A study on the nonlinear finite element analysis of reinforced concrete structures: shell finite element formulation

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.

A study on the nonlinear finite element analysis of reinforced concrete structures: shell finite element formulation

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

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

Non-linear elastic deformations

CERN Document Server

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.

Finite elements of nonlinear continua

CERN Document Server

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

Introduction to nonlinear finite element analysis

CERN Document Server

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

CERN Document Server

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...

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)

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.

Analysis of the finite deformation response of shape memory polymers: I. Thermomechanical characterization

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

A q-deformed nonlinear map

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

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.

Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure

Science.gov (United States)

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

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.)

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

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

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.

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.

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)

Numerical analysis of some problems related to the mechanics of pneumatic tires: Finite deformation/rolling contact of a viscoelastic cylinder and finite deformation of cord-reinforced rubber composites

Science.gov (United States)

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.

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

KAUST Repository

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.

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

Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses

Science.gov (United States)

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

A comparison of numerical methods used for finite element modelling of soft tissue deformation

KAUST Repository

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.

A comparison of numerical methods used for finite element modelling of soft tissue deformation

KAUST Repository

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.

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

Finite element-implementation of creep of concrete for thin-shell analysis using nonlinear constitutive relations and creep compliance functions

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.)

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 ...

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

Science.gov (United States)

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.

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.

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...

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

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.

Computational thermo-hydro-mechanics for freezing and thawing multiphase geological media in the finite deformation range

Science.gov (United States)

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.

Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

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.

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.

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

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.

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

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

CERN Document Server

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

Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

KAUST Repository

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

Optimal design of geometrically nonlinear shells of revolution with using the mixed finite element method

Science.gov (United States)

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.

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

Integral finite element analysis of turntable bearing with flexible rings

Science.gov (United States)

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.

JAC, 2-D Finite Element Method Program for Quasi Static Mechanics Problems by Nonlinear Conjugate Gradient (CG) Method

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

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.

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

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

Domain decomposition solvers for nonlinear multiharmonic finite element equations

KAUST Repository

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.

Probabilistic finite elements for transient analysis in nonlinear continua

Science.gov (United States)

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.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

Science.gov (United States)

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.

FEAST 3.1: finite-element modeling of sheath deformation such as longitudinal ridging and collapse into axial gap

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)

FEAST 3.1: finite-element modeling of sheath deformation such as longitudinal ridging and collapse into axial gap

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)

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

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

Science.gov (United States)

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 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 ...

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

Science.gov (United States)

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.

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.

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.

APPLICATION OF FINITE ELEMENT METHOD TAKING INTO ACCOUNT PHYSICAL AND GEOMETRIC NONLINEARITY FOR THE CALCULATION OF PRESTRESSED REINFORCED CONCRETE BEAMS

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. 

Effect of analysis parameters on non-linear implicit finite element analysis of marine corroded steel plate

Science.gov (United States)

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.

Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

Science.gov (United States)

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.

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

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

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.

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

Science.gov (United States)

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.

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

KAUST Repository

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.

A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

KAUST Repository

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.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

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.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

Science.gov (United States)

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.

Stress analysis and deformation prediction of sheet metal workpieces based on finite element simulation

OpenAIRE

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 ...

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.

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.

Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications

Science.gov (United States)

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.

Material model for non-linear finite element analyses of large concrete structures

NARCIS (Netherlands)

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

Nonlinear crack mechanics

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

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.)

Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load

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.

Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load

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.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

Science.gov (United States)

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.

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.

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.

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...

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

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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.

Non-linear actions of physiological agents: Finite disarrangements elicit fitness benefits.

Science.gov (United States)

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 element modeling of nanotube structures linear and non-linear models

CERN Document Server

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.

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

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

KAUST Repository

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

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/m³ respectively.

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

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

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.)

Fluid boundary of a viscoplastic Bingham flow for finite solid deformations

OpenAIRE

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...

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)

Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion.

Science.gov (United States)

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

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

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.)

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.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

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

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.

Hybrid finite difference/finite element solution method development for non-linear superconducting magnet and electrical circuit breakdown transient analysis

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)

Demonstration of finite element simulations in MOOSE using crystallographic models of irradiation hardening and plastic deformation

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 size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

Science.gov (United States)

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.

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 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.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

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

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm

Science.gov (United States)

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.

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

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

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

Stress analysis and deformation prediction of sheet metal workpieces based on finite element simulation

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.

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.

A semi-analytical finite element process for nonlinear elastoplastic analysis of arbitrarily loaded shells of revolution

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)

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

Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.

Science.gov (United States)

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.

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

Science.gov (United States)

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.

Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

KAUST Repository

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.

Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

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.

Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis

CERN Document Server

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.

FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH

Directory of Open Access Journals (Sweden)

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.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

Science.gov (United States)

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.

Optimization of deformation monitoring networks using finite element strain analysis

Science.gov (United States)

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-size giant magnons on η-deformed AdS5×S5

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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.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

Science.gov (United States)

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.

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.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

Science.gov (United States)

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.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

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.

The physics of large deformation of crystalline solids

CERN Document Server

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...

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.

Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws

Science.gov (United States)

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.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

Science.gov (United States)

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.

Nonlinear Local Deformations of Red Blood Cell Membranes: Effects of Toxins and Pharmaceuticals (Part 2

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. 

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...

Soft tissue deformation using a Hierarchical Finite Element Model.

Science.gov (United States)

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.

Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

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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.

Problems in nonlinear acoustics: Scattering of sound by sound, parametric receiving arrays, nonlinear effects in asymmetric sound beams and pulsed finite amplitude sound beams

Science.gov (United States)

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.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

Science.gov (United States)

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. (Auth.)

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

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

KAUST Repository

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.

Dynamic visual cryptography on deformable finite element grids

Science.gov (United States)

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.

A mixed finite element method for nonlinear diffusion equations

KAUST Repository

Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

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 Modeling of Thermo Creep Processes Using Runge-Kutta Method

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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.

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

Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

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

Assessment of Slope Stability and Interference of Structures Considering Seismity in Complex Engineering-Geological Conditions Using the Method of Finite Elements

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

Segmentation of deformable organs from medical images using particle swarm optimization and nonlinear shape priors

Science.gov (United States)

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.

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...

Finite element methods in a simulation code for offshore wind turbines

Science.gov (United States)

Kurz, Wolfgang

1994-06-01

Offshore installation of wind turbines will become important for electricity supply in future. Wind conditions above sea are more favorable than on land and appropriate locations on land are limited and restricted. The dynamic behavior of advanced wind turbines is investigated with digital simulations to reduce time and cost in development and design phase. A wind turbine can be described and simulated as a multi-body system containing rigid and flexible bodies. Simulation of the non-linear motion of such a mechanical system using a multi-body system code is much faster than using a finite element code. However, a modal representation of the deformation field has to be incorporated in the multi-body system approach. The equations of motion of flexible bodies due to deformation are generated by finite element calculations. At Delft University of Technology the simulation code DUWECS has been developed which simulates the non-linear behavior of wind turbines in time domain. The wind turbine is divided in subcomponents which are represented by modules (e.g. rotor, tower etc.).

Examining the validity of Stoney-equation for in-situ stress measurements in thin film electrodes using a large-deformation finite-element procedure

Science.gov (United States)

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.

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...

Nonlinear microrheology and molecular imaging to map microscale deformations of entangled DNA networks

Science.gov (United States)

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-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.

Comparative Analysis of Bulge Deformation between 2D and 3D Finite Element Models

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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.

Deformation Characteristics of Composite Structures

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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.

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

Science.gov (United States)

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.

NONLINEAR FINITE ELEMENT ANALYSIS OF NONSEISMICALLY DETAILED INTERIOR RC BEAM-COLUMN CONNECTION UNDER REVERSED CYCLIC LOAD

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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.

Effect of Punch Stroke on Deformation During Sheet Forming Through Finite Element

Science.gov (United States)

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.

Nonlinear analysis of RC cylindrical tank and subsoil accounting for a low concrete strength

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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.

SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

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.

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.

Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method.

Science.gov (United States)

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.

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

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

Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues.

Science.gov (United States)

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.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

Science.gov (United States)

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.

Elastically deformable models based on the finite element method accelerated on graphics hardware using CUDA

NARCIS (Netherlands)

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

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 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.

Geometrical nonlinear deformation model and its experimental study on bimorph giant magnetostrictive thin film

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.

Loading Deformation Characteristic Simulation Study of Engineering Vehicle Refurbished Tire

Science.gov (United States)

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.

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.)

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)

Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

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.

Quasistatic nonlinear viscoelasticity and gradient flows

OpenAIRE

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...

Delay-Dependent Finite-Time H∞ Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

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.

Extension of non-linear beam models with deformable cross sections

Science.gov (United States)

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.

A nonaffine network model for elastomers undergoing finite deformations

Science.gov (United States)

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.

VISCOT: a two-dimensional and axisymmetric nonlinear transient thermoviscoelastic and thermoviscoplastic finite-element code for modeling time-dependent viscous mechanical behavior of a rock mass

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

Nonlinear integral equations for the sausage model

Science.gov (United States)

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.

