whole (the second, macroscopic level) are considered. A method for identification of a muscle model by utilizing experimental elongation diagrams in a passive state and in isotonic contraction is put forward. The results of a biomechanical analysis are compared with known experimental data for the isotonic and isometric activation regimes of tailor's muscle of a frog. It is established that preferable is the description of a muscle that takes into account the different lengths of muscle fibers and their twist.
Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices
International Nuclear Information System (INIS)
Carusotto, Iacopo; Embriaco, Davide; La Rocca, Giuseppe C.
2002-01-01
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties
Espath, L. F R; Braun, Alexandre Luis; Awruch, Armando Miguel; Dalcin, Lisandro
2015-01-01
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Espath, L. F R
2015-02-03
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Stability of orbits in nonlinear mechanics for finite but very long times
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab
Stability of orbits in nonlinear mechanics for finite but very long times
Energy Technology Data Exchange (ETDEWEB)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
International Nuclear Information System (INIS)
Yan, Z.; Zhang, H.
2001-01-01
In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed
International Nuclear Information System (INIS)
Kraus, H.G.; Jones, J.L.
1986-01-01
The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)
Run-up on a body in waves and current. Fully nonlinear and finite-order calculations
DEFF Research Database (Denmark)
Büchmann, Bjarne; Ferrant, P.; Skourup, J.
2001-01-01
Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength...
International Nuclear Information System (INIS)
Nguyen Buong.
1992-11-01
The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...
Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke
2018-02-01
In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Mark Driscoll
2013-01-01
Full Text Available A large spectrum of medical devices exists; it aims to correct deformities associated with spinal disorders. The development of a detailed volumetric finite element model of the osteoligamentous spine would serve as a valuable tool to assess, compare, and optimize spinal devices. Thus the purpose of the study was to develop and initiate validation of a detailed osteoligamentous finite element model of the spine with simulated correction from spinal instrumentation. A finite element of the spine from T1 to L5 was developed using properties and geometry from the published literature and patient data. Spinal instrumentation, consisting of segmental translation of a scoliotic spine, was emulated. Postoperative patient and relevant published data of intervertebral disc stress, screw/vertebra pullout forces, and spinal profiles was used to evaluate the models validity. Intervertebral disc and vertebral reaction stresses respected published in vivo, ex vivo, and in silico values. Screw/vertebra reaction forces agreed with accepted pullout threshold values. Cobb angle measurements of spinal deformity following simulated surgical instrumentation corroborated with patient data. This computational biomechanical analysis validated a detailed volumetric spine model. Future studies seek to exploit the model to explore the performance of corrective spinal devices.
International Nuclear Information System (INIS)
1983-04-01
VISCOT is a non-linear, transient, thermal-stress finite-element code designed to determine the viscoelastic, fiscoplastic, or elastoplastic deformation of a rock mass due to mechanical and thermal loading. The numerical solution of the nonlinear incremental equilibrium equations within VISCOT is performed by using an explicit Euler time-stepping scheme. The rock mass may be modeled as a viscoplastic or viscoelastic material. The viscoplastic material model can be described by a Tresca, von Mises, Drucker-Prager or Mohr-Coulomb yield criteria (with or without strain hardening) with an associated flow rule which can be a power or an exponential law. The viscoelastic material model within VISCOT is a temperature- and stress-dependent law which has been developed specifically for salt rock masses by Pfeifle, Mellegard and Senseny in ONWI-314 topical report (1981). Site specific parameters for this creep law at the Richton, Permian, Paradox and Vacherie salt sites have been calculated and are given in ONWI-314 topical report (1981). A major application of VISCOT (in conjunction with a SCEPTER heat transfer code such as DOT) is the thermomechanical analysis of a rock mass such as salt in which significant time-dependent nonlinear deformations are expected to occur. Such problems include room- and canister-scale studies during the excavation, operation, and long-term post-closure stages in a salt repository. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report
International Nuclear Information System (INIS)
Franca, L.P.; Toledo, E.M.; Loula, A.F.D.; Garcia, E.L.M.
1988-12-01
A new finite element method is employed to approximate axisymmetric shell problems. This formulation enhances stability and accuracy, from thin to moderately thick shells, compared to the correspondent Galerkin finite element approximations. Numerical results illustrate the good performance of the present method on some typical pressure vessels aplications. (author) [pt
Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.
Divall, S A; Humphrey, V F
2000-03-01
Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.
Wang, Yujuan; Song, Yongduan; Ren, Wei
2017-07-06
This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.
Konkol, Jakub; Bałachowski, Lech
2017-03-01
In this paper, the whole process of pile construction and performance during loading is modelled via large deformation finite element methods such as Coupled Eulerian Lagrangian (CEL) and Updated Lagrangian (UL). Numerical study consists of installation process, consolidation phase and following pile static load test (SLT). The Poznań site is chosen as the reference location for the numerical analysis, where series of pile SLTs have been performed in highly overconsolidated clay (OCR ≈ 12). The results of numerical analysis are compared with corresponding field tests and with so-called "wish-in-place" numerical model of pile, where no installation effects are taken into account. The advantages of using large deformation numerical analysis are presented and its application to the pile designing is shown.
Directory of Open Access Journals (Sweden)
Konkol Jakub
2017-03-01
Full Text Available In this paper, the whole process of pile construction and performance during loading is modelled via large deformation finite element methods such as Coupled Eulerian Lagrangian (CEL and Updated Lagrangian (UL. Numerical study consists of installation process, consolidation phase and following pile static load test (SLT. The Poznań site is chosen as the reference location for the numerical analysis, where series of pile SLTs have been performed in highly overconsolidated clay (OCR ≈ 12. The results of numerical analysis are compared with corresponding field tests and with so-called “wish-in-place” numerical model of pile, where no installation effects are taken into account. The advantages of using large deformation numerical analysis are presented and its application to the pile designing is shown.
Finite-element analysis of the deformation of thin Mylar films due to measurement forces.
Energy Technology Data Exchange (ETDEWEB)
Baker, Michael Sean; Robinson, Alex Lockwood; Tran, Hy D.
2012-01-01
Significant deformation of thin films occurs when measuring thickness by mechanical means. This source of measurement error can lead to underestimating film thickness if proper corrections are not made. Analytical solutions exist for Hertzian contact deformation, but these solutions assume relatively large geometries. If the film being measured is thin, the analytical Hertzian assumptions are not appropriate. ANSYS is used to model the contact deformation of a 48 gauge Mylar film under bearing load, supported by a stiffer material. Simulation results are presented and compared to other correction estimates. Ideal, semi-infinite, and constrained properties of the film and the measurement tools are considered.
International Nuclear Information System (INIS)
Schwarm, Samuel C.; Mburu, Sarah; Ankem, Sreeramamurthy
2016-01-01
The phase properties and deformation behavior of the δ–ferrite and γ–austenite phases of CF–3 and CF–8 cast duplex stainless steels were characterized by nanoindentation and microstructure-based finite element method (FEM) models. We evaluated the elastic modulus of each phase and the results indicate that the mean elastic modulus of the δ–ferrite phase is greater than that of the γ–austenite phase, and the mean nanoindentation hardness values of each phase are approximately the same. Furthermore, the elastic FEM model results illustrate that greater von Mises stresses are located within the δ–ferrite phase, while greater von Mises strains are located in the γ–austenite phase in response to elastic deformation. The elastic moduli calculated by FEM agree closely with those measured by tensile testing. Finally, the plastically deformed specimens exhibit an increase in misorientation, deformed grains, and subgrain structure formation as measured by electron backscatter diffraction (EBSD).
Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.
2018-03-01
An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.
Directory of Open Access Journals (Sweden)
Teeraphot Supaviriyakit
2017-11-01
Full Text Available This paper presents a nonlinear finite element analysis of non-seismically detailed RC beam column connections under reversed cyclic load. The test of half-scale nonductile reinforced concrete beam-column joints was conducted. The tested specimens represented those of the actual mid-rise reinforced concrete frame buildings designed according to the non-seismic provisions of the ACI building code. The test results show that specimens representing small and medium column tributary area failed in brittle joint shear while specimen representing large column tributary area failed by ductile flexure though no ductile reinforcement details were provided. The nonlinear finite element analysis was applied to simulate the behavior of the specimens. The finite element analysis employs the smeared crack approach for modeling beam, column and joint, and employs the discrete crack approach for modeling the interface between beam and joint face. The nonlinear constitutive models of reinforced concrete elements consist of coupled tension-compression model to model normal force orthogonal and parallel to the crack and shear transfer model to capture the shear sliding mechanism. The FEM shows good comparison with test results in terms of load-displacement relations, hysteretic loops, cracking process and the failure mode of the tested specimens. The finite element analysis clarifies that the joint shear failure was caused by the collapse of principal diagonal concrete strut.
Wen, Jici; Wei, Yujie; Cheng, Yang-Tse
2018-05-01
During the lithiation and delithiation of a thin film electrode, stress in the electrode is deduced from the curvature change of the film using the Stoney equation. The accuracy of such a measurement is conditioned on the assumptions that (a) the mechanical properties of the electrode remain unchanged during lithiation and (b) small deformation holds. Here, we demonstrate that the change in elastic properties can influence the measurement of the stress in thin film electrodes. We consider the coupling between diffusion and deformation during lithiation and delithiation of thin film electrodes and implement the constitutive behavior in a finite-deformation finite element procedure. We demonstrate that both the variation in elastic properties in thin film electrodes and finite-deformation during lithiation and delithiation would challenge the applicability of the Stoney-equation for in-situ stress measurements of thin film electrodes.
Kong, Liang; Gu, Zexu; Li, Tao; Wu, Junjie; Hu, Kaijin; Liu, Yanpu; Zhou, Hongzhi; Liu, Baolin
2009-01-01
A nonlinear finite element method was applied to examine the effects of implant diameter and length on the maximum von Mises stresses in the jaw, and to evaluate the maximum displacement of the implant-abutment complex in immediate-loading models. The implant diameter (D) ranged from 3.0 to 5.0 mm and implant length (L) ranged from 6.0 to 16.0 mm. The results showed that the maximum von Mises stress in cortical bone was decreased by 65.8% under a buccolingual load with an increase in D. In cancellous bone, it was decreased by 71.5% under an axial load with an increase in L. The maximum displacement in the implant-abutment complex decreased by 64.8% under a buccolingual load with an increase in D. The implant was found to be more sensitive to L than to D under axial loads, while D played a more important role in enhancing its stability under buccolingual loads. When D exceeded 4.0 mm and L exceeded 11.0 mm, both minimum stress and displacement were obtained. Therefore, these dimensions were the optimal biomechanical selections for immediate-loading implants in type B/2 bone.
Nonlinear finite element analysis of liquid sloshing in complex vehicle motion scenarios
Nicolsen, Brynne; Wang, Liang; Shabana, Ahmed
2017-09-01
The objective of this investigation is to develop a new total Lagrangian continuum-based liquid sloshing model that can be systematically integrated with multibody system (MBS) algorithms in order to allow for studying complex motion scenarios. The new approach allows for accurately capturing the effect of the sloshing forces during curve negotiation, rapid lane change, and accelerating and braking scenarios. In these motion scenarios, the liquid experiences large displacements and significant changes in shape that can be captured effectively using the finite element (FE) absolute nodal coordinate formulation (ANCF). ANCF elements are used in this investigation to describe complex mesh geometries, to capture the change in inertia due to the change in the fluid shape, and to accurately calculate the centrifugal forces, which for flexible bodies do not take the simple form used in rigid body dynamics. A penalty formulation is used to define the contact between the rigid tank walls and the fluid. A fully nonlinear MBS truck model that includes a suspension system and Pacejka's brush tire model is developed. Specified motion trajectories are used to examine the vehicle dynamics in three different scenarios - deceleration during straight-line motion, rapid lane change, and curve negotiation. It is demonstrated that the liquid sloshing changes the contact forces between the tires and the ground - increasing the forces on certain wheels and decreasing the forces on other wheels. In cases of extreme sloshing, this dynamic behavior can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Directory of Open Access Journals (Sweden)
Y. S. Kong
2013-01-01
Full Text Available This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
International Nuclear Information System (INIS)
Lehmann, G.; Spatschek, K. H.
2013-01-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime
Mancilla Canales, M. A.; Leguto, A. J.; Riquelme, B. D.; León, P. Ponce de; Bortolato, S. A.; Korol, A. M.
2017-12-01
Ektacytometry techniques quantifies red blood cells (RBCs) deformability by measuring the elongation of suspended RBCs subjected to shear stress. Raw shear stress elongation plots are difficult to understand, thus most research papers apply data reduction methods characterizing the relationship between curve fitting. Our approach works with the naturally generated photometrically recorded time series of the diffraction pattern of several million of RBCs subjected to shear stress, and applies nonlinear quantifiers to study the fluctuations of these elongations. The development of new quantitative methods is crucial for restricting the subjectivity in the study of the cells behavior, mainly if they are capable of analyze at the same time biological and mechanical aspects of the cells in flowing conditions and compare their dynamics. A patented optical system called Erythrocyte Rheometer was used to evaluate viscoelastic properties of erythrocytes by Ektacytometry. To analyze cell dynamics we used the technique of Time Delay Coordinates, False Nearest Neighbors, the forecasting procedure proposed by Sugihara and May, and Hurst exponent. The results have expressive meaning on comparing healthy samples with parasite treated samples, suggesting that apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize biological and mechanical aspects of cells at the same time in flowing conditions.
Numerical simulation of bubble deformation in magnetic fluids by finite volume method
International Nuclear Information System (INIS)
Yamasaki, Haruhiko; Yamaguchi, Hiroshi
2017-01-01
Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field. - Highlights: • A magnetic field analysis is developed to simulate the bubble dynamics in magnetic fluid with two-phase interface. • The elongation of bubble increased with increasing magnetic flux intensities due to strong magnetic normal force. • Proposed technique explains the bubble dynamics, taking into account of the continuity of the magnetic flux density.
How simple can nonlinear finite element modelling be for structural concrete?
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Argirova, G.
2014-12-01
Full Text Available This paper discusses on the required level of simplicity for suitable modelling of structural concrete. Traditional equilibrium- based approaches (as strut-and-tie models are too coarse in some cases, as they account for the cracking state of concrete in a sometimes excessively simplified manner. The alternative of complex nonlinear numerical modelling is also not always satisfactory for design as the number of parameters required, their definition and the sensitivity of the structural response to them is complex and requires a high level of experience. Contrary to these approaches, this paper introduces the elastic plastic stress field method. This method is grounded on the theory of plasticity but allows considering deformation compatibility. The results are consistent both in terms of the strength and deformation field of the member. It also has the advantage of requiring only two physical material properties (modulus of elasticity and plastic strength which can be easily determined by designers.Este artículo discute sobre el nivel de sencillez ideal para un análisis no lineal de elementos de hormigón estructural. Los métodos de cálculo basados únicamente en condiciones de equilibrio (como los modelos de bielas-y-tirantes no son siempre adecuados ya que el estado de fisuración del hormigón se considera a veces de una manera excesivamente simplificada. Los análisis no lineales complejos tampoco son siempre adecuados, ya que el número de parámetros requeridos, su definición y la sensibilidad de la respuesta del elemento a sus variaciones requieren una gran experiencia. Como alternativa, se presenta el método de los campos de tensiones elasto-plásticos. Este método se basa en la teoría de la plasticidad pero incorporando condiciones de compatibilidad. Los resultados son coherentes en términos de resistencia y de deformaciones. Además, sólo necesita la definición de dos parámetros mecánicos (módulo de elasticidad y
Non-linear effects in vortex viscous flow in superconductors-role of finite heat removal velocity
International Nuclear Information System (INIS)
Bezuglyj, A.I.; Shklovskij, V.A.
1991-01-01
The role of finite heat removal velocity in experiments on non-linear effects in vortex viscous flow in superconducting films near critical temperature was investigated. It was shown that the account of thermal effects permits to explain the experimentally observed dependence of electron energy relaxation time and current break-down in voltage-current characteristic from magnetic field value. 5 refs.; 1 fig. (author)
DEFF Research Database (Denmark)
Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi
In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...
Ye, W; Bel-Brunon, A; Catheline, S; Combescure, A; Rochette, M
2018-01-01
In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment. Copyright © 2017 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Ott, R.T.; Sansoz, F.; Molinari, J.F.; Almer, J.; Ramesh, K.T.; Hufunagel, T.C.
2005-01-01
In situ X-ray scattering and finite element modeling (FEM) were used to examine the micromechanics of deformation of in situ formed metallic-glass-matrix composites consisting of Ta-rich particles dispersed in an amorphous matrix. The strain measurements show that under uniaxial compression the second-phase particles yield at an applied stress of approx. 325 MPa. After yielding, the particles do not strain harden significantly; we show that this is due to an increasingly hydrostatic stress state arising from the lateral constraint on deformation of the particles imposed by the elastic matrix. Shear band initiation in the matrix is not due to the difference in elastic properties between the matrix and the particles. Rather, the development of a plastic misfit strain causes stress concentrations around the particles, resulting in localized yielding of the matrix by shear band formation at an applied stress of approx. 1450 MPa, considerably lower than the macroscopic yield stress of the composite (approx. 1725 MPa). Shear bands do not propagate at the lower stress because the yield criterion of the matrix is only satisfied in the region immediately around the particles. At the higher stresses, the yield criterion is satisfied in large regions of the matrix, allowing extensive shear band propagation and significant macroscopic plastic deformation. However, the presence of the particles makes the stress state highly inhomogeneous, which may partially explain why fracture is suppressed in the composite, allowing the development of large plastic strains
Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.
2018-05-01
This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.
Energy Technology Data Exchange (ETDEWEB)
Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.
Real-time volumetric deformable models for surgery simulation using finite elements and condensation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten; Cotin, S.
1996-01-01
This paper discusses the application of SD solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate...
Vibrations And Deformations Of Moderately Thick Plates In Stochastic Finite Element Method
Directory of Open Access Journals (Sweden)
Grzywiński Maksym
2015-12-01
Full Text Available The paper deals with some chosen aspects of stochastic dynamical analysis of moderately thick plates. The discretization of the governing equations is described by the finite element method. The main aim of the study is to provide the generalized stochastic perturbation technique based on classical Taylor expansion with a single random variable.
Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method
Directory of Open Access Journals (Sweden)
Claudiu Iavornic
2011-01-01
Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.
Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.
2017-09-01
Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
Matsuura, Yusuke; Kuniyoshi, Kazuki; Suzuki, Takane; Ogawa, Yasufumi; Sukegawa, Koji; Rokkaku, Tomoyuki; Takahashi, Kazuhisa
2014-11-01
Distal radius fracture, which often occurs in the setting of osteoporosis, can lead to permanent deformity and disability. Great effort has been directed toward developing noninvasive methods for evaluating the distal radius strength, with the goal of assessing fracture risk. The aim of this study was to evaluate distal radius strength using a finite element model and to gauge the accuracy of finite element model measurement using cadaver material. Ten wrists were obtained from cadavers with a mean age of 89.5 years at death. CT images of each wrist in an extended position were obtained. CT-based finite element models were prepared with Mechanical Finder software. Fracture on the models was simulated by applying a mechanical load to the palm in a direction parallel to the forearm axis, after which the fracture load and the site at which the fracture began were identified. For comparison, the wrists were fractured using a universal testing machine and the fracture load and the site of fracture were identified. The fracture load was 970.9 N in the finite element model group and 990.0 N in the actual measurement group. The site of the initial fracture was extra-articular to the distal radius in both groups. The finite element model was predictive for distal radius fracture when compared to the actual measurement. In this study, a finite element model for evaluation of distal radius strength was validated and can be used to predict fracture risk. We conclude that a finite element model is useful for the evaluation of distal radius strength. Knowing distal radius strength might avoid distal radius fracture because appropriate antiosteoporotic treatment can be initiated.
Directory of Open Access Journals (Sweden)
Djillali Amar Bouzid
2018-04-01
Full Text Available A nonlinear finite element model is developed to examine the lateral behaviors of monopiles, which support offshore wind turbines (OWTs chosen from five different offshore wind farms in Europe. The simulation is using this model to accurately estimate the natural frequency of these slender structures, as a function of the interaction of the foundations with the subsoil. After a brief introduction to the wind power energy as a reliable alternative in comparison to fossil fuel, the paper focuses on concept of natural frequency as a primary indicator in designing the foundations of OWTs. Then the range of natural frequencies is provided for a safe design purpose. Next, an analytical expression of an OWT natural frequency is presented as a function of soil-monopile interaction through monopile head springs characterized by lateral stiffness KL, rotational stiffness KR and cross-coupling stiffness KLR, of which the differences are discussed. The nonlinear pseudo three-dimensional finite element vertical slices model has been used to analyze the lateral behaviors of monopiles supporting the OWTs of different wind farm sites considered. Through the monopiles head movements (displacements and rotations, the values of KL, KR and KLR were obtained and substituted in the analytical expression of natural frequency for comparison. The comparison results between computed and measured natural frequencies showed an excellent agreement for most cases. This confirms the convenience of the finite element model used for the accurate estimation of the monopile head stiffness. Keywords: Nonlinear finite element analysis, Vertical slices model, Monopiles under horizontal loading, Natural frequency, Monopile head stiffness, Offshore wind turbines (OWTs
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
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Yong Zhao
1997-01-01
Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
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K. A. Ramesh Kumar
2014-09-01
Full Text Available AlSiC is a metal matrix composite which comprises of aluminium matrix with silicon carbide particles. It is characterized by high thermal conductivity (180-200 W/m K, and its thermal expansion are attuned to match other important materials that finds enormous demand in industrial sectors. Although its application is very common, the physics behind the Al-SiC formation, functionality and behaviors are intricate owing to the temperature gradient of hundreds of degrees, over the volume, occurring on a time scale of a few seconds, involving multiple phases. In this study, various physical, metallurgical and numerical aspects such as equation of continuum for thermal, stress and deformation using finite element (FE matrix formulation, temperature dependent material properties, are analyzed. Modelling and simulation studies of Al/SiC composites are a preliminary attempt to view this research work from computational point of view.
Energy Technology Data Exchange (ETDEWEB)
Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)
2013-11-15
Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.
International Nuclear Information System (INIS)
Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi
2013-01-01
Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation
Finite element modeling of the vocal folds with deformable interface tracking
DEFF Research Database (Denmark)
Granados Corsellas, Alba; Brunskog, Jonas; Misztal, Marek Krzysztof
2014-01-01
Continuous and prolonged use of the sp eaking voice may lead to functional sp eech disorders that are not apparent for voice clinicians from high-sp eed imaging of the vo cal folds' vibration. However, it is hyp othesized that time dep endent tissue prop erties provide some insight into the injury...... pro cess. To infer material parameters via an inverse optimization problem from recorded deformation, a self sustained theoretical mo del of the vo cal folds is needed. With this purp ose, a transversely isotropic three-dimensional nite element mo del is prop osed and investigated. Sp ecial attention...
DEFF Research Database (Denmark)
Ormarsson, Sigurdur; Dahlblom, Ola
2013-01-01
Wood is a hygro-mechanical, non-isotropic and inhomogeneous material concerning both modulus of elasticity (MOE) and shrinkage properties. In stress calculations associated with ordinary timber design, these matters are often not dealt with properly. The main reason for this is that stress...... and the longitudinal shrinkage coefficient vary considerably from pith to bark. The question is how much these variations affect the stress distribution in wooden structures exposed to variable moisture climate. The paper presents a finite element implementation of a beam element with the aim of studying how wooden...
Finite-temperature Casimir effect in the presence of nonlinear dielectrics
DEFF Research Database (Denmark)
Kheirandish, Fardin; Amooghorban, Ehsan; Soltani, Morteza
2011-01-01
Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupl......Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations...
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Ratchata Theinchai
2016-01-01
Full Text Available We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM. The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.
Theinchai, Ratchata; Chankan, Siriwan; Yukunthorn, Weera
2016-01-01
We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.
International Nuclear Information System (INIS)
Kang, Mi Hyun; Seong, Back Suck; Kim, Hyoung Seop
2009-01-01
Severe plastic deformation (SPD) is one of the most promising top-down techniques, moving towards industrialization to fabricate bulk ultrafine grain materials. The strain distribution and deformation behavior during the ECAP (equal channel angular pressing), influenced by tool angles, friction and material behavior, was studied through experimental and numerical analyses. The residual stress of work piece which was straight before ECAP produces many serious problems in the next processing e.g. input of the work piece for the next ECAP. The bent work piece needs additional straightening or surface polishing even if the amount of bending is small, and residual stress need to be released before service applications. Residual stress, particularly tensile residual stress can be a very important factor in affecting the reliability and integrity of working parts. The formation of tensile residual stress may result in initiation of fatigue cracks, stress corrosion cracking, or other types of fracture. Hence, residual stress and resulting bending need to be controlled during ECAP. Thus, in current study the bending behavior and the residual stress of the work piece in ECAP are analyzed through experimental and finite element analyses by considering the effects of material, geometric, and processing parameters individually. The stress states in the ECAP processed work piece were measured by the non-destructive way using neutron diffraction. Efforts were made to suggest the alternate routes to reduce the residual stress and bending of work piece in ECAP
International Nuclear Information System (INIS)
An, Yonghao; Jiang, Hanqing
2013-01-01
Lithium-ion batteries have attracted great deal of attention recently. Silicon is one of the most promising anode materials for high-performance lithium-ion batteries, due to its highest theoretical specific capacity. However, the short lifetime confined by mechanical failure in the silicon anode is now considered to be the biggest challenge in desired applications. High stress induced by the huge volume change due to lithium insertion/extraction is the main reason underlying this problem. Some theoretical models have been developed to address this issue. In order to properly implement these models, we develop a finite element based numerical method using a commercial software package, ABAQUS, as a platform at the continuum level to study fully coupled large deformation and mass diffusion problem. Using this method, large deformation, elasticity–plasticity of the electrodes, various spatial and temporal conditions, arbitrary geometry and dimension could be fulfilled. The interaction between anode and other components of the lithium ion batteries can also be studied as an integrated system. Several specific examples are presented to demonstrate the capability of this numerical platform. (paper)
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....
International Nuclear Information System (INIS)
Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin
2014-01-01
This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)
Directory of Open Access Journals (Sweden)
Mir Hamid Reza Ghoreishy
2014-10-01
Full Text Available This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.
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G. La Rosa
2004-06-01
Full Text Available A 2D finite elements study was carried out to analyse the effects caused by dike intrusion inside a heterogeneous medium and with a realistic topography of Mt. Etna volcano. Firstly, the method (dimension domain, elements type was calibrated using plane strain models in elastic half-spaces; the results were compared with those obtained from analytical dislocation models. Then the effects caused both by the topographic variations and the presence of multi-layered medium on the surface, were studied. In particular, an application was then considered to Mt. Etna by taking into account the real topography and the stratification deduced from seismic tomography. In these conditions, the effects expected by the dike, employed to model the 2001 eruption under simple elastic half-space medium conditions, were computed, showing that topography is extremely important, at least in the near field.
Nakashima, Hiroshi; Takatsu, Yuzuru
The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.
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Nassim Kernou
2018-01-01
Full Text Available A rational three-dimensional nonlinear finite element model (NLFEAS is used for evaluating the behavior of high strength concrete slabs under monotonic transverse load. The non-linear equations of equilibrium have been solved using the incremental-iterative technique based on the modified Newton-Raphson method. The convergence of the solution was controlled by a load convergence criterion. The validity of the theoretical formulations and the program used was verified, through comparison with results obtained using ANSYS program and with available experimental test results. A parametric study was conducted to investigate the effect of different parameters on the behavior of slabs which was evaluated in terms of loaddeflection characteristics, concrete and steel stresses and strains, and failure mechanisms. Also, punching shear resistance of slabs was numerically evaluated and compared with the prediction specified by some design codes.
Zhang, Shengyong
2017-07-01
Spot welding has been widely used for vehicle body construction due to its advantages of high speed and adaptability for automation. An effort to increase the stiffness-to-weight ratio of spot-welded structures is investigated based upon nonlinear finite element analysis. Topology optimization is conducted for reducing weight in the overlapping regions by choosing an appropriate topology. Three spot-welded models (lap, doubt-hat and T-shape) that approximate “typical” vehicle body components are studied for validating and illustrating the proposed method. It is concluded that removing underutilized material from overlapping regions can result in a significant increase in structural stiffness-to-weight ratio.
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Ricardo Aguilar-López
2016-01-01
Full Text Available This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.
Energy Technology Data Exchange (ETDEWEB)
Griffith, Daniel Todd; Segalman, Daniel Joseph
2006-10-01
A technique published in SAND Report 2006-1789 ''Model Reduction of Systems with Localized Nonlinearities'' is illustrated in two problems of finite element structural dynamics. That technique, called here the Method of Locally Discontinuous Basis Vectors (LDBV), was devised to address the peculiar difficulties of model reduction of systems having spatially localized nonlinearities. It's illustration here is on two problems of different geometric and dynamic complexity, but each containing localized interface nonlinearities represented by constitutive models for bolted joint behavior. As illustrated on simple problems in the earlier SAND report, the LDBV Method not only affords reduction in size of the nonlinear systems of equations that must be solved, but it also facilitates the use of much larger time steps on problems of joint macro-slip than would be possible otherwise. These benefits are more dramatic for the larger problems illustrated here. The work of both the original SAND report and this one were funded by the LDRD program at Sandia National Laboratories.
International Nuclear Information System (INIS)
Maheshwari, B.K.; Truman, K.Z.; El Naggar, M.H.; Gould, P.L.
2004-01-01
The effects of material nonlinearity of soil and separation at the soil-pile interface on the dynamic behaviour of a single pile and pile groups are investigated. An advanced plasticity-based soil model, hierarchical single surface (HiSS), is incorporated in the finite element formulation. To simulate radiation effects, proper boundary conditions are used. The model and algorithm are verified with analytical results that are available for elastic and elastoplastic soil models. Analyses are performed for seismic excitation and for the load applied on the pile cap. For seismic analysis, both harmonic and transient excitations are considered. For loading on the pile cap, dynamic stiffness of the soil-pile system is derived and the effect of nonlinearity is investigated. The effects of spacing between piles are investigated, and it was found that the effect of soil nonlinearity on the seismic response is very much dependent on the frequency of excitation. For the loading on a pile cap, the nonlinearity increases the response for most of the frequencies of excitation while decreasing the dynamic stiffness of the soil-pile system. (author)
Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation
Pan, Huihui; Jing, Xingjian; Sun, Weichao
2017-05-01
This paper focuses on the finite-time tracking control with external disturbance for active suspension systems. In order to compensate unknown disturbance efficiently, a disturbance compensator with finite-time convergence property is studied. By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance. According to the finite-time separation principle, the design procedures of the nominal controller for the suspension system without disturbance and the disturbance compensator can be implemented in a completely independent manner. Therefore, the overall control law for the closed-loop system is continuous, which offers some distinct advantages over the existing discontinuous ones. From the perspective of practical implementation, the continuous controller can avoid effectively the unexpected chattering in active suspension control. Comparative experimental results are presented and discussed to illustrate the advantage and effectiveness of the proposed control strategy.
An Analytical Finite-Strain Parameterization for Texture Evolution in Deformed Olivine Polycrystals
Ribe, N. M.; Castelnau, O.