PRONTO3D users` instructions: A transient dynamic code for nonlinear structural analysis

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Mello, F.J.; Heinstein, M.W.; Swegle, J.W.; Ratner, J.A. [Sandia National Labs., Albuquerque, NM (United States); Zadoks, R.I. [Univ. of Texas, El Paso, TX (United States)

1998-06-01

This report provides an updated set of users` instructions for PRONTO3D. PRONTO3D is a three-dimensional, transient, solid dynamics code for analyzing large deformations of highly nonlinear materials subjected to extremely high strain rates. This Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion. Eight-node, uniform strain, hexahedral elements and four-node, quadrilateral, uniform strain shells are used in the finite element formulation. An adaptive time step control algorithm is used to improve stability and performance in plasticity problems. Hourglass distortions can be eliminated without disturbing the finite element solution using either the Flanagan-Belytschko hourglass control scheme or an assumed strain hourglass control scheme. All constitutive models in PRONTO3D are cast in an unrotated configuration defined using the rotation determined from the polar decomposition of the deformation gradient. A robust contact algorithm allows for the impact and interaction of deforming contact surfaces of quite general geometry. The Smooth Particle Hydrodynamics method has been embedded into PRONTO3D using the contact algorithm to couple it with the finite element method.

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

Non-linear finite element analyses applicable for the design of large reinforced concrete structures

NARCIS (Netherlands)

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

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.

Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

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.

Generalized multiscale finite element methods. nonlinear elliptic equations

KAUST Repository

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.

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

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

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.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

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

Asymptotic investigation of the nonlinear boundary value dynamic problem for the systems with finite sizes

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

MO-F-BRA-04: Voxel-Based Statistical Analysis of Deformable Image Registration Error via a Finite Element Method.

Science.gov (United States)

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

Stochastic analysis of laminated composite plates on elastic foundation: The cases of post-buckling behavior and nonlinear free vibration

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.

Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

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

Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.

Science.gov (United States)

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.

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.

Nonlinear interaction analysis of RC cylindrical tank with subsoil by adopting two kinds of constitutive models for ground and structure

Science.gov (United States)

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.

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

Science.gov (United States)

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.

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

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)

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

Science.gov (United States)

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.

Recent progress in modelling 3D lithospheric deformation

Science.gov (United States)

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

Finite element analysis of slot wall deformation in stainless steel and titanium orthodontic brackets during simulated palatal root torque.

Science.gov (United States)

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.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Science.gov (United States)

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.

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

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.

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.

Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods

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

A New Energy-Based Method for 3-D Finite-Element Nonlinear Flux Linkage computation of Electrical Machines

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....

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

Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics

International Nuclear Information System (INIS)

Nazem, M; Carter, J P; Airey, D W

2010-01-01

In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

Science.gov (United States)

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.

Definition of Availability Index of Deformed Building Constructions Using the Finite - Element Analysis Package

Science.gov (United States)

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.

Validation of nonlinear FEA models of a thin-walled elbow under extreme loading conditions for Sodium-cooled Fast Reactors

International Nuclear Information System (INIS)

Watakabe, Tomoyoshi; Wakai, Takashi; Jin, Chuanrong; Usui, Yoshiya; Sakai, Shinkichi; Ooshika, Junji; Tsukimori, Kazuyuki

2015-01-01

For the purpose of confirming failure modes and safety margin, some studies on the ultimate strength of thin-walled piping components for Sodium-cooled Fast Reactors (SFRs) under extreme loading conditions such as large earthquakes have been reported these several years. Nonlinear finite element analysis has been applied in these studies to simulate buckling and yielding with large deformation, whose accuracy is dependent on the element type, the mesh size, the elasto-plastic model and so on. It is important to check the validation of a finite element model for nonlinear analysis especially under extreme loading conditions. This paper presents static and dynamic analyses of a thin-walled elbow with large deformation under large seismic loading, and discusses the validation of the FEA models comparing with experimental results. The finite element analysis models in this study are generated by shell elements for a stainless steel pipe elbow of diameter-to-thickness ratio 59:1 similar to the main pipe of SFRs, which is used for shaking table tests. At first, a static analysis is carried out for an in-plane monotonic bending test, in order to confirm that the shell element is appropriate to the large deformation analysis and the material parameters are proper for the strain level in the experiments. And then, a dynamic in-plane bending test with the maximum acceleration of 11.7G is simulated by the nonlinear FEA with stiffness-proportional damping. The influence of mesh sizes on results is investigated, to determine proper mesh sizes and reduce the computational cost. Finally, comparing the results of the FEM analyses with those of experiments, it is concluded that the appropriately generated FEA models are effective and give accurate results for nonlinear analyses of the thin-walled elbow under large seismic loading. (author)

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

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

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)

Nonlinear Elasticity

Science.gov (United States)

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.

Simulation of finite-strain inelastic phenomena governed by creep and plasticity

Science.gov (United States)

Li, Zhen; Bloomfield, Max O.; Oberai, Assad A.

2017-11-01

Inelastic mechanical behavior plays an important role in many applications in science and engineering. Phenomenologically, this behavior is often modeled as plasticity or creep. Plasticity is used to represent the rate-independent component of inelastic deformation and creep is used to represent the rate-dependent component. In several applications, especially those at elevated temperatures and stresses, these processes occur simultaneously. In order to model these process, we develop a rate-objective, finite-deformation constitutive model for plasticity and creep. The plastic component of this model is based on rate-independent J_2 plasticity, and the creep component is based on a thermally activated Norton model. We describe the implementation of this model within a finite element formulation, and present a radial return mapping algorithm for it. This approach reduces the additional complexity of modeling plasticity and creep, over thermoelasticity, to just solving one nonlinear scalar equation at each quadrature point. We implement this algorithm within a multiphysics finite element code and evaluate the consistent tangent through automatic differentiation. We verify and validate the implementation, apply it to modeling the evolution of stresses in the flip chip manufacturing process, and test its parallel strong-scaling performance.

Development of a Detailed Volumetric Finite Element Model of the Spine to Simulate Surgical Correction of Spinal Deformities

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.

Three nonlinear performance relationships in the start-up state of IPMC strips based on finite element analysis

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

Multi Length Scale Finite Element Design Framework for Advanced Woven Fabrics

Science.gov (United States)

Erol, Galip Ozan

Woven fabrics are integral parts of many engineering applications spanning from personal protective garments to surgical scaffolds. They provide a wide range of opportunities in designing advanced structures because of their high tenacity, flexibility, high strength-to-weight ratios and versatility. These advantages result from their inherent multi scale nature where the filaments are bundled together to create yarns while the yarns are arranged into different weave architectures. Their highly versatile nature opens up potential for a wide range of mechanical properties which can be adjusted based on the application. While woven fabrics are viable options for design of various engineering systems, being able to understand the underlying mechanisms of the deformation and associated highly nonlinear mechanical response is important and necessary. However, the multiscale nature and relationships between these scales make the design process involving woven fabrics a challenging task. The objective of this work is to develop a multiscale numerical design framework using experimentally validated mesoscopic and macroscopic length scale approaches by identifying important deformation mechanisms and recognizing the nonlinear mechanical response of woven fabrics. This framework is exercised by developing mesoscopic length scale constitutive models to investigate plain weave fabric response under a wide range of loading conditions. A hyperelastic transversely isotropic yarn material model with transverse material nonlinearity is developed for woven yarns (commonly used in personal protection garments). The material properties/parameters are determined through an inverse method where unit cell finite element simulations are coupled with experiments. The developed yarn material model is validated by simulating full scale uniaxial tensile, bias extension and indentation experiments, and comparing to experimentally observed mechanical response and deformation mechanisms. Moreover

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

Science.gov (United States)

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.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

Science.gov (United States)

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.

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...

Assessment of natural frequency of installed offshore wind turbines using nonlinear finite element model considering soil-monopile interaction

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

Semianalytic Design Sensitivity Analysis of Nonlinear Structures With a Commercial Finite Element Package

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

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.

Fundamental observations concerning hysteresis in the deformation of intact and jointed rock with applications to nonlinear attenuation in the near source region

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

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

Science.gov (United States)

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.

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...

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

Science.gov (United States)

Al-Mayah, Adil; Moseley, Joanne; Velec, Mike; Brock, Kristy

2011-08-01

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Nonlinear failure analysis of a reinforced concrete containment under internal pressure

International Nuclear Information System (INIS)

Sharma, S.; Wang, Y.K.; Reich, M.

1984-01-01

A detailed nonlinear finite element model is used to investigate the failure response of the Indian Point containment building under severe accident pressures. Refined material models are used to describe the complex stress-strain behavior of the liner and rebar steels, the plain concrete and the reinforced concrete. Structural geometry of the containment is idealized by eight layers of axisymmetric finite elements through the wall thickness in order to closely model the actual placement of the rebars. Soil stiffness under the containment base mat is modeled by a series of nonlinear spring elements. Numerical results presented in the paper describe cracking and plastic deformation (in compression) of the concrete, yielding of the liner and rebar steels and eventual loss of the load carrying capacity of the containment. The results are compared with available data from the previous studies for this containment. 8 references, 9 figures

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.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A unified elasto-viscoplastic constitutive model

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.)

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.)

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

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...