2017-12-01
Current methods for calculating the evolution of flow-induced seismic anisotropy in the upper mantle describe crystal preferred orientation (CPO) using ensembles of 103-104 individual grains, and are too computationally expensive to be used in three-dimensional time-dependent convection models. We propose a much faster method based on the hypothesis that CPO of olivine polycrystals is a unique function of the finite strain. Our goal is then to determine how the CPO depends on the ratios r12 and r23 of the axes of the finite strain ellipsoid and on the two independent ratios p12 and p23 of the strengths (critical resolved shear stresses) of the three independent slip systems of olivine. To do this, we introduce a new analytical representation of olivine CPO in terms of three `structured basis functions' (SBFs) Fs(g, r12, r23) (s = 1, 2, 3), where g is the set of three Eulerian angles that describe the orientation of a crystal lattice relative to an external reference frame. Each SBF represents the virtual CPO that would be produced by the action of only one of the slip systems of olivine, and can be determined analytically to within an unknown time-dependent amplitude. The amplitudes are then determined by fitting the SBFs to the predictions of the second-order self-consistent (SOSC) model of Ponte-Castaneda (2002). To implement the SBF representation, we express the orientation distribution function (ODF) f(g) of the polycrystal approximately as a linear superposition of SBFs with weighting coefficients Cs. Substituting the superposition into the general evolution equation for the ODF and minimizing the residual error, we find that the weighting coefficients Cs(t) satisfy coupled evolution equations of the form αisCs + βisCs + γs = 0 where the coefficients αis, βis and γs can be calculated in advance from the expressions for the SBFs. These equations are solved numerically for different values of p12 and p23, yielding numerical values of Cs(r12, r23, p12, p23
International Nuclear Information System (INIS)
Hensel, Jennifer M.; Menard, Cynthia; Chung, Peter W.M.; Milosevic, Michael F.; Kirilova, Anna; Moseley, Joanne L.; Haider, Masoom A.; Brock, Kristy K.
2007-01-01
Purpose: Endorectal coil (ERC) magnetic resonance imaging (MRI) provides superior visualization of the prostate compared with computed tomography at the expense of deformation. This study aimed to develop a multiorgan finite element deformable method, Morfeus, to accurately co-register these images for radiotherapy planning. Methods: Patients with prostate cancer underwent fiducial marker implantation and computed tomography simulation for radiotherapy planning. A series of axial MRI scans were acquired with and without an ERC. The prostate, bladder, rectum, and pubic bones were manually segmented and assigned linear elastic material properties. Morfeus mapped the surface of the bladder and rectum between two imaged states, calculating the deformation of the prostate through biomechanical properties. The accuracy of deformation was measured as fiducial marker error and residual surface deformation between the inferred and actual prostate. The deformation map was inverted to deform from 100 cm 3 to no coil. Results: The data from 19 patients were analyzed. Significant prostate deformation occurred with the ERC (mean intrapatient range, 0.88 ± 0.25 cm). The mean vector error in fiducial marker position (n = 57) was 0.22 ± 0.09 cm, and the mean vector residual surface deformation (n = 19) was 0.15 ± 0.06 cm for deformation from no coil to 100-cm 3 ERC, with an image vector resolution of 0.22 cm. Accurately deformed MRI scans improved soft-tissue resolution of the anatomy for radiotherapy planning. Conclusions: This method of multiorgan deformable registration enabled accurate co-registration of ERC-MRI scans with computed tomography treatment planning images. Superior structural detail was visible on ERC-MRI, which has potential for improving target delineation
Alleman, Coleman N.; Foulk, James W.; Mota, Alejandro; Lim, Hojun; Littlewood, David J.
2018-02-01
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.
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A. E. Alshorbagy
2013-01-01
Full Text Available The first-order shear deformation plate model, accounting for the exact neutral plane position, is exploited to investigate the uncoupled thermomechanical behavior of functionally graded (FG plates. Functionally graded materials are mainly constructed to operate in high temperature environments. Also, FG plates are used in many applications (such as mechanical, electrical, and magnetic, where an amount of heat may be generated into the FG plate whenever other forms of energy (electrical, magnetic, etc. are converted into thermal energy. Several simulations are performed to study the behavior of FG plates, subjected to thermomechanical loadings, and focus the attention on the effect of the heat source intensity. Most of the previous studies have considered the midplane neutral one, while the actual position of neutral plane for functionally graded plates is shifted and should be firstly determined. A comparative study is performed to illustrate the effect of considering the neutral plane position. The volume fraction of the two constituent materials of the FG plate is varied smoothly and continuously, as a continuous power function of the material position, along the thickness of the plate.
Erler, Norbert; Groß, Michael
2015-05-01
Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.
International Nuclear Information System (INIS)
Siswanto, W. A.; Nagentrau, M.; Tobi, A. L. Mohd; Tamin, M. N.
2016-01-01
We compared the quasi-static and dynamic simulation responses on elastic-plastic deformation of advanced alloys using Finite element (FE) method with an explicit numerical algorithm. A geometrical model consisting of a cylinder-on-flat surface contact under a normal load and sliding motion was examined. Two aeroengine materials, Ti-6Al-4V and Super CMV (Cr-Mo-V) alloy, were employed in the FE analysis. The FE model was validated by comparative magnitudes of the FE-predicted maximum contact pressure variation along the contact half-width length with the theoretical Hertzian contact solution. Results show that the (compressive) displacement of the initial contact surface steadily increases for the quasi-static load case, but accumulates at an increasing rate to the maximum level for the dynamic loading. However, the relatively higher stiffness and yield strength of the Super CMV alloy resulted in limited deformation and low plastic strain when compared to the Ti-6Al-4V alloy. The accumulated equivalent plastic strain of the material point at the initial contact position was nearly a thousand times higher for the dynamic load case (for example, 6.592 for Ti-6Al-4V, 1.0 kN) when compared to the quasi-static loading (only 0.0072). During the loading step, the von Mises stress increased with a decreasing and increasing rate for the quasi-static and dynamic load case, respectively. A sudden increase in the stress magnitude to the respective peak value was registered due to the additional constraint to overcome the static friction of the mating surfaces during the sliding step
Energy Technology Data Exchange (ETDEWEB)
Siswanto, W. A.; Nagentrau, M.; Tobi, A. L. Mohd [Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, Batu Pahat (Malaysia); Tamin, M. N. [Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Johor Bahru (Malaysia)
2016-11-15
We compared the quasi-static and dynamic simulation responses on elastic-plastic deformation of advanced alloys using Finite element (FE) method with an explicit numerical algorithm. A geometrical model consisting of a cylinder-on-flat surface contact under a normal load and sliding motion was examined. Two aeroengine materials, Ti-6Al-4V and Super CMV (Cr-Mo-V) alloy, were employed in the FE analysis. The FE model was validated by comparative magnitudes of the FE-predicted maximum contact pressure variation along the contact half-width length with the theoretical Hertzian contact solution. Results show that the (compressive) displacement of the initial contact surface steadily increases for the quasi-static load case, but accumulates at an increasing rate to the maximum level for the dynamic loading. However, the relatively higher stiffness and yield strength of the Super CMV alloy resulted in limited deformation and low plastic strain when compared to the Ti-6Al-4V alloy. The accumulated equivalent plastic strain of the material point at the initial contact position was nearly a thousand times higher for the dynamic load case (for example, 6.592 for Ti-6Al-4V, 1.0 kN) when compared to the quasi-static loading (only 0.0072). During the loading step, the von Mises stress increased with a decreasing and increasing rate for the quasi-static and dynamic load case, respectively. A sudden increase in the stress magnitude to the respective peak value was registered due to the additional constraint to overcome the static friction of the mating surfaces during the sliding step.
Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo
2014-10-07
The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.
Labonte, Alison Louise
Detecting seafloor deformation events in the offshore convergent margin environment is of particular importance considering the significant seismic hazard at subduction zones. Efforts to gain insight into the earthquake cycle have been made at the Cascadia and Costa Rica subduction margins through recent expansions of onshore GPS and seismic networks. While these studies have given scientists the ability to quantify and locate slip events in the seismogenic zone, there is little technology available for adequately measuring offshore aseismic slip. This dissertation introduces an improved flow meter for detecting seismic and aseismic deformation in submarine environments. The value of such hydrologic measurements for quantifying the geodetics at offshore margins is verified through a finite element modeling (FEM) study in which the character of deformation in the shallow subduction zone is determined from previously recorded hydrologic events at the Costa Rica Pacific margin. Accurately sensing aseismic events is one key to determining the stress state in subduction zones as these slow-slip events act to load or unload the seismogenic zone during the interseismic period. One method for detecting seismic and aseismic strain events is to monitor the hydrogeologic response to strain events using fluid flow meters. Previous instrumentation, the Chemical Aqueous Transport (CAT) meter which measures flow rates through the sediment-water interface, can detect transient events at very low flowrates, down to 0.0001 m/yr. The CAT meter performs well in low flow rate environments and can capture gradual changes in flow rate, as might be expected during ultra slow slip events. However, it cannot accurately quantify high flow rates through fractures and conduits, nor does it have the temporal resolution and accuracy required for detecting transient flow events associated with rapid deformation. The Optical Tracer Injection System (OTIS) developed for this purpose is an
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...
Harmonic balance finite element method applications in nonlinear electromagnetics and power systems
Lu, Junwei; Yamada, Sotoshi
2016-01-01
The first book applying HBFEM to practical electronic nonlinear field and circuit problems * Examines and solves wide aspects of practical electrical and electronic nonlinear field and circuit problems presented by HBFEM * Combines the latest research work with essential background knowledge, providing an all-encompassing reference for researchers, power engineers and students of applied electromagnetics analysis * There are very few books dealing with the solution of nonlinear electric- power-related problems * The contents are based on the authors' many years' research and industry experience; they approach the subject in a well-designed and logical way * It is expected that HBFEM will become a more useful and practical technique over the next 5 years due to the HVDC power system, renewable energy system and Smart Grid, HF magnetic used in DC/DC converter, and Multi-pulse transformer for HVDC power supply * HBFEM can provide effective and economic solutions to R&D product development * Includes Matlab e...
Directory of Open Access Journals (Sweden)
Jónas Elíasson
2014-01-01
Full Text Available A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls. The method shows how many modes are unstable, the wave number instability band within each mode, the maximum growth rate (most critical wave numbers on each mode, and the nonlinear growth rates for each amplitude as a function of the porous Rayleigh number. Single amplitude controls the nonlinear growth rates and thereby the physical flow rate and fluid velocity, on each mode. They are called the flak amplitudes. A discrete Fourier transform is used for numerical simulations and here frequency combinations appear that the traditional cut-off infinite transforms do not have. The discrete show a stationary solution in the weak instability phase, but when carried past 2 unstable modes they show fluctuating motion where all amplitudes except the flak may be zero on the average. This leads to a flak amplitude scaling process of the heat conduction, producing an eddy heat conduction coefficient where a Nu-RaL relationship is found. It fits better to experiments than previously found solutions but is lower than experiments.
High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves
DEFF Research Database (Denmark)
Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...
A finite element perspective on non-linear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondřejc, J.; Peerlings, R.H.J.; Geers, M.G.D.
2016-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency
A finite element perspective on nonlinear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondrejc, J.; Peerlings, R.H.J.; Geers, M.G.D.
2017-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency
Results on stabilization of nonlinear systems under finite data-rate constraints
Persis, Claudio De
2004-01-01
We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when
Energy Technology Data Exchange (ETDEWEB)
Fusco, D [Messina Univ. (Italy). Instituto de Matematica
1979-01-01
The paper is concerned with a three-dimensional theory of non-linear magnetosonic waves in a turbulent plasma. A perturbation method is used that allows a transport equation, like Burgers equation but with a variable coefficient to be obtained.
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
DEFF Research Database (Denmark)
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
DEFF Research Database (Denmark)
Mashayekhi, Sima; Hugger, Jens
2015-01-01
Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid...
Slope Safety Calculation With A Non-Linear Mohr Criterion Using Finite Element Method
DEFF Research Database (Denmark)
Clausen, Johan; Damkilde, Lars
2005-01-01
Safety factors for soil slopes are calculated using a non-linear Mohr envelope. The often used linear Mohr-Coulomb envelope tends to overestimate the safety as the material parameters are usually determined at much higher stress levels, than those present at slope failure. Experimental data...
Nemeth, Michael P.
2013-01-01
A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.
Extensions to a nonlinear finite element axisymmetric shell model based on Reissner's shell theory
International Nuclear Information System (INIS)
Cook, W.A.
1981-01-01
A finite element shell-of-revolution model has been developed to analyze shipping containers under severe impact conditions. To establish the limits for this shell model, I studied the basic assumptions used in its development; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress. (orig./HP)
Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
Czech Academy of Sciences Publication Activity Database
Chueshov, I.; Rezunenko, Oleksandr
2015-01-01
Roč. 14, č. 5 (2015), s. 1685-1704 ISSN 1534-0392 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic evolution equations * state-dependent delay * global attractor * finite-dimension * exponential attractor Subject RIV: BC - Control Systems Theory Impact factor: 0.926, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf
Stability of nonlinear Hamiltonian motion for a finite but very long time
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1991-01-01
By constructing action variables that are very nearly invariant in a region Ω of phase space, and by examining their residual variation, we set long-term bounds on any orbit starting in an open subregion of Ω. A new and generally applicable method for constructing the required high-precision invariants is applied. The technique is illustrated for transverse oscillations in a circular accelerator, a case with 21/2 degrees of freedom and strong nonlinearity
1987-07-01
fields (see also Chapter 4 of Ref. 22). Like our investigation, theirs is based on the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) equa- tion [23,24...25,26], also based on the KZK e(iualiou, is limited to weakly nonlinear systems. However, the practical case of a focused circular source with gain of...iment. The demonstrated abihty of the KZK equation to accurately model focused sound fields from reahstic sources [i.e., having abrupt edges and
Microscopic origin of nonlinear non-affine deformation in metallic glasses
Zaccone, A.; Schall, P.; Terentjev, E.M.
2014-01-01
The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the
Directory of Open Access Journals (Sweden)
Baoyan Zhu
2015-01-01
Full Text Available Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI. Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
Townsend, Molly T; Sarigul-Klijn, Nesrin
2016-01-01
Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.
Bull, Daniel; Spearing, Simon; Sinclair, Ian
2015-01-01
This study applies mechanisms observed from previous work (the undamaged cone, toughness and extent of permanent out-of-plane deformation) to parametrically study their effects on residual compression after impact (CAI) strength using finite element models. Based on previous experimental work, tougher material systems exhibited up to 30% greater CAI strength for a given damage area. Based on this, it is necessary to understand what other parameters, beyond damage area, contribute to a loss in...
Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu
2018-04-01
In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.
On the accuracy and efficiency of finite difference solutions for nonlinear waves
DEFF Research Database (Denmark)
Bingham, Harry B.
2006-01-01
-uniform grid. Time-integration is performed using a fourth-order Runge-Kutta scheme. The linear accuracy, stability and convergence properties of the method are analyzed in two-dimensions, and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes...... on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as providing an optimal balance between accuracy and complexity for practical...
Genus two finite gap solutions to the vector nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Woodcock, Thomas; Warren, Oliver H; Elgin, John N
2007-01-01
A recently published article presents a technique used to derive explicit formulae for odd genus solutions to the vector nonlinear Schroedinger equation. In another article solutions of genus two are derived using a different approach which assumes a separable ansatz. In this communication, the extension of the first technique to the even genus case is discussed, and this extension is carried out explicitly for genus two. Furthermore, a birational mapping is found between the spectral curves that arise in the two approaches. (fast track communication)
A Non-Linear Finite Element Model for the LHC Main Dipole Coil Cross-Section
Pojer, M; Scandale, Walter
2006-01-01
The production of the dipole magnets for the Large Hadron Collider is at its final stage. Nevertheless, some mechanical instabilities are still observed for which no clear explanation has been found yet. A FE modelization of the dipole cold mass cross-section had already been developed at CERN, mainly for magnetic analysis, taking into account conductor blocks and a frictionless behavior. This paper describes a new ANSYSÂ® model of the dipole coil cross-section, featuring individual turns inside conductor blocks, and implementing friction and the mechanical non-linear behavior of insulated cables. Preliminary results, comparison with measurements performed in industry and ongoing developments are discussed.
International Nuclear Information System (INIS)
Gambolati, G.; Toffolo, F.; Uliana, F.
1984-01-01
A nonlinear finite element model based on the Dupuit-Boussinesq equation of flow in an unconfined aquifer has been developed and applied to simulate the water table fluctuation under the electronuclear plant of the test site of Trino Vercellese (northwestern Italy) in response to the flood event that occurred in the Po River from March 30 to April 4, 1981. The nonlinearity has been overcome by the aid of an efficient iterative linearization technique wherein the model equations are solved by symbolic factorization, numerical factorization, and backward-forward substitution after an optimal preliminary reordering. The model was run for uniform values of aquifer permeability and specific yield within the typical range evidenced for the Trino sands by the early data in our possession. The results show that the maximum water level elevation below the reactor is almost 3 m lower than the corresponding river flood peak even in the most unfavorable conditions, i.e., with the hydraulic conductivity in the upper range, and is rather insensitive to the specific yield values within the plausible interval. The model allowed for an easy evaluation of the effectiveness of the impermeable protection walls and of a possible secondary aquifer recharge from a minor channel. The modeling approach for the analysis of the water table behavior appears to be a very promising tool to help in the structural design of future electronuclear plants
Even and odd combinations of nonlinear coherent states
International Nuclear Information System (INIS)
De los Santos-Sanchez, O; Recamier, J
2011-01-01
In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.
Goldring, Nicholas
The impending Advanced Photon Source Upgrade (APS-U) will introduce a hard x-ray source that is set to surpass the current APS in brightness and coherence by two to three orders of magnitude. To achieve this, the storage ring light source will be equipped with a multi-bend achromat (MBA) lattice. In order to fully exploit and preserve the integrity of new beams actualized by upgraded storage ring components, improved beamline optics must also be introduced. The design process of new optics for the APS-U and other fourth generation synchrotrons involves the challenge of accommodating unprecedented heat loads. This dissertation presents an ex-situ analysis of heat load deformation and the subsequent mechanical bending correction of a 400 mm long, grazing-incidence, H2O side-cooled, reflecting mirror subjected to x-ray beams produced by the APS-U undulator source. Bending correction is measured as the smallest rms slope error, sigmarms, that can be resolved over a given length of the heat deformed geometry due to mechanical bending. Values of sigmarms in the account for finish errors or other contributions to sigmarms beyond the scope of thermal deformation and elastic bending. The methodology of this research includes finite element analysis (FEA) employed conjointly with an analytical solution for mechanical bending deflection by means of an end couple. Additionally, the study will focus on two beam power density profiles predicted by the APS-U which were created using the software SRCalc. The profiles account for a 6 GeV electron beam with second moment widths of 0.058 and 0.011 mm in the x- and y- directions respectively; the electron beam is passed through a 4.8 m long, 28 mm period APS-U undulator which produces the x-ray beam incident at a 3 mrad grazing angle on the flat mirror surface for both cases. The first power density profile is the most extreme case created by the undulator at it's closest gap with a critical energy of 3 keV (k y=2.459); the second
Non-linear finite element analyses of wide plate fracture mechanics experiments
International Nuclear Information System (INIS)
Harrop, L.P.; Gibson, S.
1988-06-01
A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)
Directory of Open Access Journals (Sweden)
Ibrahim Dauda Muhammad
2015-01-01
Full Text Available The single-walled zirconia nanotube is structurally modeled and its Young’s modulus is valued by using the finite element approach. The nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements. The properties of the beam required for input into the finite element analysis were computed by connecting energy equivalence between molecular and continuum mechanics. Simulation was conducted by applying axial tensile strain on one end of the nanotube while the other end was fixed and the corresponding reaction force recorded to compute Young’s modulus. It was found out that Young’s modulus of zirconia nanotubes is significantly affected by some geometrical parameters such as chirality, diameter, thickness, and length. The obtained values of Young’s modulus for a certain range of diameters are in agreement with what was obtained in the few experiments that have been conducted so far. This study was conducted on the cubic phase of zirconia having armchair and zigzag configuration. The optimal diameter and thickness were obtained, which will assist in designing and fabricating bulk nanostructured components containing zirconia nanotubes for various applications.
Nonlinear response arising from non self-similar crack growth in finite thickness plates
International Nuclear Information System (INIS)
Sih, G.C.; Chen, C.
1982-07-01
Described in this report is a three-dimensional finite element procedure for finding the stresses in a finite thickness plate with a through crack. The Mode I loading is increased incrementally such that crack growth occurs in segments. The individual crack profiles are assumed to coincide with the locations of minimum strain energy density, (dW/dV)/sub min/. Its shape is found to change during growth. Each successive crack growth increment will increase even though the rising load increment is kept constant. Three different plate thickness to half crack length ratios were analyzed. An average critical crack ligament distance r/sub c/ = 0.172 in (0.437 cm) being independent of crack and specimen size was obtained. This corresponds to an analytically predicted fracture toughness S/sub c/ = r/sub c/ (dW/dV)/sub c/ = 15.489 lb/in (2708.825 N/m) for A533B steel at -10 0 F. Data at low temperature were used in order to confine crack growth within the linear elastic range
Numerical Modelling of Metal-Elastomer Spring Nonlinear Response for Low-Rate Deformations
Directory of Open Access Journals (Sweden)
Sikora Wojciech
2018-03-01
Full Text Available Advanced knowledge of mechanical characteristics of metal-elastomer springs is useful in their design process and selection. It can also be used in simulating dynamics of machine where such elements are utilized. Therefore this paper presents a procedure for preparing and executing FEM modelling of a single metal-elastomer spring, also called Neidhart’s spring, for low-rate deformations. Elastomer elements were made of SBR rubber of two hardness values: 50°Sh and 70°Sh. For the description of material behaviour the Bergström-Boyce model has been used.
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
Jörn, Daniela; Kohorst, Philipp; Besdo, Silke; Borchers, Lothar; Stiesch, Meike
2016-01-01
Since bacterial leakage along the implant-abutment interface may be responsible for peri-implant infections, a realistic estimation of the interface gap width during function is important for risk assessment. The purpose of this study was to compare two methods for investigating microgap formation in a loaded dental implant, namely, microcomputed tomography (micro-CT) and three-dimensional (3D) nonlinear finite element analysis (FEA); additionally, stresses to be expected during loading were also evaluated by FEA. An implant-abutment complex was inspected for microgaps between the abutment and implant in a micro-CT scanner under an oblique load of 200 N. A numerical model of the situation was constructed; boundary conditions and external load were defined according to the experiment. The model was refined stepwise until its load-displacement behavior corresponded sufficiently to data from previous load experiments. FEA of the final, validated model was used to determine microgap widths. These were compared with the widths as measured in micro-CT inspection. Finally, stress distributions were evaluated in selected regions. No microgaps wider than 13 μm could be detected by micro-CT for the loaded implant. FEA revealed gap widths up to 10 μm between the implant and abutment at the side of load application. Furthermore, FEA predicted plastic deformation in a limited area at the implant collar. FEA proved to be an adequate method for studying microgap formation in dental implant-abutment complexes. FEA is not limited in gap width resolution as are radiologic techniques and can also provide insight into stress distributions within the loaded complex.
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
DEFF Research Database (Denmark)
Clausen, Johan
-Coulomb yield criterion and the corresponding plastic potential possess corners and an apex, which causes numerical difficulties. A simple, elegant and efficient solution to these problems is presented in this thesis. The solution is based on a transformation into principal stress space and is valid for all...... linear isotropic plasticity models in which corners and apexes are encountered. The validity and merits of the proposed solution are examined in relation to the Mohr-Coulomb and the Modified Mohr-Coulomb material models. It is found that the proposed method compares well with existing methods......-Brown material. The efficiency and validity are demonstrated by comparing the finite-element results with well-known solutions for simple geometries. A common geotechnical problem is the assessment of slope stability. For slopes with simple geometries and consisting of a linear Mohr-Coulomb material, this can...
International Nuclear Information System (INIS)
Gupta, A.; Singh, R.K.; Kushwaha, H.S.; Mahajan, S.C.; Kakodkar, A.
1996-01-01
For safety evaluation of nuclear structures a finite element code ULCA (Ultimate Load Capacity Assessment) has been developed. Eight/nine noded isoparametric quadrilateral plate/shell element with reinforcement as a through thickness discrete but integral smeared layer of the element is presented to analyze reinforced and prestressed concrete structures. Various constitutive models such as crushing, cracking in tension, tension stiffening and rebar yielding are studied and effect of these parameters on the reserve strength of structures is brought out through a number of benchmark tests. A global model is used to analyze the prestressed concrete containment wall of a typical 220 MWe Pressurized Heavy Water Reactor (PHWR) up to its ultimate capacity. This demonstrates the adequacy of Indian PHWR containment design to withstand severe accident loads
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Ghaffari, Reza; Sauer, Roger A.
2018-06-01
The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures.
PT-symmetry breaking in complex nonlinear wave equations and their deformations
International Nuclear Information System (INIS)
Cavaglia, Andrea; Fring, Andreas; Bagchi, Bijan
2011-01-01
We investigate complex versions of the Korteweg-deVries equations and an Ito-type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic and elliptic solutions for these models including those which are physically feasible in an obvious sense, that is those with real energies, but also those with complex energy spectra. The reality of the energy is usually attributed to different realizations of an antilinear symmetry, as for instance PT-symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly, the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples, some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the PT-symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
Non-linear heat transfer computer code by finite element method
International Nuclear Information System (INIS)
Nagato, Kotaro; Takikawa, Noboru
1977-01-01
The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)
Analysis of noncoplanar pressurized laminations in X2 steel pipes by non-linear finite element
Energy Technology Data Exchange (ETDEWEB)
Morales, Alfredo [Instituto Tecnologico de Puebla (Mexico). Dept. de Posgrado; Gonzalez, Jorge L.; Hallen, Jose M. [Instituto Politecnico Nacional (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE). Dept. de Ingenieria Metalurgica
2005-07-01
Hydrogen induced cracking is of great interest in the mechanical integrity assessment of sour gas pipelines. Multiple stepwise cracks with internal pressure called laminations are often observed in pipelines and their interaction and coalescence may significantly affect the residual strength of the pipes. In this work, the interacting fields of non coplanar pressurized laminations in the wall of a pipe under pressure are analyzed by non-lineal finite element, considering an isotropic hardening law and the real tensile properties of the X52 steel. The results are presented as the evolution of the stress fields in the interlaminar region as a function of the pressure inside the laminations. It is found that for two approaching stepwise laminations the critical pressure follows a hyperbolic type law, thus the effect of the lamination length is principal for greater lengths and for shorter lengths the effect is minimum. The critical pressure is defined as pressure inside the lamination that causes plastification of the interlaminar region. (author)
A Study of Nonlinear Variable Viscosity in Finite-Length Tube with Peristalsis
Directory of Open Access Journals (Sweden)
Y. Abd Elmaboud
2014-01-01
Full Text Available Peristaltic motion of an incompressible Newtonian fluid with variable viscosity induced by periodic sinusoidal traveling wave propagating along the walls of a finite-length tube has been investigated. A perturbation method of solution is sought. The viscosity parameter α (α << 1 is chosen as a perturbation parameter and the governing equations are developed up to the first-order in the viscosity parameter (α. The analytical solution has been derived for the radial velocity at the tube wall, the axial pressure gradient across the length of the tube, and the wall shear stress under the assumption of low Reynolds number and long wavelength approximation. The impacts of physical parameters such as the viscosity and the parameter determining the shape of the constriction on the pressure distribution and on the wall shear stress for integral and non-integral number of waves are illustrated. The main conclusion that can be drawn out of this study is that the peaks of pressure fluctuate with time and attain different values with non-integral numbers of peristaltic waves. The considered problem is very applicable in study of biological flow and industrial flow.
Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro
2014-05-01
This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if khthe aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.
Directory of Open Access Journals (Sweden)
E. Çelebi
2012-11-01
Full Text Available The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.
International Nuclear Information System (INIS)
Tayal, M.
1987-01-01
Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated
Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan
2017-09-01
The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.
Ricoeur, Andreas; Lange, Stephan; Avakian, Artjom
2015-04-01
Magnetoelectric (ME) coupling is an inherent property of only a few crystals exhibiting very low coupling coefficients at low temperatures. On the other hand, these materials are desirable due to many promising applications, e.g. as efficient data storage devices or medical or geophysical sensors. Efficient coupling of magnetic and electric fields in materials can only be achieved in composite structures. Here, ferromagnetic (FM) and ferroelectric (FE) phases are combined e.g. including FM particles in a FE matrix or embedding fibers of the one phase into a matrix of the other. The ME coupling is then accomplished indirectly via strain fields exploiting magnetostrictive and piezoelectric effects. This requires a poling of the composite, where the structure is exposed to both large magnetic and electric fields. The efficiency of ME coupling will strongly depend on the poling process. Besides the alignment of local polarization and magnetization, it is going along with cracking, also being decisive for the coupling properties. Nonlinear ferroelectric and ferromagnetic constitutive equations have been developed and implemented within the framework of a multifield, two-scale FE approach. The models are microphysically motivated, accounting for domain and Bloch wall motions. A second, so called condensed approach is presented which doesn't require the implementation of a spatial discretisation scheme, however still considering grain interactions and residual stresses. A micromechanically motivated continuum damage model is established to simulate degradation processes. The goal of the simulation tools is to predict the different constitutive behaviors, ME coupling properties and lifetime of smart magnetoelectric devices.
Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex.
Morales-Orcajo, Enrique; Souza, Thales R; Bayod, Javier; Barbosa de Las Casas, Estevam
2017-11-01
A three-dimensional foot finite element model with actual geometry and non-linear behavior of tendons is presented. The model is intended for analysis of the lower limb tendon forces effect in the inner foot structure. The geometry of the model was obtained from computational tomographies and magnetic resonance images. Tendon tissue was characterized with the first order Ogden material model based on experimental data from human foot tendons. Kinetic data was employed to set the load conditions. After model validation, a force sensitivity study of the five major foot extrinsic tendons was conducted to evaluate the function of each tendon. A synergic work of the inversion-eversion tendons was predicted. Pulling from a peroneus or tibialis tendon stressed the antagonist tendons while reducing the stress in the agonist. Similar paired action was predicted for the Achilles tendon with the tibialis anterior. This behavior explains the complex control motion performed by the foot. Furthermore, the stress state at the plantar fascia, the talocrural joint cartilage, the plantar soft tissue and the tendons were estimated in the early and late midstance phase of walking. These estimations will help in the understanding of the functional role of the extrinsic muscle-tendon-units in foot pronation-supination. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.
Sato, Yuichi; Kajihara, Shinichi; Kaneko, Yoshio
2011-06-01
This paper presents three-dimensional finite element (FE) analyses of an all-frame model of a three-story reinforced concrete (RC) building damaged in the 1999 Taiwan Chi-Chi Earthquake. Non-structural brick walls of the building acted as a seismic resistant element although their contributions were neglected in the design. Hence, the entire structure of a typical frame was modeled and static and dynamic nonlinear analyses were conducted to evaluate the contributions of the brick walls. However, the results of the analyses were considerably overestimated due to coarse mesh discretizations, which were unavoidable due to limited computer resources. This study corrects the overestimations by modifying (1) the tensile strengths and (2) shear stiffness reduction factors of concrete and brick. The results indicate that brick walls improve frame strength although shear failures are caused in columns shortened by spandrel walls. Then, the effectiveness of three types of seismic retrofits is evaluated. The maximum drift of the first floor is reduced by 89.3%, 94.8%, and 27.5% by Steel-confined, Full-RC, and Full-brick models, respectively. Finally, feasibility analyses of models with soils were conducted. The analyses indicated that the soils elongate the natural period of building models although no significant differences were observed.
International Nuclear Information System (INIS)
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports
Peng, Yan; Chen, Guoxing; Sun, Jianliang; Shi, Baodong
2018-04-01
The microscopic deformation of Ti-6Al-4V titanium alloy shows great inhomogeneity due to its duplex-microstructure that consists of two phases. In order to study the deformation behaviors of the constituent phases, the 2D FE model based on the realistic microstructure is established by MSC.Marc nonlinear FE software, and the tensile simulation is carried out. The simulated global stress-strain response is confirmed by the tensile testing result. Then the strain and stress distribution in the constituent phases and their evolution with the increase of the global strain are analyzed. The results show that the strain and stress partitioning between the two phases are considerable, most of the strain is concentrated in soft primary α phase, while hard transformed β matrix undertakes most of the stress. Under the global strain of 0.05, the deformation bands in the direction of 45° to the stretch direction and the local stress in primary α phase near to the interface between the two phases are observed, and they become more significant when the global strain increases to 0.1. The strain and stress concentration factors of the two phases are obviously different at different macroscopic deformation stages, but they almost tend to be stable finally.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
International Nuclear Information System (INIS)
Boitnott, G.N.