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary

Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates

Energy Technology Data Exchange (ETDEWEB)

Dombrowski, Stefan von [Institute of Robotics and Mechatronics, German Aerospace Center (DLR) (Germany)], E-mail: stefan.von.dombrowski@dlr.de

2002-11-15

To consider large deformation problems in multibody system simulations a finite element approach, called absolute nodal coordinate.formulation,has been proposed. In this formulation absolute nodal coordinates and their material derivatives are applied to represent both deformation and rigid body motion. The choice of nodal variables allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotations. The methodology is especially suited for but not limited to modeling of beams, cables and shells in multibody dynamics.This paper summarizes the absolute nodal coordinate formulation for a 3D Euler-Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae.Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape.functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined.

Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates

International Nuclear Information System (INIS)

Dombrowski, Stefan von

2002-01-01

To consider large deformation problems in multibody system simulations a finite element approach, called absolute nodal coordinate.formulation,has been proposed. In this formulation absolute nodal coordinates and their material derivatives are applied to represent both deformation and rigid body motion. The choice of nodal variables allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotations. The methodology is especially suited for but not limited to modeling of beams, cables and shells in multibody dynamics.This paper summarizes the absolute nodal coordinate formulation for a 3D Euler-Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae.Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape.functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined

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

The nonlinear finite element analysis program NUCAS (NUclear Containment Analysis System) for reinforced concrete containment building

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)

Nonlinear analysis of AS4/PEEK thermoplastic composite laminate using a one parameter plasticity model

Science.gov (United States)

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.

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%

Deformation localization at the tips of shear fractures: An analytical approach

Science.gov (United States)

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.

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

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)

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

Science.gov (United States)

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.

A mesh density study for application to large deformation rolling process evaluation

International Nuclear Information System (INIS)

Martin, J.A.

1997-12-01

When addressing large deformation through an elastic-plastic analysis the mesh density is paramount in determining the accuracy of the solution. However, given the nonlinear nature of the problem, a highly-refined mesh will generally require a prohibitive amount of computer resources. This paper addresses finite element mesh optimization studies considering accuracy of results and computer resource needs as applied to large deformation rolling processes. In particular, the simulation of the thread rolling manufacturing process is considered using the MARC software package and a Cray C90 supercomputer. Both mesh density and adaptive meshing on final results for both indentation of a rigid body to a specified depth and contact rolling along a predetermined length are evaluated

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

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)

A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

KAUST Repository

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.

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.

Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

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)

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)

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Directory of Open Access Journals (Sweden)

João Paulo de Barros Cavalcante

Full Text Available Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

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)

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

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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.

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

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

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

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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].

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

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.

Characterization of phase properties and deformation in ferritic-austenitic duplex stainless steels by nanoindentation and finite element method

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).

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

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)

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

Science.gov (United States)

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.

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)

A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

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

Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

Science.gov (United States)

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.

Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids

Science.gov (United States)

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.

A voxel-based finite element model for the prediction of bladder deformation

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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

On the stress calculation within phase-field approaches: a model for finite deformations

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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.

Experimental and Numerical Investigations on Deformation of Cylindrical Shell Panels to Underwater Explosion

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.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

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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.

Diverse Geological Applications For Basil: A 2d Finite-deformation Computational Algorithm

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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

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

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...

Finite element simulation of nanoindentation tests using a macroscopic computational model

International Nuclear Information System (INIS)

Khelifa, Mourad; Fierro, Vanessa; Celzard, Alain

2014-01-01

The aim of this work was to develop a numerical procedure to simulate nanoindentation tests using a macroscopic computational model. Both theoretical and numerical aspects of the proposed methodology, based on the coupling of isotropic elasticity and anisotropic plasticity described with the quadratic criterion of Hill are presented to model this behaviour. The anisotropic plastic behaviour accounts for the mixed nonlinear hardening (isotropic and kinematic) under large plastic deformation. Nanoindentation tests were simulated to analyse the nonlinear mechanical behaviour of aluminium alloy. The predicted results of the finite element (FE) modelling are in good agreement with the experimental data, thereby confirming the accuracy level of the suggested FE method of analysis. The effects of some technological and mechanical parameters known to have an influence during the nanoindentation tests were also investigated.

Finite element modelling of shot peening process: Prediction of the compressive residual stresses, the plastic deformations and the surface integrity

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

SU-F-I-50: Finite Element-Based Deformable Image Registration of Lung and Heart

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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.

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

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 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

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

Science.gov (United States)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

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

Three-dimensional finite element nonlinear dynamic analysis of pile groups for lateral transient and seismic excitations

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)

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

Science.gov (United States)

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.

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

KAUST Repository

Khan, Kamran

2012-11-09

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material\\'s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions. © 2012 Springer-Verlag Wien.

Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces

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

InSAR Observations and Finite Element Modeling of Crustal Deformation Around a Surging Glacier, Iceland

Science.gov (United States)

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�

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.

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.)

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.

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....

Performance analysis for minimally nonlinear irreversible refrigerators at finite cooling power

Science.gov (United States)

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.

Three-dimensional finite element impact analysis of a nuclear waste truck cask

International Nuclear Information System (INIS)

Miller, J.D.

1985-01-01

This paper presents a three-dimensional finite element impact analysis of a hypothetical accident event for the preliminary design of a shipping cask which is used to transport radioactive waste by standard tractor-semitrailer truck. The nonlinear dynamic structural analysis code DYNA3D run on Sandia's Cray-1 computer was used to calculate the effects of the cask's closure-end impacting a rigid frictionless surface on an edge of its external impact limiter after a 30-foot fall. The center of gravity of the cask (made of 304 stainless steel and depleted uranium) was assumed to be directly above the impact point. An elastic-plastic material constitutive model was used to calculate the nonlinear response of the cask components to the transient loading. Interactive color graphics (PATRAN and MOVIE BYU) were used throughout the analysis, proving to be extremely helpful for generation and verification of the geometry and boundary conditions of the finite element model and for interpretation of the analysis results. Results from the calculations show the cask sustained large localized deformations. However, these were almost entirely confined to the impact limiters built into the cask. The closure sections were determined to remain intact, and leakage would not be expected after the event. As an example of a large three-dimensional finite element dynamic impact calculation, this analysis can serve as an excellent benchmark for computer aided design procedures

Influence of Installation Effects on Pile Bearing Capacity in Cohesive Soils - Large Deformation Analysis Via Finite Element Method

Science.gov (United States)

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.

Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

Science.gov (United States)

Mostafazadeh, Ali; Oflaz, Neslihan

2017-11-01

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

Problems in nonlinear acoustics: Pulsed finite amplitude sound beams, nonlinear acoustic wave propagation in a liquid layer, nonlinear effects in asymmetric cylindrical sound beams, effects of absorption on the interaction of sound beams, and parametric receiving arrays

Science.gov (United States)

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.

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.

Finite element calculations illustrating a method of model reduction for the dynamics of structures with localized nonlinearities.

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.

Finite Element Simulation of the Presta Joining Process for Assembled Camshafts: Application to Aluminum Shafts

Directory of Open Access Journals (Sweden)

Robert Scherzer

2018-02-01

Full Text Available This work shows a sequence of numerical models for the simulation of the Presta joining process: a well-established industrial process for manufacturing assembled camshafts. The operation is divided into two sub-steps: the rolling of the shaft to widen the cam seat and the joining of the cam onto the shaft. When manufactured, the connection is tested randomly by loading it with a static torque. Subsequently, there are three numerical models using the finite element method. Additionally, a material model of finite strain viscoplasticity with nonlinear kinematic hardening is used throughout the whole simulation process, which allows a realistic representation of the material behavior even for large deformations. In addition, it enables a transfer of the deformation history and of the internal stresses between different submodels. This work also shows the required parameter identification and the associated material tests. After comparing the numerical results with experimental studies of the manufacturing process for steel-steel connections, the models are used to extend the joining process to the utilization of aluminum shafts.

Development of Multiorgan Finite Element-Based Prostate Deformation Model Enabling Registration of Endorectal Coil Magnetic Resonance Imaging for Radiotherapy Planning

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

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

TRUST: A Computer Program for Variably Saturated Flow in Multidimensional, Deformable Media

Energy Technology Data Exchange (ETDEWEB)

Reisenauer, A. E.; Key, K. T.; Narasimhan, T. N.; Nelson, R. W.

1982-01-01

The computer code, TRUST. provides a versatile tool to solve a wide spectrum of fluid flow problems arising in variably saturated deformable porous media. The governing equations express the conservation of fluid mass in an elemental volume that has a constant volume of solid. Deformation of the skeleton may be nonelastic. Permeability and compressibility coefficients may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may include hysteresis. The code developed by T. N. Narasimhan grew out of the original TRUNP code written by A. L. Edwards. The code uses an integrated finite difference algorithm for numerically solving the governing equation. Narching in time is performed by a mixed explicit-implicit numerical procedure in which the time step is internally controlled. The time step control and related feature in the TRUST code provide an effective control of the potential numerical instabilities that can arise in the course of solving this difficult class of nonlinear boundary value problem. This document brings together the equations, theory, and users manual for the code as well as a sample case with input and output.

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)

NONLINEAR ANALYSIS OF CFRP- PRESTRESSED CONCRETE BEAMS SUBJECTED TO INCREMENTAL STATIC LOADING BY FINITE ELEMENTS

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.