1993-01-01
In order to estimate yields of large underground explosions, it is important that we have a clear understanding of the near source phenomena and their effects on regional and teleseismic signals. While it is generally accepted that a considerable amount of attenuation and resultant waveform distortion occurs due to nonlinear deformation near the source, an area that has received little attention is the broad enveloping region where moderate stress perturbations occur. In this region, where strain perturbation amplitudes range from microstrains to a few millistrains, the resulting deformation of rock is inelastic and nonlinear but little to no permanent deformation results. Owing to its great extent, the moderate strain regime has the potential to influence the entire frequency band of the regional and teleseismic signals and thus may be central to the problem of inferring source characteristics from far field signals. Detailed rheological descriptions are required in order to understand the effects of the nonlinearities on the spectral content of regional and teleseismic signals
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
International Nuclear Information System (INIS)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
International Nuclear Information System (INIS)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
Gholami, Raheb; Ansari, Reza
2018-02-01
This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.
Energy Technology Data Exchange (ETDEWEB)
Park, Hyung Kui; Hahm, Dea Gi; Choi, In Kil [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-10-15
The sensitivity of the concrete strength is relatively higher compared to that of the steel strength. According to changes in the structure of the material, about 6-10% ultimate internal pressure differences occurred. Thirty sets of an FE model considering the material uncertainty of concrete and steel were composed for the internal pressure fragility assessment. From the internal pressure fragility assessment of the target containment building, the median capacity of liner leakage is estimated to be 116 psi. As can be seen from the Fukushima nuclear power plant accident, the containment building is the final protecting shield to prevent radiation leakage. Thus, a structural soundness evaluation for the containment pressure loads owing to a severe accident is very important. Recently, a probabilistic safety assessment has been commonly used to take into account the possible factors of uncertainty in a structural system. An assessment of the internal pressure fragility of the CANDU type containment buildings considering the correlation of structural material variables, and an assessment of the internal pressure fragility of the CANDU type containment buildings using a nonlinear finite element analysis, were also performed. However, for PWR type containment buildings, a fragility assessment has not been performed yet using a nonlinear finite element model (FEM) analysis. In this study, for the Hanul NPP units 3 and 4 containment building, the internal pressure fragility assessment was established using an FEM analysis. To do this, a three-dimensional finite element model, material property values, and a sensitive analysis were developed. A nonlinear finite element analysis of the Hanul NPP units 3 and 4 containment building was performed for a material sensitivity analysis and internal pressure fragility assessment.
International Nuclear Information System (INIS)
Park, Hyung Kui; Hahm, Dea Gi; Choi, In Kil
2013-01-01
The sensitivity of the concrete strength is relatively higher compared to that of the steel strength. According to changes in the structure of the material, about 6-10% ultimate internal pressure differences occurred. Thirty sets of an FE model considering the material uncertainty of concrete and steel were composed for the internal pressure fragility assessment. From the internal pressure fragility assessment of the target containment building, the median capacity of liner leakage is estimated to be 116 psi. As can be seen from the Fukushima nuclear power plant accident, the containment building is the final protecting shield to prevent radiation leakage. Thus, a structural soundness evaluation for the containment pressure loads owing to a severe accident is very important. Recently, a probabilistic safety assessment has been commonly used to take into account the possible factors of uncertainty in a structural system. An assessment of the internal pressure fragility of the CANDU type containment buildings considering the correlation of structural material variables, and an assessment of the internal pressure fragility of the CANDU type containment buildings using a nonlinear finite element analysis, were also performed. However, for PWR type containment buildings, a fragility assessment has not been performed yet using a nonlinear finite element model (FEM) analysis. In this study, for the Hanul NPP units 3 and 4 containment building, the internal pressure fragility assessment was established using an FEM analysis. To do this, a three-dimensional finite element model, material property values, and a sensitive analysis were developed. A nonlinear finite element analysis of the Hanul NPP units 3 and 4 containment building was performed for a material sensitivity analysis and internal pressure fragility assessment
International Nuclear Information System (INIS)
Villard, L.; Allfrey, S.J.; Bottino, A.
2003-01-01
The aim of this paper is to report on recent advances made on global gyrokinetic simulations of Ion Temperature Gradient modes (ITG) and other microinstabilities. The nonlinear development and saturation of ITG modes and the role of E x B zonal flows are studied with a global nonlinear δ f formulation that retains parallel nonlinearity and thus allows for a check of the energy conservation property as a means to verify the quality of the numerical simulation. Due to an optimised loading technique the conservation property is satisfied with an unprecedented quality well into the nonlinear stage. The zonal component of the perturbation establishes a quasi-steady state with regions of ITG suppression, strongly reduced radial energy flux and steepened effective temperature profile alternating with regions of higher ITG mode amplitudes, larger radial energy flux and flattened effective temperature profile. A semi-Lagrangian approach free of statistical noise is proposed as an alternative to the nonlinear δf formulation. An ASDEX-Upgrade experiment with an Internal Transport Barrier (ITB) is analysed with a global gyrokinetic code that includes trapped electron dynamics. The weakly destabilizing effect of trapped electron dynamics on ITG modes in an axisymmetric bumpy configuration modelling W7-X is shown in global linear simulations that retain the full electron dynamics. Finite β effects on microinstabilities are investigated with a linear global spectral electromagnetic gyrokinetic formulation. The radial global structure of electromagnetic modes shows a resonant behaviour with rational q values. (author)
Institute of Scientific and Technical Information of China (English)
高夫征
2005-01-01
A finite volume element predictor-correetor method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.
International Nuclear Information System (INIS)
Chen, Ming-Song; Lin, Y.C.; Li, Kuo-Kuo; Chen, Jian
2016-01-01
In authors' previous work (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0371-6, 2016), the nonlinear unloading behavior of a typical Ni-based superalloy was investigated by hot compressive experiments with intermediate unloading-reloading cycles. The characters of unloading curves were discussed in detail, and a new elasto-viscoplastic constitutive model was proposed to describe the nonlinear unloading behavior of the studied Ni-based superalloy. Still, the functional relationships between the deformation temperature, strain rate, pre-strain and the parameters of the proposed constitutive model need to be established. In this study, the effects of deformation temperature, strain rate and pre-strain on the parameters of the new constitutive model proposed in authors' previous work (Chen et al. 2016) are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate and pre-strain. (orig.)
International Nuclear Information System (INIS)
Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.
1984-01-01
The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....
Nakamura, Yoshinori; Kanbara, Ryo; Ochiai, Kent T; Tanaka, Yoshinobu
2014-10-01
The mechanical evaluation of the function of partial removable dental prostheses with 3-dimensional finite element modeling requires the accurate assessment and incorporation of soft tissue behavior. The differential behaviors of the residual ridge mucosa and periodontal ligament tissues have been shown to exhibit nonlinear displacement. The mathematic incorporation of known values simulating nonlinear soft tissue behavior has not been investigated previously via 3-dimensional finite element modeling evaluation to demonstrate the effect of prosthesis design on the supporting tissues. The purpose of this comparative study was to evaluate the functional differences of 3 different partial removable dental prosthesis designs with 3-dimensional finite element analysis modeling and a simulated patient model incorporating known viscoelastic, nonlinear soft tissue properties. Three different designs of distal extension removable partial dental prostheses were analyzed. The stress distributions to the supporting abutments and soft tissue displacements of the designs tested were calculated and mechanically compared. Among the 3 dental designs evaluated, the RPI prosthesis demonstrated the lowest stress concentrations on the tissue supporting the tooth abutment and also provided wide mucosa-borne areas of support, thereby demonstrating a mechanical advantage and efficacy over the other designs evaluated. The data and results obtained from this study confirmed that the functional behavior of partial dental prostheses with supporting abutments and soft tissues are consistent with the conventional theories of design and clinical experience. The validity and usefulness of this testing method for future applications and testing protocols are shown. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Lyu, L.H.; Kan, J.R.
1989-01-01
Nonlinear one-dimensional constant-profile hydromagnetic wave solutions are obtained in finite-temperature two-fluid collisionless plasmas under adiabatic equation of state. The nonlinear wave solutions can be classified according to the wavelength. The long-wavelength solutions are circularly polarized incompressible oblique Alfven wave trains with wavelength greater than hudreds of ion inertial length. The oblique wave train solutions can explain the high degree of alignment between the local average magnetic field and the wave normal direction observed in the solar wind. The short-wavelength solutions include rarefaction fast solitons, compression slow solitons, Alfven solitons and rotational discontinuities, with wavelength of several tens of ion inertial length, provided that the upstream flow speed is less than the fast-mode speed
International Nuclear Information System (INIS)
Figueroa-O'Farrill, J.M.; Mas, J.; Ramos, E.
1993-01-01
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W KP admitting a central extension for generic values of the parameter, reducing naturally to W n for special values of the parameter, and contracting to the centrally extended W 1+∞ , W ∞ and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to W KP . The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of W ∞ which contracts to a new nonlinear algebra of the W ∞ -type. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Wang, Yuanyuan, E-mail: 630wyy@163.com [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), Dalian University of Technology, Dalian 116024 (China); Zhao, Jijun, E-mail: zhaojj@dlut.edu.cn [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), Dalian University of Technology, Dalian 116024 (China); Zhang, Chi [Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China)
2017-05-15
Highlights: • The initial internal variable in the Anand model is modified by considering both temperature and irradiation dose. • The tensile stress-strain response is examined and analyzed under different temperatures and irradiation doses. • Yield strengths are predicted as functions of strain rate, temperature and irradiation dose. - Abstract: The viscoplastic equations with a modified initial internal variable are implemented into the finite element code to investigate stress-strain response and irradiation hardening of the materials under increased temperature and at different levels of irradiated dose. We applied this model to Mod 9Cr-1Mo steel. The predicted results are validated by the experimentally measured data. Furthermore, they show good agreement with the previous data from a constitutive crystal plasticity model in account of dislocation and interstitial loops. Three previous hardening models for predicting the yield strength of the material are discussed and compared with our simulation results.
Energy Technology Data Exchange (ETDEWEB)
Chen, Ming-Song; Li, Kuo-Kuo [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Lin, Y.C. [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Central South University, Light Alloy Research Institute, Changsha (China); Chen, Jian [Changsha University of Science and Technology, School of Energy and Power Engineering, Key Laboratory of Efficient and Clean Energy Utilization, Changsha (China)
2016-09-15
The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)
International Nuclear Information System (INIS)
Chen, Ming-Song; Li, Kuo-Kuo; Lin, Y.C.; Chen, Jian
2016-01-01
The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...
Energy Technology Data Exchange (ETDEWEB)
Rivard, MJ [Tufts University School of Medicine, Boston, MA (United States); Ghadyani, HR [SUNY Farmingdale State College, Farmingdale, NY (United States); Bastien, AD; Lutz, NN [Univeristy Massachusetts Lowell, Lowell, MA (United States); Hepel, JT [Rhode Island Hospital, Providence, RI (United States)
2015-06-15
Purpose: Noninvasive image-guided breast brachytherapy delivers conformal HDR Ir-192 brachytherapy treatments with the breast compressed, and treated in the cranial-caudal and medial-lateral directions. This technique subjects breast tissue to extreme deformations not observed for other disease sites. Given that, commercially-available software for deformable image registration cannot accurately co-register image sets obtained in these two states, a finite element analysis based on a biomechanical model was developed to deform dose distributions for each compression circumstance for dose summation. Methods: The model assumed the breast was under planar stress with values of 30 kPa for Young’s modulus and 0.3 for Poisson’s ratio. Dose distributions from round and skin-dose optimized applicators in cranial-caudal and medial-lateral compressions were deformed using 0.1 cm planar resolution. Dose distributions, skin doses, and dose-volume histograms were generated. Results were examined as a function of breast thickness, applicator size, target size, and offset distance from the center. Results: Over the range of examined thicknesses, target size increased several millimeters as compression thickness decreased. This trend increased with increasing offset distances. Applicator size minimally affected target coverage, until applicator size was less than the compressed target size. In all cases, with an applicator larger or equal to the compressed target size, > 90% of the target covered by > 90% of the prescription dose. In all cases, dose coverage became less uniform as offset distance increased and average dose increased. This effect was more pronounced for smaller target-applicator combinations. Conclusions: The model exhibited skin dose trends that matched MC-generated benchmarking results and clinical measurements within 2% over a similar range of breast thicknesses and target sizes. The model provided quantitative insight on dosimetric treatment variables over
International Nuclear Information System (INIS)
Rivard, MJ; Ghadyani, HR; Bastien, AD; Lutz, NN; Hepel, JT
2015-01-01
Purpose: Noninvasive image-guided breast brachytherapy delivers conformal HDR Ir-192 brachytherapy treatments with the breast compressed, and treated in the cranial-caudal and medial-lateral directions. This technique subjects breast tissue to extreme deformations not observed for other disease sites. Given that, commercially-available software for deformable image registration cannot accurately co-register image sets obtained in these two states, a finite element analysis based on a biomechanical model was developed to deform dose distributions for each compression circumstance for dose summation. Methods: The model assumed the breast was under planar stress with values of 30 kPa for Young’s modulus and 0.3 for Poisson’s ratio. Dose distributions from round and skin-dose optimized applicators in cranial-caudal and medial-lateral compressions were deformed using 0.1 cm planar resolution. Dose distributions, skin doses, and dose-volume histograms were generated. Results were examined as a function of breast thickness, applicator size, target size, and offset distance from the center. Results: Over the range of examined thicknesses, target size increased several millimeters as compression thickness decreased. This trend increased with increasing offset distances. Applicator size minimally affected target coverage, until applicator size was less than the compressed target size. In all cases, with an applicator larger or equal to the compressed target size, > 90% of the target covered by > 90% of the prescription dose. In all cases, dose coverage became less uniform as offset distance increased and average dose increased. This effect was more pronounced for smaller target-applicator combinations. Conclusions: The model exhibited skin dose trends that matched MC-generated benchmarking results and clinical measurements within 2% over a similar range of breast thicknesses and target sizes. The model provided quantitative insight on dosimetric treatment variables over
Choi, E.; Tan, E.; Lavier, L. L.; Calo, Victor M.
2013-01-01
Many tectonic problems require to treat the lithosphere as a compressible elastic material, which can also flow viscously or break in a brittle fashion depending on the stress level applied and the temperature conditions. We present a flexible methodology to address the resulting complex material response, which imposes severe challenges on the discretization and rheological models used. This robust, adaptive, two-dimensional, finite element method solves the momentum balance and the heat equation in Lagrangian form using unstructured meshes. An implementation of this methodology is released to the public with the publication of this paper and is named DynEarthSol2D (available at http://bitbucket.org/tan2/dynearthsol2). The solver uses contingent mesh adaptivity in places where shear strain is focused (localization) and a conservative mapping assisted by marker particles to preserve phase and facies boundaries during remeshing. We detail the solver and verify it in a number of benchmark problems against analytic and numerical solutions from the literature. These results allow us to verify and validate our software framework and show its improved performance by an order of magnitude compared against an earlier implementation of the Fast Lagrangian Analysis of Continua algorithm.
Choi, E.
2013-05-01
Many tectonic problems require to treat the lithosphere as a compressible elastic material, which can also flow viscously or break in a brittle fashion depending on the stress level applied and the temperature conditions. We present a flexible methodology to address the resulting complex material response, which imposes severe challenges on the discretization and rheological models used. This robust, adaptive, two-dimensional, finite element method solves the momentum balance and the heat equation in Lagrangian form using unstructured meshes. An implementation of this methodology is released to the public with the publication of this paper and is named DynEarthSol2D (available at http://bitbucket.org/tan2/dynearthsol2). The solver uses contingent mesh adaptivity in places where shear strain is focused (localization) and a conservative mapping assisted by marker particles to preserve phase and facies boundaries during remeshing. We detail the solver and verify it in a number of benchmark problems against analytic and numerical solutions from the literature. These results allow us to verify and validate our software framework and show its improved performance by an order of magnitude compared against an earlier implementation of the Fast Lagrangian Analysis of Continua algorithm.
Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus
2016-04-01
Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation. Copyright © 2015 Elsevier Ltd. All rights reserved.
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-09-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Serra-Hsu, Frederick; Cheng, Jiqi; Qin, Yi-Xian; Lynch, Ted
2011-01-01
Ultrasound has been widely used to nondestructively evaluate various materials, including biological tissues. Quantitative ultrasound has been used to assess bone quality and fracture risk. A pulsed phase-locked loop (PPLL) method has been proven for very sensitive tracking of ultrasound time-of-flight (TOF) changes. The objective of this work was to determine if the PPLL TOF tracking is sensitive to bone deformation changes during loading. The ability to noninvasively detect bone deformations has many implications, including assessment of bone strength and more accurate osteoporosis diagnostics and fracture risk prediction using a measure of bone mechanical quality. Fresh sheep femur cortical bone shell samples were instrumented with three 3-element rosette strain gauges and then tested under mechanical compression with eight loading levels using an MTS machine. Samples were divided into two groups based on internal marrow cavity content: with original marrow, or replaced with water. During compressive loading ultrasound waves were measured through acoustic transmission across the mid-diaphysis of bone. Finite element analysis (FEA) was used to describe ultrasound propagation path length changes under loading based on µCT-determined bone geometry. The results indicated that PPLL output correlates well to measured axial strain, with R 2 values of 0.70 ± 0.27 and 0.62 ± 0.29 for the marrow and water groups, respectively. The PPLL output correlates better with the ultrasound path length changes extracted from FEA. For the two validated FEA tests, correlation was improved to R 2 = 0.993 and R 2 = 0.879 through cortical path, from 0.815 and 0.794 via marrow path, respectively. This study shows that PPLL readings are sensitive to displacement changes during external bone loading, which may have potential to noninvasively assess bone strain and tissue mechanical properties
de Wit, A.J.; Akcay-Perdahcioglu, Didem; van den Brink, W.M.; de Boer, Andries; Rolfes, R.; Jansen, E.L.
2011-01-01
Depending on the type of analysis, Finite Element(FE) models of different fidelity are necessary. Creating these models manually is a labor intensive task. This paper discusses a generic approach for generating FE models of different fidelity from a single reference FE model. These different
Quasistatic nonlinear viscoelasticity and gradient flows
Ball, John M.; Şengül, Yasemin
2014-01-01
We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the d...
Finite element analysis of inelastic structural behavior
International Nuclear Information System (INIS)
Argyris, J.H.; Szimmat, J.; Willam, K.J.
1977-01-01
The paper describes recent achievements in the finite element analysis of inelastic material behavior. The main purpose is to examine the interaction of three disciplines; (i) the finite element formulation of large deformation problems in the light of a systematic linearization, (ii) the constitutive modelling of inelastic processes in the rate-dependent and rate-independent response regime and (iii) the numerical solution of nonlinear rate problems via incremental iteration techniques. In the first part, alternative finite element models are developed for the idealization of large deformation problems. A systematic approach is presented to linearize the field equations locally by an incremental procedure. The finite element formulation is then examined for the description of inelastic material processes. In the second part, nonlinear and inelastic material phenomena are classified and illustrated with representative examples of concrete and metal components. In particular, rate-dependent and rate-independent material behavior is examined and representative constitutive models are assessed for their mathematical characterization. Hypoelastic, elastoplastic and endochronic models are compared for the description rate-independent material phenomena. In the third part, the numerial solution of inelastic structural behavior is discussed. In this context, several incremental techniques are developed and compared for tracing the evolution of the inelastic process. The numerical procedures are examined with regard to stability and accuracy to assess the overall efficiency. The 'optimal' incremental technique is then contrasted with the computer storage requirements to retain the data for the 'memory-characteristics' of the constitutive model
Computational mechanics of nonlinear response of shells
Energy Technology Data Exchange (ETDEWEB)
Kraetzig, W.B. (Bochum Univ. (Germany, F.R.). Inst. fuer Statik und Dynamik); Onate, E. (Universidad Politecnica de Cataluna, Barcelona (Spain). Escuela Tecnica Superior de Ingenieros de Caminos) (eds.)
1990-01-01
Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs.
Computational mechanics of nonlinear response of shells
International Nuclear Information System (INIS)
Kraetzig, W.B.; Onate, E.
1990-01-01
Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs
International Nuclear Information System (INIS)
Selby, John C.; Shannon, Mark A.
2007-01-01
Details are given for the design, calibration, and operation of an apparatus for measuring the finite load-deformation behavior of a sheet of living epithelial cells cultured on a mesoscopic freestanding elastomer membrane, 10 μm thick and 5 mm in diameter. Although similar in concept to bulge tests used to investigate the mechanical properties of micromachined thin films, cell-elastomer composite diaphragm inflation tests pose a unique set of experimental challenges. Composite diaphragm (CD) specimens are extremely compliant (E MIN =0 μl, V MAX ≤40 μl) while simultaneously recording the inflation pressure acting at the fixed boundary of the specimen, p(r=a). Using a carefully prescribed six-cycle inflation test protocol, the apparatus is shown to be capable of measuring the [V,p(r=a)] inflation response of a cell-elastomer CD with random uncertainties estimated at ±0.45 μl and ±2.5 Pa, respectively
Nonlinear analysis of flexible plates lying on elastic foundation
Directory of Open Access Journals (Sweden)
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
Průša, Vít; Řehoř, Martin; Tůma, Karel
2017-02-01
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.
Finite element formulation for dynamics of planar flexible multi-beam system
International Nuclear Information System (INIS)
Liu Zhuyong; Hong Jiazhen; Liu Jinyang
2009-01-01
In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation
An efficient finite element solution for gear dynamics
International Nuclear Information System (INIS)
Cooley, C G; Parker, R G; Vijayakar, S M
2010-01-01
A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.
Directory of Open Access Journals (Sweden)
Navnit Jha
2014-04-01
Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.
International Nuclear Information System (INIS)
Sun Feng; Pan Rong
2014-01-01
According to a large-span half-steel-concrete (HSC) composited beam in the composited roof in the HTR-PM, a 1:3 scale specimen is investigated by the static load test. By analyzing the loading, deflection, strain and fracture development of the specimen in the process, studying the mechanical characteristics and failure pattern of such components. The ANSYS finite element software is utilized in this paper to analyze the nonlinearity behavior of the HSC beam specimen, and through comparing the experimental results and the numerical simulation, it can be illustrated that the finite element model can simulate the HSC beam accurately. From the test results, it can be concluded that by means of appropriate shear connection and anchorage length, steel plate and concrete can work together very well and the HSC beam has good load carrying capacity and ductility. These conclusions can serve as a preliminary design reference for the large span half-steel-concrete composite beam in NPP. (author)
Lundström, T; Jonas, T; Volkwein, A
2008-01-01
Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.
Kordy, M. A.; Wannamaker, P. E.; Maris, V.; Cherkaev, E.; Hill, G. J.
2014-12-01
We have developed an algorithm for 3D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permits incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used for the forward solution, parameter jacobians, and model update. The forward simulator, jacobians calculations, as well as synthetic and real data inversion are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequency or small material admittivity, the E-field requires divergence correction. Using Hodge decomposition, correction may be applied after the forward solution is calculated. It allows accurate E-field solutions in dielectric air. The system matrix factorization is computed using the MUMPS library, which shows moderately good scalability through 12 processor cores but limited gains beyond that. The factored matrix is used to calculate the forward response as well as the jacobians of field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure and several topographic models. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of electromagnetic waves normal to the slopes at high frequencies. Run time tests indicate that for meshes as large as 150x150x60 elements, MT forward response and jacobians can be calculated in ~2.5 hours per frequency. For inversion, we implemented data space Gauss-Newton method, which offers reduction in memory requirement and a significant speedup of the parameter step versus model space approach. For dense matrix operations we use tiling approach of PLASMA library, which shows very good scalability. In synthetic
Deformation Characteristics of Composite Structures
Directory of Open Access Journals (Sweden)
Theddeus T. AKANO
2016-08-01
Full Text Available The composites provide design flexibility because many of them can be moulded into complex shapes. The carbon fibre-reinforced epoxy composites exhibit excellent fatigue tolerance and high specific strength and stiffness which have led to numerous advanced applications ranging from the military and civil aircraft structures to the consumer products. However, the modelling of the beams undergoing the arbitrarily large displacements and rotations, but small strains, is a common problem in the application of these engineering composite systems. This paper presents a nonlinear finite element model which is able to estimate the deformations of the fibre-reinforced epoxy composite beams. The governing equations are based on the Euler-Bernoulli beam theory (EBBT with a von Kármán type of kinematic nonlinearity. The anisotropic elasticity is employed for the material model of the composite material. Moreover, the characterization of the mechanical properties of the composite material is achieved through a tensile test, while a simple laboratory experiment is used to validate the model. The results reveal that the composite fibre orientation, the type of applied load and boundary condition, affect the deformation characteristics of the composite structures. The nonlinearity is an important factor that should be taken into consideration in the analysis of the fibre-reinforced epoxy composites.
Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul
2011-08-22
We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss-Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ˜1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north-south trending, eruption-controlling shear zone is clearly imaged in the inversion.
Duddu, Ravindra
2011-10-05
We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.
Integral finite element analysis of turntable bearing with flexible rings
Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng
2018-03-01
This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.
The physics of large deformation of crystalline solids
Bell, James F
1968-01-01
Historically, a major problem for the study of the large deformation of crystalline solids has been the apparent lack of unity in experimentally determined stress-strain functions. The writer's discovery in 1949 of the unexpectedly high velocity of incremental loading waves in pre-stressed large deformation fields emphasized to him the pressing need for the independent, systematic experimental study of the subject, to provide a firm foundation upon which physically plausible theories for the finite deformation of crystalline solids could be constructed. Such a study undertaken by the writer at that time and continued uninterruptedly to the present, led in 1956 to the development of the diffraction grating experiment which permitted, for the first time, the optically accurate determination of the strain-time detail of non-linear finite amplitude wave fronts propagating into crystalline solids whose prior history was precisely known. These experimental diffraction grating studies during the past decade have led...
International Nuclear Information System (INIS)
Menabdishvili, Papuna; Eremadze, Nelly
2008-01-01
There is elaborated the calculation model of slope deformation mode stability and the methodic of calculation considering the interference of structures to be built on it using the method of finite elements. There is examined the task of slope stability using the soil physically nonlinear finite element considering the seismicity 8. The deformation mode and field of coefficients of stability are obtained and slope supposed sliding curve is determined. The elaborated calculation methodic allows to determine the slope deformation mode, stability and select the optimum version of structure foundation at any slant and composition of slope layers
Nieto, Alejandra; Roehl, Holger
2018-03-15
There has been a growing interest in recent years in the assessment of suitable vial/stopper combinations for storage and shipment of frozen drug products. Considering that the glass transition temperature (Tg) of butyl rubber stoppers used in Container Closure Systems (CCS) is between -55°C to -65°C, a storage or shipment temperature of a frozen product below the Tg of the rubber stopper, may require special attention, since below the Tg the rubber becomes more plastic-like and loses its elastic (sealing) characteristics. Thus they risk maintaining Container Closure Integrity (CCI). Given that the rubber regains its elastic properties and reseals after rewarming to ambient temperature, leaks during frozen temperature storage and transportation are transient and the CCI methods used at room temperature conditions are unable to confirm CCI in the frozen state. Hence, several experimental methods have been developed in recent years in order to evaluate CCI at low temperatures. Finite Element (FE) simulations were applied in order to investigate the sealing behaviour of rubber stoppers for the drug product CCS under frozen storage conditions. FE analysis can help reducing the experimental design space and thus number of measurements needed, as they can be used as an ad-on to experimental testing. Several scenarios have been simulated including the effect of thermal history, rubber type, storage time, worst case CCS geometric tolerances and capping pressure. The results of these calculations have been validated with experimental data derived from laboratory experiments (CCI at low temperatures), and a concept for tightness has been developed. It has been concluded that FE simulations have the potential to become a powerful predictive tool towards a better understanding of the influence of cold storage on the rubber sealing properties (and hence on CCI) when dealing with frozen drug products. Copyright © 2018, Parenteral Drug Association.
Directory of Open Access Journals (Sweden)
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Yankovskii, A. P.
2018-01-01
On the basis of constitutive equations of the Rabotnov nonlinear hereditary theory of creep, the problem on the rheonomic flexural behavior of layered plates with a regular structure is formu-lated. Equations allowing one to describe, with different degrees of accuracy, the stress-strain state of such plates with account of their weakened resistance to transverse shear were ob-tained. From them, the relations of the nonclassical Reissner- and Reddytype theories can be found. For axially loaded annular plates clamped at one edge and loaded quasistatically on the other edge, a simplified version of the refined theory, whose complexity is comparable to that of the Reissner and Reddy theories, is developed. The flexural strains of such metal-composite annular plates in shortterm and long-term loadings at different levels of heat action are calcu-lated. It is shown that, for plates with a relative thickness of order of 1/10, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee reliable results for deflections even with the rough 10% accuracy. The accuracy of these theories decreases at elevated temperatures and with time under long-term loadings of structures. On the basic of relations of the refined theory, it is revealed that, in bending of layered metal-composite heat-sensitive plates under elevated temperatures, marked edge effects arise in the neighborhood of the supported edge, which characterize the shear of these structures in the transverse direction
Mustafa, M.; Mushtaq, A.; Hayat, T.; Alsaedi, A.
2018-04-01
Mathematical model for Maxwell fluid flow in rotating frame induced by an isothermal stretching wall is explored numerically. Scale analysis based boundary layer approximations are applied to simplify the conservation relations which are later converted to similar forms via appropriate substitutions. A numerical approach is utilized to derive similarity solutions for broad range of Deborah number. The results predict that velocity distributions are inversely proportional to the stress relaxation time. This outcome is different from that observed for the elastic parameter of second grade fluid. Unlike non-rotating frame, the solution curves are oscillatory decaying functions of similarity variable. As angular velocity enlarges, temperature rises and significant drop in the heat transfer coefficient occurs. We note that the wall slope of temperature has an asymptotically decaying profile against the wall to ambient ratio parameter. From the qualitative view point, temperature ratio parameter and radiation parameter have similar effect on the thermal boundary layer. Furthermore, radiation parameter has a definite role in improving the cooling process of the stretching boundary. A comparative study of current numerical computations and those from the existing studies is also presented in a limiting case. To our knowledge, the phenomenon of non-linear radiation in rotating viscoelastic flow due to linearly stretched plate is just modeled here.
Directory of Open Access Journals (Sweden)
Chouaib Labiod
2017-01-01
Full Text Available This paper presents torque ripple reduction with speed control of 8/6 Switched Reluctance Motor (SRM by the determination of the optimal parameters of the turn on, turn off angles Theta_(on, Theta_(off, and the supply voltage using Particle Swarm Optimization (PSO algorithm and steady state Genetic Algorithm (ssGA. With SRM model, there is difficulty in the control relapsed into highly non-linear static characteristics. For this, the Finite Elements Method (FEM has been used because it is a powerful tool to get a model closer to reality. The mechanism used in this kind of machine control consists of a speed controller in order to determine current reference which must be produced to get the desired speed, hence, hysteresis controller is used to compare current reference with current measured up to achieve switching signals needed in the inverter. Depending on this control, the intelligent routing algorithms get the fitness equation from torque ripple and speed response so as to give the optimal parameters for better results. Obtained results from the proposed strategy based on metaheuristic methods are compared with the basic case without considering the adjustment of specific parameters. Optimized results found clearly confirmed the ability and the efficiency of the proposed strategy based on metaheuristic methods in improving the performances of the SRM control considering different torque loads.
Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws
Chen, Gui-Qiang; Torres, Monica
2005-02-01
Divergence-measure fields in L∞ over sets of finite perimeter are analyzed. A notion of normal traces over boundaries of sets of finite perimeter is introduced, and the Gauss-Green formula over sets of finite perimeter is established for divergence-measure fields in L∞. The normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak-star limit of the normal traces introduced in Chen & Frid [6] over the Lipschitz deformation surfaces, which implies their consistency. As a corollary, an extension theorem of divergence-measure fields in L∞ over sets of finite perimeter is also established. Then we apply the theory to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.
International Nuclear Information System (INIS)
Berthollet, A.
2003-10-01
Concrete structures are examined during their lifetime and often present important cracking states, which can progress with time and lead to change the structural behavior. The civil engineering works that the main function corresponds to protection's wall are very sensitive to this damage and its evolution. The growth of the time - dependent cracks represents an aging pathology linked with interaction between creep mechanism and the non-linear behavior of the material. In this thesis, a modeling for these mechanisms and their coupling are proposed. It based on creep strains analysis under different load levels, on the influence of the rate effect to the mechanical behavior. A stress limit is put on prominent manner, where beyond it, the creep - cracking interaction becomes important with the introduction of the ultimate tertiary creep kinetic. This level of strength is identified for infinitely slow loading rates and is also called intrinsic strength. It defines the limit on this side the viscous behavior of the cement paste limits the irreversibility processes as cracking. Thus, a constitutive law of viscoelastic - viscoplastic behavior with a high coupling between the cracking mechanism and the creep strains is proposed. The developments of the model are built on DUVAUT - LIONS approach integrated a generalized MAXWELL chain model. For one part, the viscoelastic behavior translates the creep mechanism under low stresses. For a second part, it associated with the viscoplastic behavior, which allows introducing both creep effect under high stresses and rate effect acting on micro-cracked zones. The cracking mechanism is described throughout a plasticity theory with multi-criteria, which induce a property of anisotropy for hardening. Qualitatively, ails of the creep kinetics are reproduced. An additional validation is based on experimental tests in compression, traction and flexion where the main parameters of the modeling are detailed. Thus, we can conclude on the
Inelastic analysis of finite length and depth cracked tubes
International Nuclear Information System (INIS)
Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.
1977-01-01
Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdown. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behaviour and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional as well as three-dimensional finite element analyses, were performed. The analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions. (Auth.)
Inelastic analysis of finite length and depth cracked tubes
International Nuclear Information System (INIS)
Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.
1977-01-01
Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdowns. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behavior and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional, as well as three-dimensional finite element analyses, were performed. The two-dimensional element and its formulations are similar to those of NONSAP. The three-dimensional isoparametric element with elastic-plastic material characteristics together with the large deformation formulations used in NFAP are described in the Report BNL-20684. The numerical accuracy of the program was investigated and checked with known solutions of benchmark problems. In addition to the three-dimensional element which was specifically inserted into NFAP for this problem, other features such as direct pressure inputs for isoparametric elements, automatic load increment adjustments for convergent non-linear solutions, and automatic bandwidth reduction schemes are incorporated into the program thus allowing for a more economical evaluation of three-dimensional inelastic analysis. In summary the analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions
International Nuclear Information System (INIS)
Singh, B.N.; Lal, Achchhe
2010-01-01
This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.
Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P
2011-04-01
Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.
Nonlinear integral equations for the sausage model
Ahn, Changrim; Balog, Janos; Ravanini, Francesco
2017-08-01
The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.
Pourazadi, Shahram; Ahmadi, Sadegh; Menon, Carlo
2015-11-05
One of the recommended treatments for disorders associated with the lower extremity venous insufficiency is the application of external mechanical compression. Compression stockings and elastic bandages are widely used for the purpose of compression therapy and are usually designed to exert a specified value or range of compression on the leg. However, the leg deforms under external compression, which can lead to undesirable variations in the amount of compression applied by the compression bandages. In this paper, the use of an active compression bandage (ACB), whose compression can be regulated through an electrical signal, is investigated. The ACB is based on the use of dielectric elastomer actuators. This paper specifically investigates, via both analytical and non-linear numerical simulations, the potential pressure the ACB can apply when the compliancy of the human leg is taken into account. The work underpins the need to account for the compressibility of the leg when designing compression garments for lower extremity venous insufficiency. A mathematical model is used to simulate the volumetric change of a calf when compressed. Suitable parameters for this calf model are selected from the literature where the calf, from ankle to knee, is divided into six different regions. An analytical electromechanical model of the ACB, which considers its compliancy as a function of its pre-stretch and electricity applied, is used to predict the ACB's behavior. Based on these calf and ACB analytical models, a simulation is performed to investigate the interaction between the ACB and the human calf with and without an electrical stimulus applied to the ACB. This simulation is validated by non-linear analysis performed using a software based on the finite element method (FEM). In all simulations, the ACB's elastomer is stretched to a value in the range between 140 and 220 % of its initial length. Using data from the literature, the human calf model, which is examined in
Nieto, Alejandra; Roehl, Holger; Brown, Helen; Adler, Michael; Chalus, Pascal; Mahler, Hanns-Christian
2016-01-01
Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against possible contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the container closure system with microorganisms under specified testing conditions. Physical CCI uses surrogate endpoints, such as coloration by dye solution ingress or gas flow (helium leakage testing). In order to correlate microbial CCI and physical CCI test methods and to evaluate the methods' capability to detect a given leak, artificial leaks are being introduced into the container closure system in a variety of different ways. In our study, artificial leaks were generated using inserted copper wires between the glass vial opening and rubber stopper. However, the insertion of copper wires introduces leaks of unknown size and shape. With nonlinear finite element simulations, the aperture size between the rubber stopper and the glass vial was calculated, depending on wire diameter and capping force. The dependency of the aperture size on the copper wire diameter was quadratic. With the data obtained, we were able to calculate the leak size and model leak shape. Our results suggest that the size as well as the shape of the artificial leaks should be taken into account when evaluating critical leak sizes, as flow rate does not, independently, correlate to hole size. Capping force also affected leak size. An increase in the capping force from 30 to 70 N resulted in a reduction of the aperture (leak size) by approximately 50% for all wire diameters. From 30 to 50 N, the reduction was approximately 33%. Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the
Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G
2006-01-28
A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.
International Nuclear Information System (INIS)
Deb Nath, S.K.; Deb Nath, S.K.; Wong, C.H.; Deb Nath, S.K.
2014-01-01
Perfluoro polyethers (PFPEs) are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds) are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenon affects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multi dented functional lubricants such as Ar-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
Directory of Open Access Journals (Sweden)
S. K. Deb Nath
2014-01-01
Full Text Available Perfluoropolyethers (PFPEs are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenonaffects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multidented functional lubricants such as ARJ-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations
Tessler, Alexander; Sleight, David W.
2006-01-01
Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.
Loading Deformation Characteristic Simulation Study of Engineering Vehicle Refurbished Tire
Qiang, Wang; Xiaojie, Qi; Zhao, Yang; Yunlong, Wang; Guotian, Wang; Degang, Lv
2018-05-01
The paper constructed engineering vehicle refurbished tire computer geometry model, mechanics model, contact model, finite element analysis model, did simulation study on load-deformation property of engineering vehicle refurbished tire by comparing with that of the new and the same type tire, got load-deformation of engineering vehicle refurbished tire under the working condition of static state and ground contact. The analysis result shows that change rules of radial-direction deformation and side-direction deformation of engineering vehicle refurbished tire are close to that of the new tire, radial-direction and side-direction deformation value is a little less than that of the new tire. When air inflation pressure was certain, radial-direction deformation linear rule of engineer vehicle refurbished tire would increase with load adding, however, side-direction deformation showed linear change rule, when air inflation pressure was low; and it would show increase of non-linear change rule, when air inflation pressure was very high.
CUDA accelerated simulation of needle insertions in deformable tissue
International Nuclear Information System (INIS)
Patriciu, Alexandru
2012-01-01
This paper presents a stiff needle-deformable tissue interaction model. The model uses a mesh-less discretization of continuum; avoiding thus the expensive remeshing required by the finite element models. The proposed model can accommodate both linear and nonlinear material characteristics. The needle-deformable tissue interaction is modeled through fundamental boundaries. The forces applied by the needle on the tissue are divided in tangent forces and constraint forces. The constraint forces are adaptively computed such that the material is properly constrained by the needle. The implementation is accelerated using NVidia CUDA. We present detailed analysis of the execution timing in both serial and parallel case. The proposed needle insertion model was integrated in a custom software that loads DICOM images, generate the deformable model, and can simulate different insertion strategies.
International Nuclear Information System (INIS)
Upadhyay, M.V.; Van Petegem, S.; Panzner, T.; Lebensohn, R.A.; Van Swygenhoven, H.
2016-01-01
A multi-scale elastic-plastic finite element and fast Fourier transform based approach is proposed to study lattice strain evolution during uniaxial and biaxial loading of stainless steel cruciform shaped samples. At the macroscale, finite element simulations capture the complex coupling between applied forces in the arms and gauge stresses induced by the cruciform geometry. The predicted gauge stresses are used as macroscopic boundary conditions to drive a mesoscale elasto-viscoplastic fast Fourier transform model, from which lattice strains are calculated for particular grain families. The calculated lattice strain evolution matches well with experimental values from in-situ neutron diffraction measurements and demonstrates that the spread in lattice strain evolution between different grain families decreases with increasing biaxial stress ratio. During equibiaxial loading, the model reveals that the lattice strain evolution in all grain families, and not just the 311 grain family, is representative of the polycrystalline response. A detailed quantitative analysis of the 200 and 220 grain family reveals that the contribution of elastic and plastic anisotropy to the lattice strain evolution significantly depends on the applied stress ratio.
Indian Academy of Sciences (India)
The Structures Panel of the Aeronautics Research and Development Board of India ... A great variety of topics was covered, including themes such as nonlinear finite ... or shell structures, and three are on the composite form of construction, ...
Deformation behavior of large, high-pressure vessel flanges
International Nuclear Information System (INIS)
Spaas, H.A.C.M.; Latzko, D.G.H.
1975-01-01
The analysis of the deformation behavior of large high-pressure vessel flanges poses a much more difficult problem than for low-pressure flanges due to their particular geometry. For a particularly narrow flange geometry (typical of PWR flanges) a finite-element analysis (MARC-IBM-program, eight-node, isoparametric ring elements) was used to predict the behavior of the flange rings. The nonlinear elastic problem resulting from the local closing and/or opening of the partial gap between the gasket faces was solved by an incremental technique using gap elements. The resulting deformation behavior of the flange system has been compared to that obtained from an analysis using the refined rigid ring concept for both bolt-tightening and hydro-testing conditions. The elasto-plastic analysis was solved by the same finite element program system as mentioned above. The incremental steps describing the nonlinear material behavior are allowed to be larger than those for the gap-closure mechanism. Besides a comparison with the former elastic analyses an interpretation will be given of the local plasticity effects, which result in a shift in location of the gasket reaction. Experimental data on local gasket face deformation was obtained by a specially developed laser beam apparatus, with the leak detection channel of the flange serving as a beam hole. Additionally strain gauges were used on flanges and bolts, in combination with special sensing pins for the determination of relative flange rotations. Results obtained so far indicate that for high-pressure flanges of the narrow design investigated here the deformation behavior is best described by an elasto-plastic finite element analysis
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Fast free-form deformable registration via calculus of variations
International Nuclear Information System (INIS)
Lu Weiguo; Chen Mingli; Olivera, Gustavo H; Ruchala, Kenneth J; Mackie, Thomas R
2004-01-01
In this paper, we present a fully automatic, fast and accurate deformable registration technique. This technique deals with free-form deformation. It minimizes an energy functional that combines both similarity and smoothness measures. By using calculus of variations, the minimization problem was represented as a set of nonlinear elliptic partial differential equations (PDEs). A Gauss-Seidel finite difference scheme is used to iteratively solve the PDE. The registration is refined by a multi-resolution approach. The whole process is fully automatic. It takes less than 3 min to register two three-dimensional (3D) image sets of size 256 x 256 x 61 using a single 933 MHz personal computer. Extensive experiments are presented. These experiments include simulations, phantom studies and clinical image studies. Experimental results show that our model and algorithm are suited for registration of temporal images of a deformable body. The registration of inspiration and expiration phases of the lung images shows that the method is able to deal with large deformations. When applied to the daily CT images of a prostate patient, the results show that registration based on iterative refinement of displacement field is appropriate to describe the local deformations in the prostate and the rectum. Similarity measures improved significantly after the registration. The target application of this paper is for radiotherapy treatment planning and evaluation that incorporates internal organ deformation throughout the course of radiation therapy. The registration method could also be equally applied in diagnostic radiology
International Nuclear Information System (INIS)
Yang, J H; Yang, J; Kitipornchai, S
2012-01-01
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)
Rhyu, K H; Kim, Y H; Park, W M; Kim, K; Cho, T-J; Choi, I H
2011-09-01
In experimental and clinical research, it is difficult to directly measure responses in the human body, such as contact pressure and stress in a joint, but finite element analysis (FEA) enables the examination of in vivo responses by contact analysis. Hence, FEA is useful for pre-operative planning prior to orthopaedic surgeries, in order to gain insight into which surgical options will result in the best outcome. The present study develops a numerical simulation technique based on FEA to predict the surgical outcomes of osteotomy methods for the treatment of slipped capital femoral epiphyses. The correlation of biomechanical parameters including contact pressure and stress, for moderate and severe cases, is investigated. For severe slips, a base-of-neck osteotomy is thought to be the most reliable and effective surgical treatment, while any osteotomy may produce dramatic improvement for moderate slips. This technology of pre-operative planning using FEA can provide information regarding biomechanical parameters that might facilitate the selection of optimal osteotomy methods and corresponding surgical options.
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
Nonlinear analysis of RC cylindrical tank and subsoil accounting for a low concrete strength
Directory of Open Access Journals (Sweden)
Lewiński Paweł M.
2017-01-01
Full Text Available The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Two kinds of constitutive models for ground and structure were adopted for a nonlinear interaction analysis of the RC cylindrical tank with subsoil. The constitutive laws for concrete and subsoil were developed in compliance with the deformational and flow theories of plasticity. Moreover, a non-linear elastic-brittle-plastic analysis of RC axi-symmetric structures using finite element iterative techniques is presented. The results of the two types of FE analysis of soil-structure interaction are compared taking into account a low concrete strength of tank structure.
Finite Element Modeling of Thermo Creep Processes Using Runge-Kutta Method
Directory of Open Access Journals (Sweden)
Yu. I. Dimitrienko
2015-01-01
Full Text Available Thermo creep deformations for most heat-resistant alloys, as a rule, nonlinearly depend on stresses and are practically non- reversible. Therefore, to calculate the properties of these materials the theory of plastic flow is most widely used. Finite-element computations of a stress-strain state of structures with account of thermo creep deformations up to now are performed using main commercial software, including ANSYS package. However, in most cases to solve nonlinear creep equations, one should apply explicit or implicit methods based on the Euler method of approximation of time-derivatives. The Euler method is sufficiently efficient in terms of random access memory in computations, however this method is cumbersome in computation time and does not always provide a required accuracy for creep deformation computations.The paper offers a finite-element algorithm to solve a three-dimensional problem of thermo creep based on the Runge-Kutta finite-difference schemes of different orders with respect to time. It shows a numerical test example to solve the problem on the thermo creep of a beam under tensile loading. The computed results demonstrate that using the Runge-Kutta method with increasing accuracy order allows us to obtain a more accurate solution (with increasing accuracy order by 1 a relative error decreases, approximately, by an order too. The developed algorithm proves to be efficient enough and can be recommended for solving the more complicated problems of thermo creep of structures.
Lv, Ya-ping; Li, Shao-jun; Zhang, Xiao-yong; Li, Zhi-you; Zhou, Ke-chao
2018-04-01
Evolution for the dynamic recrystallization (DRX) volume fraction of Ti-5Al-5Mo-5V-3Cr-1Zr near β titanium alloy during hot deformation was characterized by using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. To determine the equation parameters, a series of thermal simulation experiments at the temperature of 1023-1098 K and strain rate of 0.001-1 s‒1 to the true strain of 0.7 were conducted to obtain the essential data about stress σ and strain ɛ. By further transforming the relationship of σ versus ɛ into the relationship of strain hardening rate dσ/dɛ versus σ, two characteristic strains at the beginning of DRX (critical strain ɛc) and at the peak stress (peak strain ɛp) were identified from the dσ/dɛ-σ curves. Sequentially, the parameters in the JMAK equation were determined from the linear fitting of the different relationships among critical strain ɛc, peak strain ɛp and deformation conditions (including temperature T, strain rate \\dot ɛ and strain ɛ). The as-obtained JMAK equation was expressed as XDRX=1-exp[-0.0053((ɛ-ɛc)/ɛc)2.1], where ɛc=0.6053ɛp and ɛp=0.0031 \\dot ɛ .0081exp(28,781/RT). Finally, the JMAK equation was implanted into finite element program to simulate the hot compression of thermal simulation experiments. The simulation predictions and experimental results about the DRX volume fraction distribution showed a good consistency.