Application of optical deformation analysis system on wedge splitting test and its inverse analysis

DEFF Research Database (Denmark)

Skocek, Jan; Stang, Henrik

2010-01-01

. Results of the inverse analysis are compared with traditional inverse analysis based on clip gauge data. Then the optically measured crack profile and crack tip position are compared with predictions done by the non-linear hinge model and a finite element analysis. It is shown that the inverse analysis...... based on the optically measured data can provide material parameters of the fictitious crack model matching favorably those obtained by classical inverse analysis based on the clip gauge data. Further advantages of using of the optical deformation analysis lie in identification of such effects...

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A new elasto-viscoplastic constitutive model

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.)

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A new elasto-viscoplastic constitutive model

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.)

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

Science.gov (United States)

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.

Analysis of intelligent hinged shell structures: deployable deformation and shape memory effect

Science.gov (United States)

Shi, Guang-Hui; Yang, Qing-Sheng; He, X. Q.

2013-12-01

Shape memory polymers (SMPs) are a class of intelligent materials with the ability to recover their initial shape from a temporarily fixable state when subjected to external stimuli. In this work, the thermo-mechanical behavior of a deployable SMP-based hinged structure is modeled by the finite element method using a 3D constitutive model with shape memory effect. The influences of hinge structure parameters on the nonlinear loading process are investigated. The total shape memory of the processes the hinged structure goes through, including loading at high temperature, decreasing temperature with load carrying, unloading at low temperature and recovering the initial shape with increasing temperature, are illustrated. Numerical results show that the present constitutive theory and the finite element method can effectively predict the complicated thermo-mechanical deformation behavior and shape memory effect of SMP-based hinged shell structures.

Analysis of intelligent hinged shell structures: deployable deformation and shape memory effect

International Nuclear Information System (INIS)

Shi, Guang-Hui; Yang, Qing-Sheng; He, X Q

2013-01-01

Shape memory polymers (SMPs) are a class of intelligent materials with the ability to recover their initial shape from a temporarily fixable state when subjected to external stimuli. In this work, the thermo-mechanical behavior of a deployable SMP-based hinged structure is modeled by the finite element method using a 3D constitutive model with shape memory effect. The influences of hinge structure parameters on the nonlinear loading process are investigated. The total shape memory of the processes the hinged structure goes through, including loading at high temperature, decreasing temperature with load carrying, unloading at low temperature and recovering the initial shape with increasing temperature, are illustrated. Numerical results show that the present constitutive theory and the finite element method can effectively predict the complicated thermo-mechanical deformation behavior and shape memory effect of SMP-based hinged shell structures. (paper)

A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

Directory of Open Access Journals (Sweden)

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.

Assessment of the Internal Pressure Fragility of the Hanul NPP Units 3 and 4 Containment Building Using a Nonlinear Finite Element Analysis

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.

Assessment of the Internal Pressure Fragility of the Hanul NPP Units 3 and 4 Containment Building Using a Nonlinear Finite Element Analysis

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

Applying DTI white matter orientations to finite element head models to examine diffuse TBI under high rotational accelerations.

LENUS (Irish Health Repository)

Colgan, Niall C

2010-12-01

The in-vivo mechanical response of neural tissue during impact loading of the head is simulated using geometrically accurate finite element (FE) head models. However, current FE models do not account for the anisotropic elastic material behaviour of brain tissue. In soft biological tissue, there is a correlation between internal microscopic structure and macroscopic mechanical properties. Therefore, constitutive equations are important for the numerical analysis of the soft biological tissues. By exploiting diffusion tensor techniques the anisotropic orientation of neural tissue is incorporated into a non-linear viscoelastic material model for brain tissue and implemented in an explicit FE analysis. The viscoelastic material parameters are derived from published data and the viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. The constitutive model was applied in the University College Dublin brain trauma model (UCDBTM) (i.e. three-dimensional finite element head model) to predict the mechanical response of the intra-cranial contents due to rotational injury.

Topology optimization of nonlinear optical devices

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2011-01-01

This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....

Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

Directory of Open Access Journals (Sweden)

J. Machalová

2015-01-01

Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

M theory on deformed superspace

Science.gov (United States)

Faizal, Mir

2011-11-01

In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in N=1 superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.

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

Moisture movement in nonisothermal deformable media

International Nuclear Information System (INIS)

Edgar, T.V.

1983-01-01

Many inactive uranium mill tailings impoundments currently exist in the United States. One facet of the Department of Energy's reclamation plan for these sites is to enclose the impoundments with a cover. Placement of any cover material could cause the water content of the tailings to change due to changes in the evaporation and infiltration rates. This report investigates the effects of changing mechanical and fluid stresses on deformable media. A set of one dimensional equilibrium and balance equations for both two and three phase soils are developed based on a coordinate system which is defined by the soil solids. A finite difference model was developed to solve the three coupled nonlinear partial differential equations which permits the study of the effects of liquid, gas and heat flows on the deformation of the soil. A series of example problems were selected to analyze the effects of varying the soil and environmental parameters. Four significant cases were: (1) Drainage of an originally saturated soil, (2) Consolidation of a partially saturated soil due to placement of a cover, (3) the effect of a low permeability layer on drainage, and (4) the effects of soil drying and crusting on evaporation

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

Science.gov (United States)

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.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

Science.gov (United States)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Analysis of warping deformation modes using higher order ANCF beam element

Science.gov (United States)

Orzechowski, Grzegorz; Shabana, Ahmed A.

2016-02-01

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

International Nuclear Information System (INIS)

Lee, Kye Hyung; Im, Se Yong; Lim, Jae Hyuk; Sohn, Dong Woo

2015-01-01

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

Energy Technology Data Exchange (ETDEWEB)

Lee, Kye Hyung; Im, Se Yong [KAIST, Daejeon (Korea, Republic of); Lim, Jae Hyuk [KARI, Daejeon (Korea, Republic of); Sohn, Dong Woo [Korea Maritime and Ocean University, Busan (Korea, Republic of)

2015-02-15

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

Nonlinear rheology of complex fluid-fluid interfaces

NARCIS (Netherlands)

Sagis, L.M.C.; Fischer, P.

2014-01-01

Fluid–fluid interfaces stabilized by proteins, protein aggregates, polymers, or colloidal particles, tend to have a complex microstructure. Their response to an applied deformation is often highly nonlinear, even at small deformation (rates). The nonlinearity of the response is a result of changes

Deformation and transport of micro-fibers and helices in viscous flows

Science.gov (United States)

Lindner, Anke

Fluid-structure interactions between flexible objects and viscous flows are, to a large extent, governed by the shape of the flexible object. Using microfabrication methods, we obtain complex ``particles'' in fiber and helix form with perfect control not only over the material properties, but also the particle geometry. We then perform an experimental study on the deformation and transport of these particles in microfluidic flows. Fibers are shown to drift laterally in confined flows due to the transport anisotropy of the elongated object. When these fibers interact with lateral walls, complex dynamics are observed, such as fiber oscillation. Fiber flexibility modifies these dynamics. Flexible microhelices are easily stretched by a viscous flow and we characterize the overall shape as a function of the frictional properties. The deformation of these helices is well-described by non-linear finite extensibility. Due to the non-uniform distribution of the pitch of a helix subject to viscous drag, linear and nonlinear behavior is identified along the contour length of a single helix. When a polymer solution is used for the viscous flow, an interesting multiscale problem arises and the typical polymer size needs to be compared not only to the global size of the helix, but also to the dimensions of the ribbon.

Accuracy of specimen-specific nonlinear finite element analysis for evaluation of distal radius strength in cadaver material.

Science.gov (United States)

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.

Finite Element Analysis of Reinforced Concrete Beam-Column Connections with Governing Joint Shear Failure Mode

Directory of Open Access Journals (Sweden)

M.A. Najafgholipour

Full Text Available Abstract Reinforced concrete (RC beam-column connections especially those without transverse reinforcement in joint region can exhibit brittle behavior when intensive damage is concentrated in the joint region during an earthquake event. Brittle behavior in the joint region can compromise the ductile design philosophy and the expected overall performance of structure when subjected to seismic loading. Considering the importance of joint shear failure influences on strength, ductility and stability of RC moment resisting frames, a finite element modeling which focuses on joint shear behavior is presented in this article. Nonlinear finite element analysis (FEA of RC beam-column connections is performed in order to investigate the joint shear failure mode in terms of joint shear capacity, deformations and cracking pattern. A 3D finite element model capable of appropriately modeling the concrete stress-strain behavior, tensile cracking and compressive damage of concrete and indirect modeling of steel-concrete bond is used. In order to define nonlinear behavior of concrete material, the concrete damage plasticity is applied to the numerical model as a distributed plasticity over the whole geometry. Finite element model is then verified against experimental results of two non-ductile beam-column connections (one exterior and one interior which are vulnerable to joint shear failure. The comparison between experimental and numerical results indicates that the FE model is able to simulate the performance of the beam-column connections and is able to capture the joint shear failure in RC beam-column connections.

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

Dorfmann, Luis

2014-01-01

This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

Efficient inversion of volcano deformation based on finite element models : An application to Kilauea volcano, Hawaii

Science.gov (United States)

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.

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.

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

Non-linear finite element analysis of reinforced concrete members and punching shear strength of HSC slabs

Directory of Open Access Journals (Sweden)

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.

Finite element analysis of an underground protective test station subjected to severe ground motion

International Nuclear Information System (INIS)

Burchett, S.N.; Milloy, J.A.; Von Riesemann, W.A.

1974-01-01

A recoverable test station, to be used at a location very close to the detonation point of an underground nuclear test, was designed and tested. The design required that the station survive the very severe free-field stress and that the acceleration of the station be limited to a tolerable level. The predicted magnitude and time history of the free-field stress and acceleration indicated that the volcanic tuff medium and the materials of the proposed structure would exhibit nonlinear behavior, so that a transient dynamic analysis of a composite type structure involving nonlinear materials and large deformations was necessary. Parameter studies using a linear elastic dynamic finite element technique were first done to gain an understanding of the effect of the material properties and to study the response of various configurations of the protective structure to the transient loading. Based upon the results of these parameter studies and upon fielding considerations, a tentative design was chosen. This design was then evaluated using a newly developed finite element computer program. The results obtained from this analysis are compared to the field test results. (U.S.)

Analysis of Blood Flow Through a Viscoelastic Artery using the Cosserat Continuum with the Large-Amplitude Oscillatory Shear Deformation Model

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....

Calculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method

Science.gov (United States)

Agapov, Vladimir; Golovanov, Roman; Aidemirov, Kurban

2017-10-01

The technique of calculation of prestressed reinforced concrete trusses with taking into account geometrical and physical nonlinearity is considered. As a tool for solving the problem, the finite element method has been chosen. Basic design equations and methods for their solution are given. It is assumed that there are both a prestressed and nonprestressed reinforcement in the bars of the trusses. The prestress is modeled by setting the temperature effect on the reinforcement. The ways of taking into account the physical and geometrical nonlinearity for bars of reinforced concrete trusses are considered. An example of the analysis of a flat truss is given and the behavior of the truss on various stages of its loading up to destruction is analyzed. A program for the analysis of flat and spatial concrete trusses taking into account the nonlinear deformation is developed. The program is adapted to the computational complex PRINS. As a part of this complex it is available to a wide range of engineering, scientific and technical workers

On measurement of the acoustic nonlinearity parameter using the finite amplitude insertion substitution (FAIS) technique

Science.gov (United States)

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

Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects

Directory of Open Access Journals (Sweden)

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.

Influence of Installation Effects on Pile Bearing Capacity in Cohesive Soils – Large Deformation Analysis Via Finite Element Method

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.

Nonlinear elasticity in resonance experiments

Science.gov (United States)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

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.

Creep model of unsaturated sliding zone soils and long-term deformation analysis of landslides

Science.gov (United States)

Zou, Liangchao; Wang, Shimei; Zhang, Yeming

2015-04-01

Sliding zone soil is a special soil layer formed in the development of a landslide. Its creep behavior plays a significant role in long-term deformation of landslides. Due to rainfall infiltration and reservoir water level fluctuation, the soils in the slide zone are often in unsaturated state. Therefore, the investigation of creep behaviors of the unsaturated sliding zone soils is of great importance for understanding the mechanism of the long-term deformation of a landslide in reservoir areas. In this study, the full-process creep curves of the unsaturated soils in the sliding zone in different net confining pressure, matric suctions and stress levels were obtained from a large number of laboratory triaxial creep tests. A nonlinear creep model for unsaturated soils and its three-dimensional form was then deduced based on the component model theory and unsaturated soil mechanics. This creep model was validated with laboratory creep data. The results show that this creep model can effectively and accurately describe the nonlinear creep behaviors of the unsaturated sliding zone soils. In order to apply this creep model to predict the long-term deformation process of landslides, a numerical model for simulating the coupled seepage and creep deformation of unsaturated sliding zone soils was developed based on this creep model through the finite element method (FEM). By using this numerical model, we simulated the deformation process of the Shuping landslide located in the Three Gorges reservoir area, under the cycling reservoir water level fluctuation during one year. The simulation results of creep displacement were then compared with the field deformation monitoring data, showing a good agreement in trend. The results show that the creeping deformations of landslides have strong connections with the changes of reservoir water level. The creep model of unsaturated sliding zone soils and the findings obtained by numerical simulations in this study are conducive to

WHAMSE: a program for three-dimensional nonlinear structural dynamics

International Nuclear Information System (INIS)

Belytschko, T.; Tsay, C.S.

1982-02-01

WHAMSE is a computer program for the nonlinear, transient analysis of structures. The formulation includes both geometric and material nonlinearities, so problems with large displacements and elastic-plastic behavior can be treated. Explicit time integration is used, so the program is most suitable for implusive loads. Energy balance calculations are provided to check numerical stability. The mass matrix is lumped. A finite element format is used for the description of the problem geometry, so the program is quite versatile in treating complex engineering structures. The following elements are included: a triangular element for thin plates and shells, a beam element, a spring element and a rigid body. Mesh generation features are provided to simplify program input. Other features of the program are: (1) a restart capability; (2) a variety of output options, such as printer plots or CALCOMP plots of selected time histories, picture (snapshot) output, and CALCOMP plots of the undeformed and deformed structure

Nonlinear deformation of skeletal muscles in a passive state and in isotonic contraction

Science.gov (United States)

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.

Non-linear finite element analysis in structural mechanics

CERN Document Server

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.

NONINVASIVE DETERMINATION OF KNEE CARTILAGE DEFORMATION DURING JUMPING

Directory of Open Access Journals (Sweden)

Djordje Kosanic

2009-12-01

Full Text Available The purpose of this investigation was to use a combination of image processing, force measurements and finite element modeling to calculate deformation of the knee cartilage during jumping. Professional athletes performed jumps analyzed using a force plate and high-speed video camera system. Image processing was performed on each frame of video using a color recognition algorithm. A simplified mass-spring-damper model was utilized for determination of global force and moment on the knee. Custom software for fitting the coupling characteristics was created. Simulated results were used as input data for the finite element calculation of cartilage deformation in the athlete's knee. Computer simulation data was compared with the average experimental ground reaction forces. The results show the three-dimensional mechanical deformation distribution inside the cartilage volume. A combination of the image recognition technology, force plate measurements and the finite element cartilage deformation in the knee may be used in the future as an effective noninvasive tool for prediction of injury during jumping

Coupled distinct element-finite element numerical modelling of fluid circulation in deforming sedimentary basins.

Science.gov (United States)

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

Dynamics and rheology of finitely extensible polymer coils: An overview

Science.gov (United States)

Yao, Donggang

2017-05-01

One contemporary research issue in non-Newtonian fluid mechanics is to accurately and effectively model viscoelastic polymer flow of practical relevance. In the past several years, we have been working on the formulation of a finitely extensible coil model for polymer flow, particularly including these elements: (1) decoupled equations for kinematical and dynamical variables, (2) logarithmic relaxation at large deformation, (3) rotational retardation, (4) controllable straining, and (5) finite stretch. In this paper, we provide a constructive overview of this nonlinear coil formulation focusing on integration of these elements in a single, unified constitutive model with a minimal number of model parameters that are linked with corresponding physical processes. We also use this opportunity to share the rationale and thought process in the model development. In one particular implement of the general formulation, three parameters are used to tackle with the principal dynamics of a deforming polymer coil: one for finite stretch dictated by a ceiling stretch of the coil, the second one for rotational recovery/retardation, and the third one for adjusting stretch hardening of the rubbery coil. The new model, even in a single mode, is able to simultaneously predict practical material functions in simple shear and coaxial extension and to fit well to representative experimental data. Particularly in the steady-state (or quasi-steady state) flow case, a nearly closed-form stress to velocity gradient relationship can be derived with which shear thinning and elongational thickening can be simultaneously considered while computational advantages of a classical GNF model is retained. The model also fits reasonably well to representative experimental transient data for both shear and extension.

Local and global deformations in a strain-stiffening fibrin gel

Energy Technology Data Exchange (ETDEWEB)

Wen Qi [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States); Basu, Anindita [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States); Winer, Jessamine P [Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia, PA 19104 (United States); Yodh, Arjun [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States); Janmey, Paul A [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States)

2007-11-15

Extracellular matrices composed of filamentous biopolymers like collagen and fibrin have viscoelastic properties that differ from those of rubberlike elastomers or hydrogels formed by flexible polymers. Compared to flexible polymer gels, filamentous biopolymer networks generally have larger elastic moduli, a striking increase in elastic modulus with increasing strain, and a pronounced negative normal stress when deformed in simple shear. All three of these unusual features can be accounted for by a theory that extends concepts of entropic elasticity to a regime where the polymer chains are already significantly extended in the absence of external forces because of their finite bending stiffness. An essential assumption of the theories that relate microscopic structural parameters such as persistence length and mesh size of biopolymer gels to their macroscopic rheology is that the deformation of these materials is affine: that is, the macroscopic strain of the bulk material is equal to the local strain within the material at each point. The validity of this assumption for the dilute open meshworks of most biopolymer gels has been experimentally tested by embedding micron diameter fluorescent beads within the networks formed by fibrin and quantifying their displacements as the macroscopic samples are deformed in a rheometer. Measures of non-affine deformation are small at small strains and decrease as strain increases and the sample stiffens. These results are consistent with the entropic model for non-linear elasticity of semiflexible polymer networks and show that strain-stiffening does not require non-affine deformations.