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Sun, C. T.; Yoon, K. J.
1990-01-01
A one-parameter plasticity model was shown to adequately describe the orthotropic plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The nonlinear stress-strain relations were measured and compared with those predicted by the finite element analysis using the one-parameter elastic-plastic constitutive model. The results show that the one-parameter orthotropic plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.
Directory of Open Access Journals (Sweden)
R. A. González Carbonell
2007-05-01
Full Text Available En este trabajo se aborda la problemática del tratamiento en menores que presentan torsión tibial y la necesidad de undispositivo ortopédico para su corrección. En particular, se presentan los elementos necesarios para el diseño de un tacón detorque. Se estudiaron los fenómenos no lineales presentes en el diseño mecánico de piezas que no cumplen con la ley deHooke, específicamente para materiales hiperelásticos. El modelo de las cargas que actúan sobre el tacón de torque fuedefinido teniendo en cuenta la acción dinámica de las cargas producto de la marcha. Para realizar los cálculos de tensionesy visualizar las deformaciones durante su funcionamiento se utilizó el Método de los Elementos Finitos. Finalmente con losresultados obtenidos fue propuesto un diseño del tacón de torque.Palabras claves: Torsión tibial, dispositivo ortopédico, elastómeros, elementos finitos, tensión, diseñomecánico, análisis no lineal.______________________________________________________________________________Abstract:In this work a problem of treatment of the internal tibial torsion and the necessity of an orthopedic device werestudied. The needed knowledge for design the torque heel was mentioned. The study of non lineal phenomena inmechanical design of elastomers was carried out. The load model of the torque heels was defined taken into accountthe action of dynamic loads. The Stress and Strain of the torque heel were obtained using the Finite Elements Method.Finally, the results were analyzed and the definitive design of the torque heel was obtained.Key words: Tibial torsion, orthopedic device, elastomers, finite elements, stress, mechanic design, nonlinear analysis.
Finite element modeling of fluid/thermal/structural interaction for a gas-cooled fast reactor core
International Nuclear Information System (INIS)
Bennett, J.G.; Ju, F.D.
1980-01-01
Two nonlinear finite element formulations for application to a series of experiments in the Gas-Cooled Fast Reactor (GCFR) development program are described. An efficient beam column element for moderately large deformations is combined with a finite element developed for an engineering description of a convecting fluid. Typical results from both elements are illustrated. A combined application for a problem typical of the GCFR loss-of-coolant experiments is illustrated. These problems are not the usual fluid structural interaction problems in that the inertia coupling is negligible while the thermal coupling is very important
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano
2015-01-01
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....
Deformation localization at the tips of shear fractures: An analytical approach
Misra, Santanu
2011-04-01
Mechanical heterogeneities are important features in rocks which trigger deformation localization in brittle, ductile or brittle-ductile modes during deformation. In a recent study Misra et al. (2009) have investigated these different processes of deformation localization at the tips of pre-existing planar shear fractures. The authors identified four mechanisms of deformation, ranging from brittle to ductile, operating at the crack tips. Mechanism A: brittle deformation is the dominant process that forms a pair of long tensile fractures at the two crack tips. Mechanism B: nature of deformation is mixed where the tensile fractures grow to a finite length with incipient plastic deformation at the tips. Mechanism C: mixed mode deformation characterized by dominating macro-scale shear bands, and short, opened-out tensile fissures. Mechanism D: localization of plastic bands in the form of a pair of shear bands at each tip without any discernible brittle fracturing. The transition of the mechanisms is a function of orientation ( α) of the crack with respect to the bulk compression direction and the finite length ( l) of the crack. The aim of this study is to present a theoretical analysis to account for the variability of deformation localization in the vicinity of pre-existing shear cracks considering an elastic-plastic rheological model. The analysis calculates the principal tensile stress ( σ1) and the second stress invariant ( I2) of the stress field at the fracture tip to explain the transition from Mechanism A (tensile fracturing) to Mechanism D (ductile strain). The results show that σ1 at the fracture tip increases non-linearly with increasing α and Ar (aspect ratio of the shear crack), and assumes a large value when α > 50 o, promoting tensile fractures. On the other hand, I2 is a maximum at α < 45°, resulting in nucleation of ductile shear bands.
A fully coupled finite element model for stress distribution in buried gas pipeline
International Nuclear Information System (INIS)
Yahya Sukirman; Zainal Zakaria; Woong Soon Yue
2001-01-01
The study of stress-strain relationship is very important in many designs of buried structures over the years. The behavior and mechanism between the interaction of soil and buried structures such as a natural pipeline will mostly contributes to the integrity of the pipeline. This paper presents a fully coupled finite element of consolidation analysis model to study the stress-strain distribution along a buried pipeline before it excess its maximum deformation limit. The behavior of the soil-pipeline system can be modelled by a non-linear elasto-plastic based on Mohr-Coulomb and critical state yield surfaces. The deformation and deflection of the pipeline due to drained and external loading condition will be considered here. Finally the stress-strain distribution of the buried pipeline will be utilised to obtain the maximum deformation limit and the deflection of the buried pipeline. (Author)
International Nuclear Information System (INIS)
Luyt, P.C.B.; Theron, N.J.; Pietra, F.
2017-01-01
It is well known that gasket creep-relaxation results in a reduction of contact pressure between the surface of a gasket and the face of a flange over an extended period of time. This reduction may result in the subsequent failure of the circular bolted flange connection due to leakage. In this paper a pair of flat and raised face integral flanges, PN 10 DN 50 (in accordance with the European EN 1092-1 standard), with non-asbestos compressed fibre ring gaskets with aramid and a nitrile rubber binder were considered. Finite element modelling and analyses were done, for both the circular bolted flange configurations, during the seating condition. The results of the finite element analyses were experimentally validated. It was found that the number of bolt tightening increments as well as the time between the bolt tightening increments had a significant impact on the effect which gasket creep-relaxation had after the seating condition. An increase in either the number of bolting increments or the time between the bolting increments will reduce the effect which gasket creep-relaxation has once the bolts had been fastened. Based on these results it is possible to develop an optimisation scheme to minimize the effect which gasket creep-relaxation has on the contact pressure between the face of the flange and the gasket, after seating, by either increasing or decreasing the number of bolt tightening increments or the time between the bolt tightening increments. - Highlights: • Number of bolt tightening increments and time between bolt tightening increments had significant impact on effect of gasket creep-relaxation after the seating condition. • Impact of gasket creep-relaxation during seating and operating phases investigated by means of finite element analysis and experimentally verified. • Possible to develop optimisation scheme to minimize effect ofh gasket creep-relaxation on contact pressure between flange face and gasket. • Knowing the contact pressure is
AUTHOR|(CDS)2067087
In one of its acceptation, the word quench is synonym of destruction. And this is even more consistent with reality in the case of the Large Hadron Collider dipole magnets, whose magnetic field and stored energy are unprecedented: the uncontrolled transition from the superconducting to the resistive state can be the origin of dramatic events. This is why the protection of magnets is so important, and why so many studies and investigations have been carried out on quench origin. The production, cold testing and installation of the 1232 arc dipole magnets is completed. They have fulfilled all the requirements and the operation reliability of these magnets has already been partially confirmed. From an academic standpoint, nevertheless, the anomalous mechanical behaviour, which was sometimes observed during power tests, has not yet been given a clear explanation. The work presented in this thesis aims at providing an instrument to better understand the reasons for such anomalies, by means of finite element modell...
Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells
Institute of Scientific and Technical Information of China (English)
WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun
2007-01-01
Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.
A new dedicated finite element for push-over analysis of reinforced concrete shear wall systems
Directory of Open Access Journals (Sweden)
Delal Doğru ORMANCI
2016-06-01
Full Text Available In this study, a finite element which has been analyzed based on anisotropic behavior of reinforced shear walls is developed. Element stiffness matrices were varied based on whether the element is in the tension or the compression zone of the cross-section. Nonlinear behavior of reinforced shear wall model is investigated under horizontal loads. This behavior is defined with a similar approach to plastic hinge assumption in frame structures that the finite element behaves lineer elastic between joints and plastic deformations are concentrated on joints as vertical plastic displacements. According to this acceptance, plastic behavior of reinforced shear wall occurs when the vertical strain reaches elastic strain limit. In the definition of finite element, displacement functions are chosen considering that the partition of shear walls just at floor levels, are enough for solution. Results of this study are compared with the solution obtained from a different computer programme and experimental results.
Directory of Open Access Journals (Sweden)
K. Ramajeyathilagam
2001-01-01
Full Text Available Experimental and numerical investigations on cylindrical shell panels subjected to underwater explosion loading are presented. Experiments were conducted on panels of size 0.8 × 0.6 × 0.00314 m and shell rise-to-span ratios h/l = 0.0, 0.05, 0.1 , using a box model set-up under air backed conditions in a shock tank. Small charges of PEK I explosive were employed. The plastic deformation of the panels was measured for three loading conditions. Finite element analysis was carried out using the CSA/GENSA [DYNA3D] software to predict the plastic deformation for various loading conditions. The analysis included material and geometric non-linearities, with strain rate effects incorporated based on the Cowper-Symonds relation. The numerical results for plastic deformation are compared with those from experiments.
Recent progress in modelling 3D lithospheric deformation
Kaus, B. J. P.; Popov, A.; May, D. A.
2012-04-01
Modelling 3D lithospheric deformation remains a challenging task, predominantly because the variations in rock types, as well as nonlinearities due to for example plastic deformation result in sharp and very large jumps in effective viscosity contrast. As a result, there are only a limited number of 3D codes available, most of which are using direct solvers which are computationally and memory-wise very demanding. As a result, the resolutions for typical model runs are quite modest, despite the use of hundreds of processors (and using much larger computers is unlikely to bring much improvement in this situation). For this reason we recently developed a new 3D deformation code,called LaMEM: Lithosphere and Mantle Evolution Model. LaMEM is written on top of PETSc, and as a result it runs on massive parallel machines and we have a large number of iterative solvers available (including geometric and algebraic multigrid methods). As it remains unclear which solver combinations work best under which conditions, we have implemented most currently suggested methods (such as schur complement reduction or Fully coupled iterations). In addition, we can use either a finite element discretization (with Q1P0, stabilized Q1Q1 or Q2P-1 elements) or a staggered finite difference discretization for the same input geometry, which is based on a marker and cell technique). This gives us he flexibility to test various solver methodologies on the same model setup, in terms of accuracy, speed, memory usage etc. Here, we will report on some features of LaMEM, on recent code additions, as well as on some lessons we learned which are important for modelling 3D lithospheric deformation. Specifically we will discuss: 1) How we combine a particle-and-cell method to make it work with both a finite difference and a (lagrangian, eulerian or ALE) finite element formulation, with only minor code modifications code 2) How finite difference and finite element discretizations compare in terms of
DEFF Research Database (Denmark)
Sedaghatizadeh, N.; Atefi, G.; Fardad, A. A.
2011-01-01
In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite differenc...... method was used to solve the governing equations, and the particle swarm optimization algorithm was utilized to identify the non-Newtonian coefficients (kυ and γυ). The numerical results agreed well with previous experimental results....
Lewiński, Paweł M.; Dudziak, Sławomir
2018-01-01
In the paper, two kinds of constitutive models for ground and structure were adopted for the nonlinear interaction analysis of the RC cylindrical tank with subsoil. The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Moreover, a non-linear elastic-brittle-plastic analysis of RC axisymmetric structures using finite element iterative techniques is presented. The constitutive laws for concrete and subsoil are developed in compliance with the deformational and plastic flow theories of plasticity. Two examples of an FE analysis of soil-structure interaction were performed and the results were analysed.
Directory of Open Access Journals (Sweden)
Luis Pérez P
2011-12-01
Full Text Available La formulación sin malla del método de puntos finitos permite aprovechar en toda su potencialidad la ventaja de este tipo de técnica numérica, habiéndose comprobado su buen funcionamiento para aplicaciones en los campos de la mecánica de fluidos, mecánica de sólidos, ciencia de materiales y más tarde en adaptividad y electromagnetismo. En el presente trabajo se desarrolla una metodología numérica para aproximar el comportamiento no-lineal de un material mediante el método de puntos finitos, basada en la teoría de deformación total de Hencky, en conjunto con un enfoque elástico para aproximar la distribución de tensiones y de deformaciones. Esta aproximación introduce el concepto de propiedades efectivas del material, las cuales se obtienen en forma iterativa mediante un procedimiento de corrección aplicado sobre la curva experimental de tensión-deformación. Los ejemplos desarrollados demuestran el correcto comportamiento de la metodología utilizada, siendo una de sus principales ventajas la sencillez y facilidad de su implementación, puesto que no es necesaria la partición o subdivisión del dominio de solución.The use of fully meshless formulation of the finite point method allows taking advantage the benefit of this type of numerical technique for applications in the fields of fluid mechanics, solid mechanics, material science and later in adaptivity and electromagnetism. In this work a meshless numerical method to approximate the non-linear behavior of a material using the finite point method, based on the theory of Hencky total strain and elastic approach to approximate the distribution of stresses and deformation, is developed. This approach introduces the concept of effective properties of the material which are obtained using a correction procedure applied to the stress-strain curve. The examples show the good behavior of the methodology that is used, being one of the main advantages the simplicity and the ease of
A Novel Nonlinear Parameter Estimation Method of Soft Tissues
Directory of Open Access Journals (Sweden)
Qianqian Tong
2017-12-01
Full Text Available The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young’s modulus and Poisson’s ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg–Marquardt (LM algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.
Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh
2018-02-01
The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.
Carvalho, Marco Aurélio; Sotto-Maior, Bruno Salles; Del Bel Cury, Altair Antoninha; Pessanha Henriques, Guilherme Elias
2014-11-01
Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2012-07-01
Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...
Multiphase poroelastic finite element models for soft tissue structures
International Nuclear Information System (INIS)
Simon, B.R.
1992-01-01
During the last two decades, biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains; and may swell or shrink when tissue ionic concentrations are altered. Give the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law ans a total Lagrangian view for the formulation. The associated FEMs are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested. 62 refs., 11 figs., 3 tabs
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
Matsuura, Yusuke; Rokkaku, Tomoyuki; Suzuki, Takane; Thoreson, Andrew Ryan; An, Kai-Nan; Kuniyoshi, Kazuki
2017-08-01
Forearm diaphysis fractures are usually managed by open reduction internal fixation. Recently, locking plates have been used for treatment. In the long-term period after surgery, some patients present with bone atrophy adjacent to the plate. However, a comparison of locking and conventional plates as a cause of atrophy has not been reported. The aim of this study was to investigate long-term bone atrophy associated with use of locking and conventional plates for forearm fracture treatment. In this study we included 15 patients with forearm fracture managed by either locking or conventional plates and with more than 5 years of follow-up. Computed tomographic imaging of both forearms was performed to assess bone thickness and local bone mineral density and to predict bone strength without plate reinforcement based on finite element analysis. Mean patient age at surgery was 48.0 years. Eight patients underwent reduction with fixed locking plates and were followed up for a mean of 79.5 months; the remaining 7 patients were treated with conventional plates and were followed up for a mean of 105.0 months. Compared with the conventional plate group, the locking plate group had the same fractured limb-contralateral limb ratio of cortex bone thickness, but had significantly lower ratios of mineral density adjacent to the plate and adjusted bone strength. This study demonstrated bone atrophy after locking plate fixation for forearm fractures. Treatment plans for forearm fracture should take into consideration the impact of bone atrophy long after plate fixation. Therapeutic IV. Copyright © 2017 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.