Deformation behavior of carbon-fiber reinforced shape-memory-polymer composites used for deployable structures (Conference Presentation)

Science.gov (United States)

Lan, Xin; Liu, Liwu; Li, Fengfeng; Pan, Chengtong; Liu, Yanju; Leng, Jinsong

2017-04-01

Shape memory polymers (SMPs) are a new type of smart material, they perform large reversible deformation with a certain external stimulus (e.g., heat and electricity). The properties (e.g., stiffness, strength and other mechanically static or quasi-static load-bearing capacity) are primarily considered for conventional resin-based composite materials which are mainly used for structural materials. By contrast, the mechanical actuating performance with finite deformation is considered for the shape memory polymers and their composites which can be used for both structural materials and functional materials. For shape memory polymers and their composites, the performance of active deformation is expected to further promote the development in smart active deformation structures, such as deployable space structures and morphing wing aircraft. The shape memory polymer composites (SMPCs) are also one type of High Strain Composite (HSC). The space deployable structures based on carbon fiber reinforced shape memory polymer composites (SMPCs) show great prospects. Considering the problems that SMPCs are difficult to meet the practical applications in space deployable structures in the recent ten years, this paper aims to research the mechanics of deformation, actuation and failure of SMPCs. In the overall view of the shape memory polymer material's nonlinearity (nonlinearity and stress softening in the process of pre-deformation and recovery, relaxation in storage process, irreversible deformation), by the multiple verifications among theory, finite element and experiments, one obtains the deformation and actuation mechanism for the process of "pre-deformation, energy storage and actuation" and its non-fracture constraint domain. Then, the parameters of SMPCs will be optimized. Theoretical analysis is realized by the strain energy function, additionally considering the interaction strain energy between the fiber and the matrix. For the common resin-based or soft

Formulation of stiffness equation for a three-dimensional isoparametric element with elastic-plastic material and large deformation

International Nuclear Information System (INIS)

Chang, T.Y.; Prachuktam, S.; Reich, M.

1975-01-01

The formulation of the stiffness equation for an 8 to 21 node isoparametric element with elastic-plastic material and large deformation is presented. The formulation has been implemented in a nonlinear finite element program for the analysis of three-dimensional continuums. To demonstrate the utility of the formulation, a thick-walled cylinder was analyzed and the results are compared favorably with a known solution. The element type presented can be applied not only to 3-D continuums, but also to plate or shell structures, for which degenerated isoparametric elements may be used

Finite element method used in strength calculations of nuclear power plant pressure vessels

International Nuclear Information System (INIS)

Hanulak, E.

1987-01-01

A software system based on the use of the finite element method in linear and nonlinear elastomechanics was developed for assessing the strength and service life of steam generators and pressurizers for WWER type nuclear power plants. The individual programs are briefly described. They are written in FORTRAN IV, some modules are in ASSEMBLER. Programs EGUSAP, NEANKO, ROSYNA are designed for the calculation of stress and deformation, programs ROSYNA, NEANKO and NTEPLO are used for the calculation of temperature fields. Programs SPOJ and STATES are used for assessing the strength and service life of screw joints and other nodes of the WWER-440 type steam generators and pressurizers. (Z.M.)

Nonlinear micromechanics-based finite element analysis of the interfacial behaviour of FRP-strengthened reinforced concrete beams

Science.gov (United States)

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

A finite element study on the effects of toughness and permanent out-of-plane deformation on post-impact compressive strength

OpenAIRE

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...

Deformation of two-phase aggregates using standard numerical methods

Science.gov (United States)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

An optimal approach to active damping of nonlinear vibrations in composite plates using piezoelectric patches

International Nuclear Information System (INIS)

Saviz, M R

2015-01-01

In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain–displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman–type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations. (paper)

Toward transient finite element simulation of thermal deformation of machine tools in real-time

Science.gov (United States)

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.

A finite element method with contact for tensile analysis in fuel rods

International Nuclear Information System (INIS)

Tanajura, C.A.S.; Galeao, A.C.N.R.

1987-01-01

Elements for mechanical analysis of fuel rod of a PWR type reactor, are presented. The rod, consists basically in a cylindrical coating of zircalloy which contains pilling of UO 2 pellets, is submitted to strong internal and external pressures, intense temperature gradients and neutron flux. These conditions lead several phenomena in the pellet (swelling, fracture, densification, creep) and in the cladding (embrittlement, corrosion, creep) which undergo deformations leading them to contact the restriction for the interpenetration is included in the problem without restriction by Lagrange multipliers. Considering a non-linear problem, due to the surface of contact to be not known a priori, the numerical solutions were obtained using the finite element method. (M.C.K.) [pt

Crack Tip Creep Deformation Behavior in Transversely Isotropic Materials

International Nuclear Information System (INIS)

Ma, Young Wha; Yoon, Kee Bong

2009-01-01

Theoretical mechanics analysis and finite element simulation were performed to investigate creep deformation behavior at the crack tip of transversely isotropic materials under small scale creep (SCC) conditions. Mechanical behavior of material was assumed as an elastic-2 nd creep, which elastic modulus ( E ), Poisson's ratio (v ) and creep stress exponent ( n ) were isotropic and creep coefficient was only transversely isotropic. Based on the mechanics analysis for material behavior, a constitutive equation for transversely isotropic creep behavior was formulated and an equivalent creep coefficient was proposed under plain strain conditions. Creep deformation behavior at the crack tip was investigated through the finite element analysis. The results of the finite element analysis showed that creep deformation in transversely isotropic materials is dominant at the rear of the crack-tip. This result was more obvious when a load was applied to principal axis of anisotropy. Based on the results of the mechanics analysis and the finite element simulation, a corrected estimation scheme of the creep zone size was proposed in order to evaluate the creep deformation behavior at the crack tip of transversely isotropic creeping materials

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)

Thermoelectrically induced nonlinear free vibration analysis of piezo laminated composite conical shell panel with random fiber orientation

Directory of Open Access Journals (Sweden)

Lal Achchhe

2017-09-01

Full Text Available This paper presents the free vibration response of piezo laminated composite geometrically nonlinear conical shell panel subjected to a thermo-electrical loading. The temperature field is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E2 only. The material properties are assumed to be independent of the temperature and the electric field. The basic formulation is based on higher order shear deformation plate theory (HSDT with von-Karman nonlinearity. A C0 nonlinear finite element method based on direct iterative approach is outlined and applied to solve nonlinear generalized eigenvalue problem. Parametric studies are carried out to examine the effect of amplitude ratios, stacking sequences, cone angles, piezoelectric layers, applied voltages, circumferential length to thickness ratios, change in temperatures and support boundary conditions on the nonlinear natural frequency of laminated conical shell panels. The present outlined approach has been validated with those available results in the literature.

Improving Stiffness-to-weight Ratio of Spot-welded Structures based upon Nonlinear Finite Element Modelling

Science.gov (United States)

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.

Crystal plasticity finite element analysis of deformation behaviour in SAC305 solder joint

Science.gov (United States)

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

COVE-1: a finite difference creep collapse code for oval fuel pin cladding material

International Nuclear Information System (INIS)

Mohr, C.L.

1975-03-01

COVE-1 is a time-dependent incremental creep collapse code that estimates the change in ovality of a fuel pin cladding tube. It uses a finite difference method of solving the differential equations which describe the deflection of the tube walls as a function of time. The physical problem is nonlinear, both with respect to geometry and material properties, which requires the use of an incremental, analytical, path-dependent solution. The application of this code is intended primarily for tubes manufactured from Zircaloy. Therefore, provision has been made to include some of the effects of anisotropy in the flow equations for inelastic incremental deformations. 10 references. (U.S.)

A finite element simulation on transient large deformation and mass diffusion in electrodes for lithium ion batteries

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)

Deformation analysis of rotary combustion engine housings

Science.gov (United States)

Vilmann, Carl

1991-01-01

This analysis of the deformation of rotary combustion engine housings targeted the following objectives: (1) the development and verification of a finite element model of the trochoid housing, (2) the prediction of the stress and deformation fields present within the trochoid housing during operating conditions, and (3) the development of a specialized preprocessor which would shorten the time necessary for mesh generation of a trochoid housing's FEM model from roughly one month to approximately two man hours. Executable finite element models were developed for both the Mazda and the Outboard Marine Corporation trochoid housings. It was also demonstrated that a preprocessor which would hasten the generation of finite element models of a rotary engine was possible to develop. The above objectives are treated in detail in the attached appendices. The first deals with finite element modeling of a Wankel engine center housing, and the second with the development of a preprocessor that generates finite element models of rotary combustion engine center housings. A computer program, designed to generate finite element models of user defined rotary combustion engine center housing geometries, is also included.

Eddy Heat Conduction and Nonlinear Stability of a Darcy Lapwood System Analysed by the Finite Spectral Method

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.

Nonlinear two-fluid hydromagnetic waves in the solar wind: Rotational discontinuity, soliton, and finite-extent Alfven wave train solutions

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

Decomposition of a hierarchy of nonlinear evolution equations

International Nuclear Information System (INIS)

Geng Xianguo

2003-01-01

The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

International Nuclear Information System (INIS)

Scheffold, F; Cardinaux, F; Mason, T G

2013-01-01

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid. (fast track communication)

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

Science.gov (United States)

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.

Tearing mode saturation with finite pressure

International Nuclear Information System (INIS)

Lee, J.K.

1988-01-01

With finite pressure, the saturation of the current-driven tearing mode is obtained in three-dimensional nonlinear resistive magnetohydrodynamic simulations for Tokamak plasmas. To effectively focus on the tearing modes, the perturbed pressure effects are excluded while the finite equilibrium pressure effects are retained. With this model, the linear growth rates of the tearing modes are found to be very insensitive to the equilibrium pressure increase. The nonlinear aspects of the tearing modes, however, are found to be very sensitive to the pressure increase in that the saturation level of the nonlinear harmonics of the tearing modes increases monotonically with the pressure rise. The increased level is associated with enhanced tearing island sizes or increased stochastic magnetic field region. (author)

Implicit three-dimensional finite-element formulation for the nonlinear structural response of reactor components

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

Measuring localized nonlinear components in a circular accelerator with a nonlinear tune response matrix

Directory of Open Access Journals (Sweden)

G. Franchetti

2008-09-01

Full Text Available In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed. We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles. A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.

Earthquake analysis with nonlinear soil-structure interaction and nonlinear supports of components

International Nuclear Information System (INIS)

Hansson, V.

1990-01-01

For the determination of the seismic response of a structure the soil-structure interaction in most cases is modelled by a mass-spring-damper-system. Normally design concepts for components and piping are based on linear calculations and stress limitations. A concept for a reactor building for the HTR 100 consisted of a relatively high structure compared with the dimensions of the foundation. The structure was comparatively deep embedded in the soil, so here the embedment influences significantly the soil-structure interaction. The assembly of reactor vessel, heat exchanger and circulators has a height of about 37 m. Supports are arranged at different levels. Due to temperature deformations of the vessel and of the support constructions small gaps at the supports may only be avoided by complicated constructions of the supports. Nonlinear analyses were performed for soil, building and component with all supports. The finite element analyses used time histories. In order to describe the radiation damping the hysteresis of the soil with 1 percent material damping was considered. Nonlinearities in the interface of soil and foundation and due to gaps and friction at the supports were taken into account. The stiffness of the support constructions influences reactions and accelerations to a high extent. Properly chosen stiffnesses of the support constructions lead to a behaviour similar to linear elastic behaviour. 13 figs

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

KAUST Repository

Copeland, Dylan

2010-10-05

The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

KAUST Repository

Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich

2010-01-01

The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

The application of structural nonlinearity in the development of linearly tunable MEMS capacitors

International Nuclear Information System (INIS)

Shavezipur, M; Khajepour, A; Hashemi, S M

2008-01-01

Electrostatically actuated parallel-plate tunable capacitors are the most desired MEMS capacitors because of their smaller sizes and higher Q-factors. However, these capacitors suffer from low tunability and exhibit high sensitivity near the pull-in voltage which counters the concept of tunability. In this paper, a novel design for parallel-plate tunable capacitors with high tunability and linear capacitance–voltage (C–V) response is developed. The design uses nonlinear structural rigidities to relieve intrinsic electrostatic nonlinearity in MEMS capacitors. Based on the force–displacement characteristic of an ideally linear capacitor, a real beam-like nonlinear spring model is developed. The variable stiffness coefficients of such springs improve the linearity of the C–V curve. Moreover, because the structural stiffness increases with deformations, the pull-in is delayed and higher tunability is achieved. Finite element simulations reveal that capacitors with air gaps larger than 4 µm and supporting beams thinner than 1 µm can generate highly linear C–V responses and tunabilities over 120%. Experimental results for capacitors fabricated by PolyMUMPs verify the effect of weak nonlinear geometric stiffness on improving the tunability for designs with a small air gap and relatively thick structural layers

Material equations for rock salt under mechanical and thermal load including treatment of boundary value problems by the finite element method

International Nuclear Information System (INIS)

Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.

1981-01-01

This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used. (orig./HP) [de

Numerical Modeling of Subglacial Sediment Deformation

DEFF Research Database (Denmark)

Damsgaard, Anders

2015-01-01

may cause mass loss in the near future to exceed current best estimates. Ice flow in larger ice sheets focuses in fast-moving streams due to mechanical non-linearity of ice. These ice streams often move at velocities several magnitudes larger than surrounding ice and consequentially constitute...... glaciers move by deforming their sedimentary beds. Several modern ice streams, in particular, move as plug flows due to basal sediment deformation. An intense and long-winded discussion about the appropriate description for subglacial sediment mechanics followed this discovery, with good reason...... incompatible with commonly accepted till rheology models. Variation in pore-water pressure proves to cause reorganization in the internal stress network and leads to slow creeping deformation. The rate of creep is non-linearly dependent on the applied stresses. Granular creep can explain slow glacial...

Nonlinear analysis of the GFRP material wheel hub

Directory of Open Access Journals (Sweden)

Dong Yun-Feng

2015-01-01

Full Text Available In this paper, the current bicycle wheel was replaced by the ones which composed by the wheel hub with Glassfiber Reinforced Plastic (alkali free thin-walled cylinder material, hereinafter referred to as GFRP material and the protective components made up of rubber outer pneumatic pad. With the help of the basic theory of elastic-plastic mechanics, the finite element “Nonlinear buckling” analysis of the wheel was carried out. The results show that the maximum elastic deformation of the wheel hub and the critical value of buckling failure load were restricted by the elasticity under the condition of external loads. Considering with the tensile strength and elastic modulus of the GFRP value of the material, it is demonstrated that the material is feasible to be used for wheel hub.

Finite field-dependent symmetries in perturbative quantum gravity

International Nuclear Information System (INIS)

Upadhyay, Sudhaker

2014-01-01

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

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.)

A novel method for visualising and quantifying through-plane skin layer deformations.

Science.gov (United States)

Gerhardt, L-C; Schmidt, J; Sanz-Herrera, J A; Baaijens, F P T; Ansari, T; Peters, G W M; Oomens, C W J

2012-10-01

Skin is a multilayer composite and exhibits highly non-linear, viscoelastic, anisotropic material properties. In many consumer product and medical applications (e.g. during shaving, needle insertion, patient re-positioning), large tissue displacements and deformations are involved; consequently large local strains in the skin tissue can occur. Here, we present a novel imaging-based method to study skin deformations and the mechanics of interacting skin layers of full-thickness skin. Shear experiments and real-time video recording were combined with digital image correlation and strain field analysis to visualise and quantify skin layer deformations during dynamic mechanical testing. A global shear strain of 10% was applied to airbrush-patterned porcine skin (thickness: 1.2-1.6mm) using a rotational rheometer. The recordings were analysed with ARAMIS image correlation software, and local skin displacement, strain and stiffness profiles through the skin layers determined. The results of this pilot study revealed inhomogeneous skin deformation, characterised by a gradual transition from a low (2.0-5.0%; epidermis) to high (10-22%; dermis) shear strain regime. Shear moduli ranged from 20 to 130kPa. The herein presented method will be used for more extended studies on viable human skin, and is considered a valuable foundation for further development of constitutive models which can be used in advanced finite element analyses of skin. Copyright © 2012 Elsevier Ltd. All rights reserved.

Formulation and integration of constitutive models describing large deformations in thermoplasticity and thermoviscoplasticity

International Nuclear Information System (INIS)

Jansohn, W.

1997-10-01

This report deals with the formulation and numerical integration of constitutive models in the framework of finite deformation thermomechanics. Based on the concept of dual variables, plasticity and viscoplasticity models exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules are presented. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. In view of the development of an efficient numerical integration procedure, simplified versions of these constitutive models are supposed. In these versions, the thermoelastic strains are assumed to be small and a simplified kinematic hardening rule is considered. Additionally, in view of an implementation into the ABAQUS finite element code, the elasticity law is approximated by a hypoelasticity law. For the simplified onstitutive models, an implicit time-integration algorithm is developed. First, in order to obtain a numerical objective integration scheme, use is made of the HUGHES-WINGET-Algorithm. In the resulting system of ordinary differential equations, it can be distinguished between three differential operators representing different physical effects. The structure of this system of differential equations allows to apply an operator split scheme, which leads to an efficient integration scheme for the constitutive equations. By linearizing the integration algorithm the consistent tangent modulus is derived. In this way, the quadratic convergence of Newton's method used to solve the basic finite element equations (i.e. the finite element discretization of the governing thermomechanical field equations) is preserved. The resulting integration scheme is implemented as a user subroutine UMAT in ABAQUS. The properties of the applied algorithm are first examined by test calculations on a single element under tension-compression-loading. For demonstrating the capabilities of the constitutive theory

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.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

Science.gov (United States)

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

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 ...

Finite element simulations of internal stresses generated during the ferroelastic deformation of NiTi bodies

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.)

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation.

Science.gov (United States)

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.

Analysis of HD Journal Bearings Considering Elastic Deformation and Non-Newtonian Rabinowitsch Fluid Model

Directory of Open Access Journals (Sweden)

J. Javorova

2016-06-01

Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

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.

Quantitative research on microscopic deformation behavior of Ti-6Al-4V two-phase titanium alloy based on finite element method

Science.gov (United States)

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.

Finite-difference analysis of shells impacting rigid barriers

International Nuclear Information System (INIS)

Pirotin, S.D.; Witmer, E.A.

1977-01-01

Nuclear power plants must be protected from the adverse effects of missile impacts. A significant category of missile impact involves deformable structures (pressure vessel components, whipping pipes) striking relatively rigid targets (concrete walls, bumpers) which act as protective devices. The response and interaction of these structures is needed to assess the adequacy of these barriers for protecting vital safety related equipment. The present investigation represents an initial attempt to develop an efficient numerical procedure for predicting the deformations and impact force time-histories of shells which impact upon a rigid target. The general large-deflection equations of motion of the shell are expressed in finite-difference form in space and integrated in time through application of the central-difference temporal operator. The effect of material nonlinearities is treated by a mechanical sublayer material model which handles the strain-hardening, Bauschinger, and strain-rate effects. The general adequacy of this shell treatment has been validated by comparing predictions with the results of various experiments in which structures have been subjected to well-defined transient forcing functions (typically high-explosive impulse loading). The 'new' ingredient addressed in the present study involves an accounting for impact interaction and response of both the target structure and the attacking body. (Auth.)

Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

Science.gov (United States)

Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

2018-02-01

In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

A finite element evaluation of mechanical function for 3 distal extension partial dental prosthesis designs with a 3-dimensional nonlinear method for modeling soft tissue.

Science.gov (United States)

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.

Linear and Nonlinear Finite Elements.

Science.gov (United States)

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 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Stiffness design of geometrically nonlinear structures using topology optimization

DEFF Research Database (Denmark)

Buhl, Thomas; Pedersen, Claus B. Wittendorf; Sigmund, Ole

2000-01-01

of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective......The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities...... functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear...

Shape Changing Nonlocal Molecular Deformations in a Nematic Liquid Crystal

International Nuclear Information System (INIS)

Kavitha, L.; Venkatesh, M.; Gopi, D.

2010-07-01

The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformation mapped onto an integro-differential perturbed Nonlinear Schroedinger equation which includes the nonlocal term. By invoking the modified extended tangent hyperbolic function method aided with symbolic computation, we obtain a series of solitary wave solutions. Under the influence of the nonlocality induced by the reorientation nonlinearity due to fluctuations in the molecular orientation, the solitary wave exhibits shape changing property for different choices of parameters. This intriguing property, as a result of the relation between the coherence of the solitary deformation and the nonlocality, reveals a strong need for deeper understanding in the theory of self-localization in NLC systems. (author)

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....

Corneal biomechanical properties from air-puff corneal deformation imaging

Science.gov (United States)

Marcos, Susana; Kling, Sabine; Bekesi, Nandor; Dorronsoro, Carlos

2014-02-01

The combination of air-puff systems with real-time corneal imaging (i.e. Optical Coherence Tomography (OCT), or Scheimpflug) is a promising approach to assess the dynamic biomechanical properties of the corneal tissue in vivo. In this study we present an experimental system which, together with finite element modeling, allows measurements of corneal biomechanical properties from corneal deformation imaging, both ex vivo and in vivo. A spectral OCT instrument combined with an air puff from a non-contact tonometer in a non-collinear configuration was used to image the corneal deformation over full corneal cross-sections, as well as to obtain high speed measurements of the temporal deformation of the corneal apex. Quantitative analysis allows direct extraction of several deformation parameters, such as apex indentation across time, maximal indentation depth, temporal symmetry and peak distance at maximal deformation. The potential of the technique is demonstrated and compared to air-puff imaging with Scheimpflug. Measurements ex vivo were performed on 14 freshly enucleated porcine eyes and five human donor eyes. Measurements in vivo were performed on nine human eyes. Corneal deformation was studied as a function of Intraocular Pressure (IOP, 15-45 mmHg), dehydration, changes in corneal rigidity (produced by UV corneal cross-linking, CXL), and different boundary conditions (sclera, ocular muscles). Geometrical deformation parameters were used as input for inverse finite element simulation to retrieve the corneal dynamic elastic and viscoelastic parameters. Temporal and spatial deformation profiles were very sensitive to the IOP. CXL produced a significant reduction of the cornea indentation (1.41x), and a change in the temporal symmetry of the corneal deformation profile (1.65x), indicating a change in the viscoelastic properties with treatment. Combining air-puff with dynamic imaging and finite element modeling allows characterizing the corneal biomechanics in-vivo.

Finite element computational fluid mechanics

International Nuclear Information System (INIS)

Baker, A.J.

1983-01-01

This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows

An Efficient Virtual Trachea Deformation Model

Directory of Open Access Journals (Sweden)

Cui Tong

2016-01-01

Full Text Available In this paper, we present a virtual tactile model with the physically based skeleton to simulate force and deformation between a rigid tool and the soft organ. When the virtual trachea is handled, a skeleton model suitable for interactive environments is established, which consists of ligament layers, cartilage rings and muscular bars. In this skeleton, the contact force goes through the ligament layer, and produces the load effects of the joints , which are connecting the ligament layer and cartilage rings. Due to the nonlinear shape deformation inside the local neighbourhood of a contact region, the RBF method is applied to modify the result of linear global shape deformation by adding the nonlinear effect inside. Users are able to handle the virtual trachea, and the results from the examples with the mechanical properties of the human trachea are given to demonstrate the effectiveness of the approach.

Micromechanics of deformation of metallic-glass-matrix composites from in situ synchrotron strain measurements and finite element modeling

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

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...

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

International Nuclear Information System (INIS)

Li Qing; Wang Tianshu; Ma Xingrui

2009-01-01

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems

Differential Calculus on h-Deformed Spaces

Science.gov (United States)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

Directory of Open Access Journals (Sweden)

Adailton S. Borges

Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.

Three-Dimensional Nonlinear Finite Element Analysis and Microcomputed Tomography Evaluation of Microgap Formation in a Dental Implant Under Oblique Loading.

Science.gov (United States)

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.

Deformation of nanotubes in peeling contact with flat substrate: An in situ electron microscopy nanomechanical study

Energy Technology Data Exchange (ETDEWEB)

Chen, Xiaoming; Zheng, Meng; Wei, Qing; Ke, Changhong, E-mail: cke@binghamton.edu [Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, New York 13902-6000 (United States); Signetti, Stefano [Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento (Italy); Pugno, Nicola M. [Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento (Italy); Centre for Materials and Microsystems, Fondazione Bruno Kessler, Povo (Trento) (Italy); School of Engineering and Materials Science, Queen Mary University of London, London (United Kingdom)

2016-04-21

Peeling of one-dimensional (1D) nanostructures from flat substrates is an essential technique in studying their adhesion properties. The mechanical deformation of the nanostructure in the peeling experiment is critical to the understanding of the peeling process and the interpretation of the peeling measurements, but it is challenging to measure directly and quantitatively at the nanoscale. Here, we investigate the peeling deformation of a bundled carbon nanotube (CNT) fiber by using an in situ scanning electron microscopy nanomechanical peeling technique. A pre-calibrated atomic force microscopy cantilever is utilized as the peeling force sensor, and its back surface acts as the peeling contact substrate. The nanomechanical peeling scheme enables a quantitative characterization of the deformational behaviors of the CNT fiber in both positive and negative peeling configurations with sub-10 nm spatial and sub-nN force resolutions. Nonlinear continuum mechanics models and finite element simulations are employed to interpret the peeling measurements. The measurements and analysis reveal that the structural imperfections in the CNT fiber may have a substantial influence on its peeling deformations and the corresponding peeling forces. The research findings reported in this work are useful to the study of mechanical and adhesion properties of 1D nanostructures by using nanomechanical peeling techniques.

A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach

KAUST Repository

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.

A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach

KAUST Repository

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.

Introduction to nonlinear acoustics

Science.gov (United States)

Bjørnø, Leif

2010-01-01

A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

Liu, Lili; Wu, Xiaozhi; Wang, Rui; Gan, Liyong; Wei, Qunyi

2014-01-01

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

Liu, Lili

2014-05-22

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

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

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

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

Collapse in a forced three-dimensional nonlinear Schrodinger equation

DEFF Research Database (Denmark)

Lushnikov, P.M.; Saffman, M.

2000-01-01

We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....

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.

Robust Finite-Time Terminal Sliding Mode Control for a Francis Hydroturbine Governing System

OpenAIRE

Fengjiao Wu; Junling Ding; Zhengzhong Wang

2016-01-01

The robust finite-time control for a Francis hydroturbine governing system is investigated in this paper. Firstly, the mathematical model of a Francis hydroturbine governing system is presented and the nonlinear vibration characteristics are analyzed. Then, on the basis of finite-time control theory and terminal sliding mode scheme, a new robust finite-time terminal sliding mode control method is proposed for nonlinear vibration control of the hydroturbine governing system. Furthermore, the d...

Twist operators in N=4 beta-deformed theory

NARCIS (Netherlands)

de Leeuw, M.; Łukowski, T.

2010-01-01

In this paper we derive both the leading order finite size corrections for twist-2 and twist-3 operators and the next-to-leading order finite-size correction for twist-2 operators in beta-deformed SYM theory. The obtained results respect the principle of maximum transcendentality as well as

Real analytic solutions for marginal deformations in open superstring field theory

International Nuclear Information System (INIS)

Okawa, Yuji

2007-01-01

We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction