Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Non-linear finite element modeling
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Linear and Nonlinear Finite Elements.
1983-12-01
Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y , (1-y)’ 1-y’ 2 - y" (6) that change eq. (5) to V) = , [yŖ(1 + y") - Qy
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Nonlinear finite element analysis of concrete structures
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)
Finite element model for nonlinear shells of revolution
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 analysis of nonlinear creeping flows
Loula, A.F.D.; Guerreiro, J.N.C.
1988-12-01
Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Advances in dynamic relaxation techniques for nonlinear finite element analysis
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
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.
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
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.
Nonlinear finite element analyses: advances and challenges in dental applications.
Wakabayashi, N; Ona, M; Suzuki, T; Igarashi, Y
2008-07-01
To discuss the development and current status of application of nonlinear finite element method (FEM) in dentistry. The literature was searched for original research articles with keywords such as nonlinear, finite element analysis, and tooth/dental/implant. References were selected manually or searched from the PUBMED and MEDLINE databases through November 2007. The nonlinear problems analyzed in FEM studies were reviewed and categorized into: (A) nonlinear simulations of the periodontal ligament (PDL), (B) plastic and viscoelastic behaviors of dental materials, (C) contact phenomena in tooth-to-tooth contact, (D) contact phenomena within prosthodontic structures, and (E) interfacial mechanics between the tooth and the restoration. The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress-strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model. The definition of contact area critically affects the reliability of the contact analyses, especially for implant-abutment complexes. To predict the failure risk of a bonded tooth-restoration interface, it is essential to assess the normal and shear stresses relative to the interface. The inclusion of viscoelasticity and plastic deformation to the program to account for the time-dependent, thermal sensitive, and largely deformable nature of dental materials would enhance its application. Further improvement of the nonlinear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Nonlinear magnetohydrodynamics simulation using high-order finite elements
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.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin; Carrillo, José
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
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.
Finite element solution of quasistationary nonlinear magnetic field
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
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Nonlinear Finite Element Analysis of Reinforced Concrete Shells
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.
Nonlinear Finite Element Analysis of Pull-Out Test
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region...
Nonlinear nonstationary analysis with the finite element method
Vaz, L.E.
1981-01-01
In this paper, after some introductory remarks on numerical methods for the integration of initial value problems, the applicability of the finite element method for transient diffusion analysis as well as dynamic and inelastic analysis is discussed, and some examples are presented. (RW) [de
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
Jokhio, G. A.; Izzuddin, B. A.
2015-05-01
This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.
Material model for non-linear finite element analyses of large concrete structures
Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.
2016-01-01
A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
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...
Finite elements for non-linear analysis of pipelines
Benjamim, A.C.; Ebecken, N.F.F.
1982-01-01
The application of a three-dimensional lagrangian formulation for the great dislocations analysis and great rotation of pipelines systems is studied. This formulation is derived from the soil mechanics and take into account the shear stress effects. Two finite element models are implemented. The first, of right axis, uses as interpolation functions the conventional gantry functions, defined in relation to mobile coordinates. The second, of curve axis and variable cross sections, is obtained from the degeneration of the three-dimensional isoparametric element, and uses as interpolation functions third degree polynomials. (E.G.) [pt
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
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.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells
Humberto Breves Coda
2009-01-01
Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
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.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH
Q. A. HASAN
2017-11-01
Full Text Available The paper presents Finite Element Analysis to determine the ultimate shear capacity of tapered composite plate girder. The effect of degree of taper on the ultimate shear capacity of tapered steel-concrete composite plate girder with a nonlinear varying web depth, effect of slenderness ratio on the ultimate shear capacity, and effect of flange stiffness on the ductility were considered as the parametric studies. Effect of concrete slab on the ultimate shear capacity of tapered plate girders was also considered and it was found to be so effective on the ultimate shear capacity of the tapered plate girder compared with the steel one. The accuracy of the finite element method is established by comparing the finite element with the results existing in the literature. The study was conducted using nonlinear finite element modelling with computer software LUSAS 14.7.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu
2011-01-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.; Langer, U.
2010-01-01
of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series
A finite element model for nonlinear shells of revolution
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.)
Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures
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.
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.
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
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.
Non-linear finite element analyses applicable for the design of large reinforced concrete structures
Engen, M; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik
2017-01-01
In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises
Modal representation of geometrically nonlinear behavior by the finite element method
Nagy, D.A.
1977-01-01
A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. (Auth.)
Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine
Wong, Christian; Gehrchen, P Martin; Darvann, Tron
2003-01-01
A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompressible nucleus surrounded by nonlinear annulus fibe...
Nonlinear finite element analysis of reinforced and prestressed concrete shells with edge beams
Srinivasa Rao, P.; Duraiswamy, S.
1994-01-01
The structural design of reinforced and prestressed concrete shells demands the application of nonlinear finite element analysis (NFEM) procedures to ensure safety and serviceability. In this paper the details of a comprehensive NFEM program developed are presented. The application of the program is highlighted by solving two numerical problems and comparing the results with experimental results. (author). 20 refs., 15 figs
COYOTE: a finite element computer program for nonlinear heat conduction problems
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
Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio
Chang, T. Y.; Sawamiphakdi, K.
1984-01-01
A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.
Nonlinear Finite Element Analysis of a General Composite Shell
1988-12-01
for (t) in Equation (B.15) (Appendix B) and writes it as a function of displacements for I the nonlinear problem one obtains [8] 3 29 (*(a)) - [K(a...linked to the main program before execution. Isubroutine upress(t,pa,pb,iunit, ielt ,x,y,z,live,press) c c Pressure distribution subroutine for c...then compiled and linked to the main program before execution. I SUBROUTINE UPRESS(T,PA,PB,IUNIT, IELT ,X,Y,Z,LIVE,PRESS) C c Pressure distribution
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
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
Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)
2006-04-01
In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.
Research of carbon composite material for nonlinear finite element method
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
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.
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
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)
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)
Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.
Shang, Xituan; Yen, Michael R T; Gaber, M Waleed
2010-06-01
The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.
Modal representation of geometrically nonlinear behavior by the finite element method
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
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.
Non-linear shape functions over time in the space-time finite element method
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.
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
Clausen, Johan; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...
Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model
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.
ABAQUS/EPGEN - a general purpose finite element code with emphasis on nonlinear applications
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.)
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.
Hawileh, Rami A.; El-Maaddawy, Tamer A.; Naser, Mohannad Z.
2012-01-01
Highlights: ► A 3D nonlinear FE model is developed of RC deep beams with web openings. ► We used cohesion elements to simulate bond. ► The developed FE model is suitable for analysis of such complex structures. -- Abstract: This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.
Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames
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.
An axisymmetrical non-linear finite element model for induction heating in injection molding tools
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...
Nonlinear finite element formulation for analyzing shape memory alloy cylindrical panels
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
FEAST: a two-dimensional non-linear finite element code for calculating stresses
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%
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.
Compatible-strain mixed finite element methods for incompressible nonlinear elasticity
Faghih Shojaei, Mostafa; Yavari, Arash
2018-05-01
We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.
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)
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated...... as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis
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
Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory
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
Frost heave modelling of buried pipelines using non-linear Fourier finite elements
Wan, R. G.; You, R.
1998-01-01
Numerical analysis of the response of a three-dimensional soil-pipeline system in a freezing environment using non-linear Fourier finite elements was described as an illustration of the effectiveness of this technique in analyzing plasticity problems. Plastic deformations occur when buried pipeline is under the action of non-uniform frost heave. The three-dimensional frost heave which develops over time including elastoplastic deformations of the soil and pipe are computed. The soil heave profile obtained in the numerical analysis was consistent with experimental findings for similar configurations. 8 refs., 8 figs
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
Whiteley, J. P.
2017-10-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
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.
Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.
Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen
2008-08-01
Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
A nonlinear finite element model of a piezoelectric tube actuator with hysteresis and creep
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
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet
2012-02-01
Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
Solving nonlinear nonstationary problem of heat-conductivity by finite element method
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
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 time-domain finite element model reduction method for viscoelastic linear and nonlinear systems
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.
A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems
Gambolati, Giuseppe; Teatini, Pietro
1996-01-01
A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.
Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K
2014-06-01
Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently
Espath, L. F R; Braun, Alexandre Luis; Awruch, Armando Miguel; Dalcin, Lisandro
2015-01-01
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Espath, L. F R
2015-02-03
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
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].
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.
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
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....
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...
Nonlinear finite element analysis of liquid sloshing in complex vehicle motion scenarios
Nicolsen, Brynne; Wang, Liang; Shabana, Ahmed
2017-09-01
The objective of this investigation is to develop a new total Lagrangian continuum-based liquid sloshing model that can be systematically integrated with multibody system (MBS) algorithms in order to allow for studying complex motion scenarios. The new approach allows for accurately capturing the effect of the sloshing forces during curve negotiation, rapid lane change, and accelerating and braking scenarios. In these motion scenarios, the liquid experiences large displacements and significant changes in shape that can be captured effectively using the finite element (FE) absolute nodal coordinate formulation (ANCF). ANCF elements are used in this investigation to describe complex mesh geometries, to capture the change in inertia due to the change in the fluid shape, and to accurately calculate the centrifugal forces, which for flexible bodies do not take the simple form used in rigid body dynamics. A penalty formulation is used to define the contact between the rigid tank walls and the fluid. A fully nonlinear MBS truck model that includes a suspension system and Pacejka's brush tire model is developed. Specified motion trajectories are used to examine the vehicle dynamics in three different scenarios - deceleration during straight-line motion, rapid lane change, and curve negotiation. It is demonstrated that the liquid sloshing changes the contact forces between the tires and the ground - increasing the forces on certain wheels and decreasing the forces on other wheels. In cases of extreme sloshing, this dynamic behavior can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.
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.
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.
Finite element modeling of nanotube structures linear and non-linear models
Awang, Mokhtar; Muhammad, Ibrahim Dauda
2016-01-01
This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.
Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses
Agata, R.; Ichimura, T.; Hyodo, M.; Barbot, S.; Hori, T.
2017-12-01
To explain earthquake generation processes, simulation methods of earthquake cycles have been studied. For such simulations, the combination of the rate- and state-dependent friction law at the fault plane and the boundary integral method based on Green's function in an elastic half space is widely used (e.g. Hori 2009; Barbot et al. 2012). In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, while the effects of complex physics such as mantle rheology and gravity are generally not taken into account. To consider such effects, we seek to develop an earthquake cycle simulation combining crustal deformation computation based on the finite element (FE) method with the rate- and state-dependent friction law. Since the drawback of this approach is the computational cost associated with obtaining numerical solutions, we adopt a recently developed fast and scalable FE solver (Ichimura et al. 2016), which assumes use of supercomputers, to solve the problem in a realistic time. As in the previous approach, we solve the governing equations consisting of the rate- and state-dependent friction law. In solving the equations, we compute stress changes along the fault plane due to crustal deformation using FE simulation, instead of computing them by superimposing slip response function as in the previous approach. In stress change computation, we take into account nonlinear viscoelastic deformation in the asthenosphere. In the presentation, we will show simulation results in a normative three-dimensional problem, where a circular-shaped velocity-weakening area is set in a square-shaped fault plane. The results with and without nonlinear viscosity in the asthenosphere will be compared. We also plan to apply the developed code to simulate the post-earthquake deformation of a megathrust earthquake, such as the 2011 Tohoku earthquake. Acknowledgment: The results were obtained using the K computer at the RIKEN (Proposal number
Kong, Liang; Gu, Zexu; Li, Tao; Wu, Junjie; Hu, Kaijin; Liu, Yanpu; Zhou, Hongzhi; Liu, Baolin
2009-01-01
A nonlinear finite element method was applied to examine the effects of implant diameter and length on the maximum von Mises stresses in the jaw, and to evaluate the maximum displacement of the implant-abutment complex in immediate-loading models. The implant diameter (D) ranged from 3.0 to 5.0 mm and implant length (L) ranged from 6.0 to 16.0 mm. The results showed that the maximum von Mises stress in cortical bone was decreased by 65.8% under a buccolingual load with an increase in D. In cancellous bone, it was decreased by 71.5% under an axial load with an increase in L. The maximum displacement in the implant-abutment complex decreased by 64.8% under a buccolingual load with an increase in D. The implant was found to be more sensitive to L than to D under axial loads, while D played a more important role in enhancing its stability under buccolingual loads. When D exceeded 4.0 mm and L exceeded 11.0 mm, both minimum stress and displacement were obtained. Therefore, these dimensions were the optimal biomechanical selections for immediate-loading implants in type B/2 bone.
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Y. S. Kong
2013-01-01
Full Text Available This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.
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
Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.
A finite element perspective on non-linear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondřejc, J.; Peerlings, R.H.J.; Geers, M.G.D.
2016-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency
A finite element perspective on nonlinear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondrejc, J.; Peerlings, R.H.J.; Geers, M.G.D.
2017-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency
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)
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.
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.
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
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
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.
Extensions to a nonlinear finite element axisymmetric shell model based on Reissner's shell theory
Cook, W.A.
1981-01-01
A finite element shell-of-revolution model has been developed to analyze shipping containers under severe impact conditions. To establish the limits for this shell model, I studied the basic assumptions used in its development; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress. (orig./HP)
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
Gupta, A.; Singh, R.K.; Kushwaha, H.S.; Mahajan, S.C.; Kakodkar, A.
1996-01-01
For safety evaluation of nuclear structures a finite element code ULCA (Ultimate Load Capacity Assessment) has been developed. Eight/nine noded isoparametric quadrilateral plate/shell element with reinforcement as a through thickness discrete but integral smeared layer of the element is presented to analyze reinforced and prestressed concrete structures. Various constitutive models such as crushing, cracking in tension, tension stiffening and rebar yielding are studied and effect of these parameters on the reserve strength of structures is brought out through a number of benchmark tests. A global model is used to analyze the prestressed concrete containment wall of a typical 220 MWe Pressurized Heavy Water Reactor (PHWR) up to its ultimate capacity. This demonstrates the adequacy of Indian PHWR containment design to withstand severe accident loads
Ibrahim Dauda Muhammad
2015-01-01
Full Text Available The single-walled zirconia nanotube is structurally modeled and its Young’s modulus is valued by using the finite element approach. The nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements. The properties of the beam required for input into the finite element analysis were computed by connecting energy equivalence between molecular and continuum mechanics. Simulation was conducted by applying axial tensile strain on one end of the nanotube while the other end was fixed and the corresponding reaction force recorded to compute Young’s modulus. It was found out that Young’s modulus of zirconia nanotubes is significantly affected by some geometrical parameters such as chirality, diameter, thickness, and length. The obtained values of Young’s modulus for a certain range of diameters are in agreement with what was obtained in the few experiments that have been conducted so far. This study was conducted on the cubic phase of zirconia having armchair and zigzag configuration. The optimal diameter and thickness were obtained, which will assist in designing and fabricating bulk nanostructured components containing zirconia nanotubes for various applications.
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
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.
Non-linear finite element analyses of wide plate fracture mechanics experiments
Harrop, L.P.; Gibson, S.
1988-06-01
A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)
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
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.
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.
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.
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
Clausen, Johan
-Coulomb yield criterion and the corresponding plastic potential possess corners and an apex, which causes numerical difficulties. A simple, elegant and efficient solution to these problems is presented in this thesis. The solution is based on a transformation into principal stress space and is valid for all...... linear isotropic plasticity models in which corners and apexes are encountered. The validity and merits of the proposed solution are examined in relation to the Mohr-Coulomb and the Modified Mohr-Coulomb material models. It is found that the proposed method compares well with existing methods......-Brown material. The efficiency and validity are demonstrated by comparing the finite-element results with well-known solutions for simple geometries. A common geotechnical problem is the assessment of slope stability. For slopes with simple geometries and consisting of a linear Mohr-Coulomb material, this can...
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.
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)
Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.
2014-01-01
Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS
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.
Finite element computational fluid mechanics
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
Non-linear heat transfer computer code by finite element method
Nagato, Kotaro; Takikawa, Noboru
1977-01-01
The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)
Analysis of noncoplanar pressurized laminations in X2 steel pipes by non-linear finite element
Morales, Alfredo [Instituto Tecnologico de Puebla (Mexico). Dept. de Posgrado; Gonzalez, Jorge L.; Hallen, Jose M. [Instituto Politecnico Nacional (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE). Dept. de Ingenieria Metalurgica
2005-07-01
Hydrogen induced cracking is of great interest in the mechanical integrity assessment of sour gas pipelines. Multiple stepwise cracks with internal pressure called laminations are often observed in pipelines and their interaction and coalescence may significantly affect the residual strength of the pipes. In this work, the interacting fields of non coplanar pressurized laminations in the wall of a pipe under pressure are analyzed by non-lineal finite element, considering an isotropic hardening law and the real tensile properties of the X52 steel. The results are presented as the evolution of the stress fields in the interlaminar region as a function of the pressure inside the laminations. It is found that for two approaching stepwise laminations the critical pressure follows a hyperbolic type law, thus the effect of the lamination length is principal for greater lengths and for shorter lengths the effect is minimum. The critical pressure is defined as pressure inside the lamination that causes plastification of the interlaminar region. (author)
Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan
2017-09-01
The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.
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.
Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu
2018-04-01
In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.
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.
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.
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)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Townsend, Molly T; Sarigul-Klijn, Nesrin
2016-01-01
Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.
Tayal, M.
1987-01-01
Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated
Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi
In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...
Harmonic balance finite element method applications in nonlinear electromagnetics and power systems
Lu, Junwei; Yamada, Sotoshi
2016-01-01
The first book applying HBFEM to practical electronic nonlinear field and circuit problems * Examines and solves wide aspects of practical electrical and electronic nonlinear field and circuit problems presented by HBFEM * Combines the latest research work with essential background knowledge, providing an all-encompassing reference for researchers, power engineers and students of applied electromagnetics analysis * There are very few books dealing with the solution of nonlinear electric- power-related problems * The contents are based on the authors' many years' research and industry experience; they approach the subject in a well-designed and logical way * It is expected that HBFEM will become a more useful and practical technique over the next 5 years due to the HVDC power system, renewable energy system and Smart Grid, HF magnetic used in DC/DC converter, and Multi-pulse transformer for HVDC power supply * HBFEM can provide effective and economic solutions to R&D product development * Includes Matlab e...
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
Gambolati, G.; Toffolo, F.; Uliana, F.
1984-01-01
A nonlinear finite element model based on the Dupuit-Boussinesq equation of flow in an unconfined aquifer has been developed and applied to simulate the water table fluctuation under the electronuclear plant of the test site of Trino Vercellese (northwestern Italy) in response to the flood event that occurred in the Po River from March 30 to April 4, 1981. The nonlinearity has been overcome by the aid of an efficient iterative linearization technique wherein the model equations are solved by symbolic factorization, numerical factorization, and backward-forward substitution after an optimal preliminary reordering. The model was run for uniform values of aquifer permeability and specific yield within the typical range evidenced for the Trino sands by the early data in our possession. The results show that the maximum water level elevation below the reactor is almost 3 m lower than the corresponding river flood peak even in the most unfavorable conditions, i.e., with the hydraulic conductivity in the upper range, and is rather insensitive to the specific yield values within the plausible interval. The model allowed for an easy evaluation of the effectiveness of the impermeable protection walls and of a possible secondary aquifer recharge from a minor channel. The modeling approach for the analysis of the water table behavior appears to be a very promising tool to help in the structural design of future electronuclear plants
Wachspress, E.
2009-01-01
Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
GPU-based acceleration of computations in nonlinear finite element deformation analysis.
Mafi, Ramin; Sirouspour, Shahin
2014-03-01
The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.
Slope Safety Calculation With A Non-Linear Mohr Criterion Using Finite Element Method
Clausen, Johan; Damkilde, Lars
2005-01-01
Safety factors for soil slopes are calculated using a non-linear Mohr envelope. The often used linear Mohr-Coulomb envelope tends to overestimate the safety as the material parameters are usually determined at much higher stress levels, than those present at slope failure. Experimental data...
E. Çelebi
2012-11-01
Full Text Available The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.
Sato, Yuichi; Kajihara, Shinichi; Kaneko, Yoshio
2011-06-01
This paper presents three-dimensional finite element (FE) analyses of an all-frame model of a three-story reinforced concrete (RC) building damaged in the 1999 Taiwan Chi-Chi Earthquake. Non-structural brick walls of the building acted as a seismic resistant element although their contributions were neglected in the design. Hence, the entire structure of a typical frame was modeled and static and dynamic nonlinear analyses were conducted to evaluate the contributions of the brick walls. However, the results of the analyses were considerably overestimated due to coarse mesh discretizations, which were unavoidable due to limited computer resources. This study corrects the overestimations by modifying (1) the tensile strengths and (2) shear stiffness reduction factors of concrete and brick. The results indicate that brick walls improve frame strength although shear failures are caused in columns shortened by spandrel walls. Then, the effectiveness of three types of seismic retrofits is evaluated. The maximum drift of the first floor is reduced by 89.3%, 94.8%, and 27.5% by Steel-confined, Full-RC, and Full-brick models, respectively. Finally, feasibility analyses of models with soils were conducted. The analyses indicated that the soils elongate the natural period of building models although no significant differences were observed.
A Non-Linear Finite Element Model for the LHC Main Dipole Coil Cross-Section
Pojer, M; Scandale, Walter
2006-01-01
The production of the dipole magnets for the Large Hadron Collider is at its final stage. Nevertheless, some mechanical instabilities are still observed for which no clear explanation has been found yet. A FE modelization of the dipole cold mass cross-section had already been developed at CERN, mainly for magnetic analysis, taking into account conductor blocks and a frictionless behavior. This paper describes a new ANSYSÂ® model of the dipole coil cross-section, featuring individual turns inside conductor blocks, and implementing friction and the mechanical non-linear behavior of insulated cables. Preliminary results, comparison with measurements performed in industry and ongoing developments are discussed.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Damkilde, Lars; Pedersen, Ronnie
2012-01-01
This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...... often show a very slow convergence, and the numerical solutions will in general overestimate the bearing capacity and underestimate the displacements. The examples show that the extended incompatible element behaves much better than the corresponding compatible elements especially for coarse meshes....
Ricoeur, Andreas; Lange, Stephan; Avakian, Artjom
2015-04-01
Magnetoelectric (ME) coupling is an inherent property of only a few crystals exhibiting very low coupling coefficients at low temperatures. On the other hand, these materials are desirable due to many promising applications, e.g. as efficient data storage devices or medical or geophysical sensors. Efficient coupling of magnetic and electric fields in materials can only be achieved in composite structures. Here, ferromagnetic (FM) and ferroelectric (FE) phases are combined e.g. including FM particles in a FE matrix or embedding fibers of the one phase into a matrix of the other. The ME coupling is then accomplished indirectly via strain fields exploiting magnetostrictive and piezoelectric effects. This requires a poling of the composite, where the structure is exposed to both large magnetic and electric fields. The efficiency of ME coupling will strongly depend on the poling process. Besides the alignment of local polarization and magnetization, it is going along with cracking, also being decisive for the coupling properties. Nonlinear ferroelectric and ferromagnetic constitutive equations have been developed and implemented within the framework of a multifield, two-scale FE approach. The models are microphysically motivated, accounting for domain and Bloch wall motions. A second, so called condensed approach is presented which doesn't require the implementation of a spatial discretisation scheme, however still considering grain interactions and residual stresses. A micromechanically motivated continuum damage model is established to simulate degradation processes. The goal of the simulation tools is to predict the different constitutive behaviors, ME coupling properties and lifetime of smart magnetoelectric devices.
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
Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex.
Morales-Orcajo, Enrique; Souza, Thales R; Bayod, Javier; Barbosa de Las Casas, Estevam
2017-11-01
A three-dimensional foot finite element model with actual geometry and non-linear behavior of tendons is presented. The model is intended for analysis of the lower limb tendon forces effect in the inner foot structure. The geometry of the model was obtained from computational tomographies and magnetic resonance images. Tendon tissue was characterized with the first order Ogden material model based on experimental data from human foot tendons. Kinetic data was employed to set the load conditions. After model validation, a force sensitivity study of the five major foot extrinsic tendons was conducted to evaluate the function of each tendon. A synergic work of the inversion-eversion tendons was predicted. Pulling from a peroneus or tibialis tendon stressed the antagonist tendons while reducing the stress in the agonist. Similar paired action was predicted for the Achilles tendon with the tibialis anterior. This behavior explains the complex control motion performed by the foot. Furthermore, the stress state at the plantar fascia, the talocrural joint cartilage, the plantar soft tissue and the tendons were estimated in the early and late midstance phase of walking. These estimations will help in the understanding of the functional role of the extrinsic muscle-tendon-units in foot pronation-supination. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.
How simple can nonlinear finite element modelling be for structural concrete?
Argirova, G.
2014-12-01
Full Text Available This paper discusses on the required level of simplicity for suitable modelling of structural concrete. Traditional equilibrium- based approaches (as strut-and-tie models are too coarse in some cases, as they account for the cracking state of concrete in a sometimes excessively simplified manner. The alternative of complex nonlinear numerical modelling is also not always satisfactory for design as the number of parameters required, their definition and the sensitivity of the structural response to them is complex and requires a high level of experience. Contrary to these approaches, this paper introduces the elastic plastic stress field method. This method is grounded on the theory of plasticity but allows considering deformation compatibility. The results are consistent both in terms of the strength and deformation field of the member. It also has the advantage of requiring only two physical material properties (modulus of elasticity and plastic strength which can be easily determined by designers.Este artículo discute sobre el nivel de sencillez ideal para un análisis no lineal de elementos de hormigón estructural. Los métodos de cálculo basados únicamente en condiciones de equilibrio (como los modelos de bielas-y-tirantes no son siempre adecuados ya que el estado de fisuración del hormigón se considera a veces de una manera excesivamente simplificada. Los análisis no lineales complejos tampoco son siempre adecuados, ya que el número de parámetros requeridos, su definición y la sensibilidad de la respuesta del elemento a sus variaciones requieren una gran experiencia. Como alternativa, se presenta el método de los campos de tensiones elasto-plásticos. Este método se basa en la teoría de la plasticidad pero incorporando condiciones de compatibilidad. Los resultados son coherentes en términos de resistencia y de deformaciones. Además, sólo necesita la definición de dos parámetros mecánicos (módulo de elasticidad y
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.
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
de Wit, A.J.; Akcay-Perdahcioglu, Didem; van den Brink, W.M.; de Boer, Andries; Rolfes, R.; Jansen, E.L.
2011-01-01
Depending on the type of analysis, Finite Element(FE) models of different fidelity are necessary. Creating these models manually is a labor intensive task. This paper discusses a generic approach for generating FE models of different fidelity from a single reference FE model. These different
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.)
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
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
Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol
2010-12-01
Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
Belytschko, Ted; Wing, Kam Liu
1987-01-01
In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.
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.
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
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.
高夫征
2005-01-01
A finite volume element predictor-correetor method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.
Optical Finite Element Processor
Casasent, David; Taylor, Bradley K.
1986-01-01
A new high-accuracy optical linear algebra processor (OLAP) with many advantageous features is described. It achieves floating point accuracy, handles bipolar data by sign-magnitude representation, performs LU decomposition using only one channel, easily partitions and considers data flow. A new application (finite element (FE) structural analysis) for OLAPs is introduced and the results of a case study presented. Error sources in encoded OLAPs are addressed for the first time. Their modeling and simulation are discussed and quantitative data are presented. Dominant error sources and the effects of composite error sources are analyzed.
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.
Probabilistic fracture finite elements
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-05-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
Tonks, M.R.; Williamson, R.; Masson, R.
2015-01-01
The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. While FEM is commonly used to solve solid mechanics equations, it can be applied to a large range of BVPs from many different fields. FEM has been used for reactor fuels modelling for many years. It is most often used for fuel performance modelling at the pellet and pin scale, however, it has also been used to investigate properties of the fuel material, such as thermal conductivity and fission gas release. Recently, the United Stated Department Nuclear Energy Advanced Modelling and Simulation Program has begun using FEM as the basis of the MOOSE-BISON-MARMOT Project that is developing a multi-dimensional, multi-physics fuel performance capability that is massively parallel and will use multi-scale material models to provide a truly predictive modelling capability. (authors)
Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus
2016-04-01
Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation. Copyright © 2015 Elsevier Ltd. All rights reserved.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Massively Parallel Finite Element Programming
Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang
2010-01-01
Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Nieto, Alejandra; Roehl, Holger
2018-03-15
There has been a growing interest in recent years in the assessment of suitable vial/stopper combinations for storage and shipment of frozen drug products. Considering that the glass transition temperature (Tg) of butyl rubber stoppers used in Container Closure Systems (CCS) is between -55°C to -65°C, a storage or shipment temperature of a frozen product below the Tg of the rubber stopper, may require special attention, since below the Tg the rubber becomes more plastic-like and loses its elastic (sealing) characteristics. Thus they risk maintaining Container Closure Integrity (CCI). Given that the rubber regains its elastic properties and reseals after rewarming to ambient temperature, leaks during frozen temperature storage and transportation are transient and the CCI methods used at room temperature conditions are unable to confirm CCI in the frozen state. Hence, several experimental methods have been developed in recent years in order to evaluate CCI at low temperatures. Finite Element (FE) simulations were applied in order to investigate the sealing behaviour of rubber stoppers for the drug product CCS under frozen storage conditions. FE analysis can help reducing the experimental design space and thus number of measurements needed, as they can be used as an ad-on to experimental testing. Several scenarios have been simulated including the effect of thermal history, rubber type, storage time, worst case CCS geometric tolerances and capping pressure. The results of these calculations have been validated with experimental data derived from laboratory experiments (CCI at low temperatures), and a concept for tightness has been developed. It has been concluded that FE simulations have the potential to become a powerful predictive tool towards a better understanding of the influence of cold storage on the rubber sealing properties (and hence on CCI) when dealing with frozen drug products. Copyright © 2018, Parenteral Drug Association.
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.
Sun Feng; Pan Rong
2014-01-01
According to a large-span half-steel-concrete (HSC) composited beam in the composited roof in the HTR-PM, a 1:3 scale specimen is investigated by the static load test. By analyzing the loading, deflection, strain and fracture development of the specimen in the process, studying the mechanical characteristics and failure pattern of such components. The ANSYS finite element software is utilized in this paper to analyze the nonlinearity behavior of the HSC beam specimen, and through comparing the experimental results and the numerical simulation, it can be illustrated that the finite element model can simulate the HSC beam accurately. From the test results, it can be concluded that by means of appropriate shear connection and anchorage length, steel plate and concrete can work together very well and the HSC beam has good load carrying capacity and ductility. These conclusions can serve as a preliminary design reference for the large span half-steel-concrete composite beam in NPP. (author)
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Finite element analysis of inelastic structural behavior
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
Lundström, T; Jonas, T; Volkwein, A
2008-01-01
Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.
On symmetric pyramidal finite elements
Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal
2004-01-01
Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
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
An introduction to the UNCLE finite element scheme
Enderby, J.A.
1983-01-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
A finite element thermohydrodynamic analyis of profile bore bearing
Shah Nor bin Basri
1994-01-01
A finite element-based method is presented for analysing the thermohydrodynamic (THD) behaviour of profile bore bearing. A variational statement for the governing equation is derived and used to formulate a non-linear quadrilateral finite element of serendipity family. The predicted behaviour is compared with experimental evidence where possible and favorable correlation is obtained
An introduction to the UNCLE finite element scheme
Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)
1983-05-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior
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.
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette; Murat, Franç ois; Salgado, Abner
2010-01-01
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and
FINITE ELEMENT ANALYSIS OF STRUCTURES
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Chouaib Labiod
2017-01-01
Full Text Available This paper presents torque ripple reduction with speed control of 8/6 Switched Reluctance Motor (SRM by the determination of the optimal parameters of the turn on, turn off angles Theta_(on, Theta_(off, and the supply voltage using Particle Swarm Optimization (PSO algorithm and steady state Genetic Algorithm (ssGA. With SRM model, there is difficulty in the control relapsed into highly non-linear static characteristics. For this, the Finite Elements Method (FEM has been used because it is a powerful tool to get a model closer to reality. The mechanism used in this kind of machine control consists of a speed controller in order to determine current reference which must be produced to get the desired speed, hence, hysteresis controller is used to compare current reference with current measured up to achieve switching signals needed in the inverter. Depending on this control, the intelligent routing algorithms get the fitness equation from torque ripple and speed response so as to give the optimal parameters for better results. Obtained results from the proposed strategy based on metaheuristic methods are compared with the basic case without considering the adjustment of specific parameters. Optimized results found clearly confirmed the ability and the efficiency of the proposed strategy based on metaheuristic methods in improving the performances of the SRM control considering different torque loads.
Kasahara, Naoto
1997-01-01
Supposing that the nuclear reactor stops on any reason, the temperature of flown out coolant from the reactor core will decrease and the temperature of elements touched with the coolant in the nuclear plant equipments also decreases on response to this. On the other hand, temperature pursuit at non-touched portions is delayed to form a thermal stress due to their temperature difference. In particular, a stress over its yield value at discontinuous portion of structure due to stress concentration generates, which could be thought of possibility to form a creep fatigue crack if repeating such thermal stress under high temperature. The Power Reactor and Nuclear Fuel Development Corporation has developed the transient thermal stress real time simulation code for calculating thermal stress formed within a construction in accompany with temperature changes of the coolant once and at high speed since 1994 FY, and after 1995 FY the development of FEM simulation technique from macroscopic region to microscopic region which set an objective regions from construction level to material texture has been promoted. In future, development of total simulation technique connected both and optimum design technique due to its results will be planned. (G.K.)
Finite element computation of plasma equilibria
Rivier, M.
1977-01-01
The applicability of the finite element method is investigated for the numerical solution of the nonlinear Grad-Shafranov equation with free boundary for the flux function of a plasma at equilibrium. This method is based on the case of variational principles and finite dimensional subspaces whose elements are piecewise polynomial functions obtained by a Lagrange type interpolation procedure over a triangulation of the domain. Two cases of plasma pressure (exponential and quadratic including a vacuum region) were examined. In both cases the nonuniqueness of the solutions was shown in exhibiting a deeper solution in the case of exponential pressure function, and a non-constant solution for a quadratic pressure function. In order to get this ''other'' solution, two linearization methods were tested with two different constraints. Different cross sections are investigated
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Nieto, Alejandra; Roehl, Holger; Brown, Helen; Adler, Michael; Chalus, Pascal; Mahler, Hanns-Christian
2016-01-01
Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against possible contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the container closure system with microorganisms under specified testing conditions. Physical CCI uses surrogate endpoints, such as coloration by dye solution ingress or gas flow (helium leakage testing). In order to correlate microbial CCI and physical CCI test methods and to evaluate the methods' capability to detect a given leak, artificial leaks are being introduced into the container closure system in a variety of different ways. In our study, artificial leaks were generated using inserted copper wires between the glass vial opening and rubber stopper. However, the insertion of copper wires introduces leaks of unknown size and shape. With nonlinear finite element simulations, the aperture size between the rubber stopper and the glass vial was calculated, depending on wire diameter and capping force. The dependency of the aperture size on the copper wire diameter was quadratic. With the data obtained, we were able to calculate the leak size and model leak shape. Our results suggest that the size as well as the shape of the artificial leaks should be taken into account when evaluating critical leak sizes, as flow rate does not, independently, correlate to hole size. Capping force also affected leak size. An increase in the capping force from 30 to 70 N resulted in a reduction of the aperture (leak size) by approximately 50% for all wire diameters. From 30 to 50 N, the reduction was approximately 33%. Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the
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.
An efficient finite element solution for gear dynamics
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.
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN ... the transverse residual stress in the x-direction (σx) had a maximum value of 375MPa ... the finite element method are in fair agreement with the experimental results.
Variational approach to probabilistic finite elements
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1991-08-01
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Structural modeling techniques by finite element method
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
Peridynamic Multiscale Finite Element Methods
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
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.
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.
A finite element code for electric motor design
Campbell, C. Warren
1994-01-01
FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.
Finite element application to global reactor analysis
Schmidt, F.A.R.
1981-01-01
The Finite Element Method is described as a Coarse Mesh Method with general basis and trial functions. Various consequences concerning programming and application of Finite Element Methods in reactor physics are drawn. One of the conclusions is that the Finite Element Method is a valuable tool in solving global reactor analysis problems. However, problems which can be described by rectangular boxes still can be solved with special coarse mesh programs more efficiently. (orig.) [de
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
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.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
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.
A first course in finite elements
Fish, Jacob
2007-01-01
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Why do probabilistic finite element analysis ?
Thacker, Ben H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Finite-Element Software for Conceptual Design
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
Finite element analysis of a finite-strain plasticity problem
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.)
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Luyt, P.C.B.; Theron, N.J.; Pietra, F.
2017-01-01
It is well known that gasket creep-relaxation results in a reduction of contact pressure between the surface of a gasket and the face of a flange over an extended period of time. This reduction may result in the subsequent failure of the circular bolted flange connection due to leakage. In this paper a pair of flat and raised face integral flanges, PN 10 DN 50 (in accordance with the European EN 1092-1 standard), with non-asbestos compressed fibre ring gaskets with aramid and a nitrile rubber binder were considered. Finite element modelling and analyses were done, for both the circular bolted flange configurations, during the seating condition. The results of the finite element analyses were experimentally validated. It was found that the number of bolt tightening increments as well as the time between the bolt tightening increments had a significant impact on the effect which gasket creep-relaxation had after the seating condition. An increase in either the number of bolting increments or the time between the bolting increments will reduce the effect which gasket creep-relaxation has once the bolts had been fastened. Based on these results it is possible to develop an optimisation scheme to minimize the effect which gasket creep-relaxation has on the contact pressure between the face of the flange and the gasket, after seating, by either increasing or decreasing the number of bolt tightening increments or the time between the bolt tightening increments. - Highlights: • Number of bolt tightening increments and time between bolt tightening increments had significant impact on effect of gasket creep-relaxation after the seating condition. • Impact of gasket creep-relaxation during seating and operating phases investigated by means of finite element analysis and experimentally verified. • Possible to develop optimisation scheme to minimize effect ofh gasket creep-relaxation on contact pressure between flange face and gasket. • Knowing the contact pressure is
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
Evaluation of Concrete Cylinder Tests Using Finite Elements
Saabye Ottosen, Niels
1984-01-01
Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete is emplo......Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete...... uniaxial strength the use of geometrically matched loading plates seems to be advantageous. Finally, it is observed that for variations of the element size within limits otherwise required to obtain a realistic analysis, the results are insensitive to the element size....
Books and monographs on finite element technology
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
AUTHOR|(CDS)2067087
In one of its acceptation, the word quench is synonym of destruction. And this is even more consistent with reality in the case of the Large Hadron Collider dipole magnets, whose magnetic field and stored energy are unprecedented: the uncontrolled transition from the superconducting to the resistive state can be the origin of dramatic events. This is why the protection of magnets is so important, and why so many studies and investigations have been carried out on quench origin. The production, cold testing and installation of the 1232 arc dipole magnets is completed. They have fulfilled all the requirements and the operation reliability of these magnets has already been partially confirmed. From an academic standpoint, nevertheless, the anomalous mechanical behaviour, which was sometimes observed during power tests, has not yet been given a clear explanation. The work presented in this thesis aims at providing an instrument to better understand the reasons for such anomalies, by means of finite element modell...
Probabilistic finite elements for fracture mechanics
Besterfield, Glen
1988-01-01
The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Finite element analysis of piezoelectric materials
Lowrie, F.; Stewart, M.; Cain, M.; Gee, M.
1999-01-01
This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)
On higher order pyramidal finite elements
Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.
2011-01-01
Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011
Carvalho, Marco Aurélio; Sotto-Maior, Bruno Salles; Del Bel Cury, Altair Antoninha; Pessanha Henriques, Guilherme Elias
2014-11-01
Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
ANSYS mechanical APDL for finite element analysis
Thompson, Mary Kathryn
2017-01-01
ANSYS Mechanical APDL for Finite Element Analysis provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS. The book is written in a lecture/lab style, and each topic is supported by examples, exercises and suggestions for additional readings in the program documentation. Exercises gradually increase in difficulty and complexity, helping readers quickly gain confidence to independently use the program. This provides a solid foundation on which to build, preparing readers...
Review on Finite Element Method * ERHUNMWUN, ID ...
ADOWIE PERE
ABSTRACT: In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and ... residual procedures, are examples of the direct approach ... The paper centred on the "stiffness and deflection of ...
Finite element bending behaviour of discretely delaminated ...
user
due to their light weight, high specific strength and stiffness properties. ... cylindrical shell roofs respectively using finite element method with centrally located .... where { }ε and { }γ are the direct and shear strains in midplane and { }κ denotes ...
Bibliography for finite elements. [2200 references
Whiteman, J R [comp.
1975-01-01
This bibliography cites almost all of the significant papers on advances in the mathematical theory of finite elements. Reported are applications in aeronautical, civil, mechanical, nautical and nuclear engineering. Such topics as classical analysis, functional analysis, approximation theory, fluids, and diffusion are covered. Over 2200 references to publications up to the end of 1974 are included. Publications are listed alphabetically by author and also by keywords. In addition, finite element packages are listed.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Surgery simulation using fast finite elements
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
Finite Element Residual Stress Analysis of Planetary Gear Tooth
Jungang Wang
2013-01-01
Full Text Available A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.
Al-Akhrass, Dina
2014-01-01
Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code
Integral finite element analysis of turntable bearing with flexible rings
Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng
2018-03-01
This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.
Matsuura, Yusuke; Rokkaku, Tomoyuki; Suzuki, Takane; Thoreson, Andrew Ryan; An, Kai-Nan; Kuniyoshi, Kazuki
2017-08-01
Forearm diaphysis fractures are usually managed by open reduction internal fixation. Recently, locking plates have been used for treatment. In the long-term period after surgery, some patients present with bone atrophy adjacent to the plate. However, a comparison of locking and conventional plates as a cause of atrophy has not been reported. The aim of this study was to investigate long-term bone atrophy associated with use of locking and conventional plates for forearm fracture treatment. In this study we included 15 patients with forearm fracture managed by either locking or conventional plates and with more than 5 years of follow-up. Computed tomographic imaging of both forearms was performed to assess bone thickness and local bone mineral density and to predict bone strength without plate reinforcement based on finite element analysis. Mean patient age at surgery was 48.0 years. Eight patients underwent reduction with fixed locking plates and were followed up for a mean of 79.5 months; the remaining 7 patients were treated with conventional plates and were followed up for a mean of 105.0 months. Compared with the conventional plate group, the locking plate group had the same fractured limb-contralateral limb ratio of cortex bone thickness, but had significantly lower ratios of mineral density adjacent to the plate and adjusted bone strength. This study demonstrated bone atrophy after locking plate fixation for forearm fractures. Treatment plans for forearm fracture should take into consideration the impact of bone atrophy long after plate fixation. Therapeutic IV. Copyright © 2017 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.
Ikman Ishak, Muhammad; Shafi, Aisyah Ahmad; Mohamad, Su Natasha; Jizat, Noorlindawaty Md
2018-03-01
The design of dental implant body has a major influence on the stress dissipation over adjacent bone as numbers of implant failure cases reported in past clinical studies. Besides, the inappropriate implant features may cause excessive high or low stresses which could possibly contribute to pathologic bone resorption or atrophy. The aim of this study is to evaluate the effect of different configurations of implant neck on stress dispersion within the adjacent bone via three-dimensional (3-D) finite element analysis (FEA). A set of computed tomography (CT) images of craniofacial was used to reconstruct a 3-D model of mandible using an image-processing software. The selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone model consisted of both compact (cortical) and porous (cancellous) structures. Three dental implant sets (crown, implant body, and abutment) with different designs of implant neck – straight, tapered with 15°, and tapered with 30° were modelled using a computer-aided design (CAD) software and all models were then analysed via 3-D FEA software. Top surface of first molar crown was subjected to occlusal forces of 114.6 N, 17.2 N, and 23.4 N in the axial, lingual, and mesio-distal directions, respectively. All planes of the mandible model were rigidly constrained in all directions. The result has demonstrated that the straight implant body neck is superior in attributing to high stress generation over adjacent bone as compared to others. This may associate with lower frictional resistance produced than those of tapered designs to withstand the applied loads.
Finite element analysis of tibial fractures
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Quadrature representation of finite element variational forms
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
A finite element for plates and shells
Muller, A.; Feijoo, R.A.; Bevilacqua, L.
1981-08-01
A simple triangular finite element for plates and shells, is presented. Since the rotation fields are assumed independent of the displacement fields, the element allows one to solve thick shells problems. In the limit for thin shell, the Kirchoff-Love hypothesis is automatically satisfied, thus enlarging its range of application. (Author) [pt
Modelling drawbeads with finite elements and verification
Carleer, B.D.; Carleer, B.D.; Vreede, P.T.; Vreede, P.T.; Louwes, M.F.M.; Louwes, M.F.M.; Huetink, Han
1994-01-01
Drawbeads are commonly used in deep drawing processes to control the flow of the blank during the forming operation. In finite element simulations of deep drawing the drawbead geometries are seldom included because of the small radii; because of these small radii a very large number of elements is
Finite elements for partial differential equations: An introductory survey
Succi, S.
1988-03-01
After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs
Thermohydraulic analysis in pipelines using the finite element method
Costa, L.E.; Idelsohn, S.R.
1984-01-01
The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
The finite element response matrix method
Nakata, H.; Martin, W.R.
1983-02-01
A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt
Verification of Orthogrid Finite Element Modeling Techniques
Steeve, B. E.
1996-01-01
The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.
On the reliability of finite element solutions
Prasad, K.S.R.K.
1975-01-01
The extent of reliability of the finite element method for analysis of nuclear reactor structures, and that of reactor vessels in particular and the need for the engineer to guard against the pitfalls that may arise out of both physical and mathematical models have been high-lighted. A systematic way of checking the model to obtain reasonably accurate solutions is presented. Quite often sophisticated elements are suggested for specific design and stress concentration problems. The desirability or otherwise of these elements, their scope and utility vis-a-vis the use of large stack of conventional elements are discussed from the view point of stress analysts. The methods of obtaining a check on the reliability of the finite element solutions either through modelling changes or an extrapolation technique are discussed. (author)
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Finite-element analysis of dynamic fracture
Aberson, J. A.; Anderson, J. M.; King, W. W.
1976-01-01
Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.
Crack Propagation by Finite Element Method
Luiz Carlos H. Ricardo
2018-01-01
Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Finite element modelling of solidification phenomena
Unknown
Abstract. The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation ...
Image segmentation with a finite element method
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Orthodontic treatment: Introducing finite element analysis
Driel, W.D. van; Leeuwen, E.J. van
1998-01-01
The aim of orthodontic treatment is the displacement of teeth by means ofspecial appliances, like braces and brackets. Through these appliances the orthodontist can apply a set of forces to the teeth which wilt result in its displacement through the jawbone. Finite Element analysis of this process
Isogeometric finite element analysis of poroelasticity
Irzal, F.; Remmers, J.J.C.; Verhoosel, C.V.; Borst, de R.
2013-01-01
We present an alternative numerical approach for predicting the behaviour of a deformable fluid-saturated porous medium. The conventional finite element technology is replaced by isogeometric analysis that uses non-uniform rational B-splines. The ability of these functions to provide higher-order
Fast finite elements for surgery simulation
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix...
Simplicial Finite Elements in Higher Dimensions
Brandts, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 52, č. 3 (2007), s. 251-265 ISSN 0862-7940 R&D Projects: GA ČR GA201/04/1503 Institutional research plan: CEZ:AV0Z10190503 Keywords : n-simplex * finite element method * superconvergence Subject RIV: BA - General Mathematics
Finite element method - theory and applications
Baset, S.
1992-01-01
This paper summarizes the mathematical basis of the finite element method. Attention is drawn to the natural development of the method from an engineering analysis tool into a general numerical analysis tool. A particular application to the stress analysis of rubber materials is presented. Special advantages and issues associated with the method are mentioned. (author). 4 refs., 3 figs
Finite-Element Modeling of Timber Joints with Punched Metal Plate Fasteners
Ellegaard, Peter
2006-01-01
The focus of this paper is to describe the idea and the theory behind a finite-element model developed for analysis of timber trusses with punched metal plate fasteners (nail plates). The finite-element model includes the semirigid and nonlinear behavior of the joints (nonlinear nail and plate...... elements) and contact between timber beams, if any (bilinear contact elements). The timber beams have linear-elastic properties. The section forces needed for design of the joints are given directly by the finite-element model, since special elements are used to model the nail groups and the nail plate...... the behavior of the joints very well at lower load levels. At higher load levels the stiffness is overestimated due to development of cracks in the timber and the linear-elastic timber properties in the finite-element model....
Investigation of Shear Stud Performance in Flat Plate Using Finite Element Analysis
T.S. Viswanathan
2014-09-01
Full Text Available Three types of shear stud arrangement, respectively featuring an orthogonal, a radial and a critical perimeter pattern, were evaluated numerically. A numerical investigation was conducted using the finite element software ABAQUS to evaluate their ability to resist punching shear in a flat plate. The finite element analysis here is an application of the nonlinear analysis of reinforced concrete structures using three-dimensional solid finite elements. The nonlinear characteristics of concrete were achieved by employing the concrete damaged plasticity model in the finite element program. Transverse shear stress was evaluated using finite element analysis in terms of shear stress distribution for flat plate with and without shear stud reinforcement. The model predicted that shear studs placed along the critical perimeter are more effective compared to orthogonal and radial patterns.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
A set of pathological tests to validate new finite elements
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
The finite element method entails several approximations. Hence it ... researchers have designed several pathological tests to validate any new finite element. The .... Three dimensional thick shell elements using a hybrid/mixed formu- lation.
ZONE: a finite element mesh generator
Burger, M.J.
1976-05-01
The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures
Finite-element analysis of flawed and unflawed pipe tests
James, R.J.; Nickell, R.E.; Sullaway, M.F.
1989-12-01
Contemporary versions of the general purpose, nonlinear finite element program ABAQUS have been used in structural response verification exercises on flawed and unflawed austenitic stainless steel and ferritic steel piping. Among the topics examined, through comparison between ABAQUS calculations and test results, were: (1) the effect of using variations in the stress-strain relationship from the test article material on the calculated response; (2) the convergence properties of various finite element representations of the pipe geometry, using shell, beam and continuum models; (3) the effect of test system compliance; and (4) the validity of ABAQUS J-integral routines for flawed pipe evaluations. The study was culminated by the development and demonstration of a ''macroelement'' representation for the flawed pipe section. The macroelement can be inserted into an existing piping system model, in order to accurately treat the crack-opening and crack-closing static and dynamic response. 11 refs., 20 figs., 1 tab
A finite element calculation of flux pumping
Campbell, A. M.
2017-12-01
A flux pump is not only a fascinating example of the power of Faraday’s concept of flux lines, but also an attractive way of powering superconducting magnets without large electronic power supplies. However it is not possible to do this in HTS by driving a part of the superconductor normal, it must be done by exceeding the local critical density. The picture of a magnet pulling flux lines through the material is attractive, but as there is no direct contact between flux lines in the magnet and vortices, unless the gap between them is comparable to the coherence length, the process must be explicable in terms of classical electromagnetism and a nonlinear V-I characteristic. In this paper a simple 2D model of a flux pump is used to determine the pumping behaviour from first principles and the geometry. It is analysed with finite element software using the A formulation and FlexPDE. A thin magnet is passed across one or more superconductors connected to a load, which is a large rectangular loop. This means that the self and mutual inductances can be calculated explicitly. A wide strip, a narrow strip and two conductors are considered. Also an analytic circuit model is analysed. In all cases the critical state model is used, so the flux flow resistivity and dynamic resistivity are not directly involved, although an effective resistivity appears when J c is exceeded. In most of the cases considered here is a large gap between the theory and the experiments. In particular the maximum flux transferred to the load area is always less than the flux of the magnet. Also once the threshold needed for pumping is exceeded the flux in the load saturates within a few cycles. However the analytic circuit model allows a simple modification to allow for the large reduction in I c when the magnet is over a conductor. This not only changes the direction of the pumped flux but leads to much more effective pumping.
FINITE ELEMENT ANALYSIS OF ELEMENT ANALYSIS OF A FREE ...
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the stairs and to compare the finite element ana ... tual three dimensional behavior of the stair slab system. ..... due to its close relation of output with the propo .... flights. It is best not to consider any open well when .... thermodynamics of solids.
A finite element method for neutron transport
Ackroyd, R.T.
1983-01-01
A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)
Finite element reliability analysis of fatigue life
Harkness, H.H.; Belytschko, T.; Liu, W.K.
1992-01-01
Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)
Finite Element Simulation of Fracture Toughness Test
Chu, Seok Jae; Liu, Cong Hao
2013-01-01
Finite element simulations of tensile tests were performed to determine the equivalent stress - equivalent plastic strain curves, critical equivalent stresses, and critical equivalent plastic strains. Then, the curves were used as inputs to finite element simulations of fracture toughness tests to determine the plane strain fracture toughness. The critical COD was taken as the COD when the equivalent plastic strain at the crack tip reached a critical value, and it was used as a crack growth criterion. The relationship between the critical COD and the critical equivalent plastic strain or the reduction of area was found. The relationship between the plane strain fracture toughness and the product of the critical equivalent stress and the critical equivalent plastic strain was also found
Finite element analysis of ARPS structures
Ruhkamp, J.D.; McDougal, J.R.; Kramer, D.P.
1998-01-01
Algor finite element software was used to determine the stresses and deflections in the metallic walls of Advanced Radioisotope Power Systems (ARPS) designs. The preliminary design review of these systems often neglects the structural integrity of the design which can effect fabrication and the end use of the design. Before finite element analysis (FEA) was run on the canister walls of the thermophotovoltaic (TPV) generator, hand calculations were used to approximate the stresses and deflections in a flat plate. These results compared favorably to the FEA results of a similar size flat plate. The AMTEC (Alkali Metal Thermal-to-Electric Conversion) cells were analyzed by FEA and the results compared to two cells that were mechanically tested. The mechanically tested cells buckled in the thin sections, one at the top and one in the lower section. The FEA predicted similar stress and shape results but the critical buckling load was found to be very shape dependent
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Finite element based electric motor design optimization
Campbell, C. Warren
1993-01-01
The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Upstand Finite Element Analysis of Slab Bridges
O'Brien, Eugene J.; Keogh, D.L.
1998-01-01
For slab bridge decks with wide transverse edge cantilevers, the plane grillage analogy is shown to be an inaccurate method of linear elastic analysis due to variations in the vertical position of the neutral axis. The upstand grillage analogy is also shown to give inaccurate results, this time due to inappropriate modelling of in-plane distortions. An alternative method, known as upstand finite element analysis, is proposed which is sufficiently simple to be used on an everyday basis in the ...
Crack Propagation by Finite Element Method
H. Ricardo, Luiz Carlos
2017-01-01
Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FD&E SAE Keyh...
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
FINELM: a multigroup finite element diffusion code
Higgs, C.E.; Davierwalla, D.M.
1981-06-01
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
Finite element method for time-space-fractional Schrodinger equation
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Finite element method for simulation of the semiconductor devices
Zikatanov, L.T.; Kaschiev, M.S.
1991-01-01
An iterative method for solving the system of nonlinear equations of the drift-diffusion representation for the simulation of the semiconductor devices is worked out. The Petrov-Galerkin method is taken for the discretization of these equations using the bilinear finite elements. It is shown that the numerical scheme is a monotonous one and there are no oscillations of the solutions in the region of p-n transition. The numerical calculations of the simulation of one semiconductor device are presented. 13 refs.; 3 figs
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan
2012-01-01
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite
Application of finite-element-methods in food processing
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Finite element analysis of plastic recycling machine designed for ...
... design was evaluated using finite element analysis (FEA) tool in Solid Works Computer ... Also, a minimum factor of safety value of 5.3 was obtained for shredder shaft ... Machine; Design; Recycling; Sustainability; Finite Element; Simulation ...
Error-controlled adaptive finite elements in solid mechanics
Stein, Erwin; Ramm, E
2003-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error-controlled Adaptive Finite-element-methods . . . . . . . . . . . . Missing Features and Properties of Today's General Purpose FE Programs for Structural...
FEHM, Finite Element Heat and Mass Transfer Code
Zyvoloski, G.A.
2002-01-01
1 - Description of program or function: FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities. 2 - Methods: FEHM uses a preconditioned conjugate gradient solution of coupled linear equations and a fully implicit, fully coupled Newton Raphson solution of nonlinear equations. It has the capability of simulating transport using either a advection/diffusion solution or a particle tracking method. 3 - Restriction on the complexity of the problem: Disk space and machine memory are the only limitations
Finite element analysis of FRP-strengthened RC beams
Teeraphot Supaviriyakit
2004-05-01
Full Text Available This paper presents a non-linear finite element analysis of reinforced concrete beam strengthened with externally bonded FRP plates. The finite element modeling of FRP-strengthened beams is demonstrated. Concrete and reinforcing bars are modeled together as 8-node isoparametric 2D RC element. The FRP plate is modeled as 8-node isoparametric 2D elastic element. The glue is modeled as perfect compatibility by directly connecting the nodes of FRP with those of concrete since there is no failure at the glue layer. The key to the analysis is the correct material models of concrete, steel and FRP. Cracks and steel bars are modeled as smeared over the entire element. Stress-strain properties of cracked concrete consist of tensile stress model normal to crack, compressive stress model parallel to crack and shear stress model tangential to crack. Stressstrain property of reinforcement is assumed to be elastic-hardening to account for the bond between concrete and steel bars. FRP is modeled as elastic-brittle material. From the analysis, it is found that FEM can predict the load-displacement relation, ultimate load and failure mode of the beam correctly. It can also capture the cracking process for both shear-flexural peeling and end peeling modes similar to the experiment.
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Modelling bucket excavation by finite element
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
The finite element method in engineering, 2nd edition
Rao, S.S.
1986-01-01
This work provides a systematic introduction to the various aspects of the finite element method as applied to engineering problems. Contents include: introduction to finite element method; solution of finite element equations; solid and structural mechanics; static analysis; dynamic analysis; heat transfer; fluid mechanics and additional applications
Finite element analysis of hysteresis effects in piezoelectric transducers
Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard
2000-06-01
The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.
New mixed finite-element methods
Franca, L.P.
1987-01-01
New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates
A finite element method for neutron transport
Ackroyd, R.T.
1978-01-01
A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)
Finite element simulation of piezoelectric transformers.
Tsuchiya, T; Kagawa, Y; Wakatsuki, N; Okamura, H
2001-07-01
Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.
On constitutive modelling in finite element analysis
Bathe, K.J.; Snyder, M.D.; Cleary, M.P.
1979-01-01
This compact contains a brief introduction to the problems involved in constitutive modeling as well as an outline of the final paper to be submitted. Attention is focussed on three important areas: (1) the need for using theoretically sound material models and the importance of recognizing the limitations of the models, (2) the problem of developing stable and effective numerical representations of the models, and (3) the necessity for selection of an appropriate finite element mesh that can capture the actual physical response of the complete structure. In the final paper, we will be presenting our recent research results pertaining to each of these problem areas. (orig.)
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
TITUS: a general finite element system
Bougrelle, P.
1983-01-01
TITUS is a general finite element structural analysis system which performs linear/non-linear, static/dynamic analyses of heat-transfer/thermo-mechanical problems. One of the major features of TITUS is that it was designed by engineers, to address engineers in an industrial environment. This has resulted in an easy to use system, with a high-level free-formatted problem oriented language, a large selection of pre- and post processors and sophisticated graphic capabilities. TITUS has many references in civil, mechanical and nuclear engineering applications. The TITUS system is available on various types of machines, from large mainframes to mini computers
Finite element analysis of permanent magnet motors
Boglietti, A.; Chiampi, M.; Tartaglia, M.; Chiarabaglio, D.
1989-01-01
The analysis of permanent magnet D.C. brushless motors, supplied by current control inverters, is developed employing a finite element package tailored for such devices. The study is devoted to predicting the performance of a set of four poles machines, under different operating conditions (no-load, rated load). The over-load conditions are also considered including the saturation effect. Moreover the influence of such design parameters, as the tooth shape and the number of magnet segments, is investigated. Computed results are found in satisfactory agreement with experimental ones
Probalistic Finite Elements (PFEM) structural dynamics and fracture mechanics
Liu, Wing-Kam; Belytschko, Ted; Mani, A.; Besterfield, G.
1989-01-01
The purpose of this work is to develop computationally efficient methodologies for assessing the effects of randomness in loads, material properties, and other aspects of a problem by a finite element analysis. The resulting group of methods is called probabilistic finite elements (PFEM). The overall objective of this work is to develop methodologies whereby the lifetime of a component can be predicted, accounting for the variability in the material and geometry of the component, the loads, and other aspects of the environment; and the range of response expected in a particular scenario can be presented to the analyst in addition to the response itself. Emphasis has been placed on methods which are not statistical in character; that is, they do not involve Monte Carlo simulations. The reason for this choice of direction is that Monte Carlo simulations of complex nonlinear response require a tremendous amount of computation. The focus of efforts so far has been on nonlinear structural dynamics. However, in the continuation of this project, emphasis will be shifted to probabilistic fracture mechanics so that the effect of randomness in crack geometry and material properties can be studied interactively with the effect of random load and environment.
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Multiphase poroelastic finite element models for soft tissue structures
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
The finite element response Matrix method
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
A multigrid solution method for mixed hybrid finite elements
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Probabilistic finite elements for fatigue and fracture analysis
Belytschko, Ted; Liu, Wing Kam
1993-04-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
Finite element modeling of piezoelectric elements with complex electrode configuration
Paradies, R; Schläpfer, B
2009-01-01
It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been
Olson, R.; Scott, P.; Wilkowski, G.M.
1992-01-01
As part of the US NRC's Degraded Piping Program, the concept of using a nonlinear spring element to simulate the response of cracked pipe in dynamic finite element pipe evaluations was initially proposed. The nonlinear spring element is used to represent the moment versus rotation response of the cracked pipe section. The moment-rotation relationship for the crack size and material of interest is determined from either J-estimation scheme analyses or experimental data. In this paper, a number of possible approaches for modeling the nonlinear stiffness of the cracked pipe section are introduced. One approach, modeling the cracked section moment rotation response with a series of spring-slider elements, is discussed in detail. As part of this discussion, results from a series of finite element predictions using the spring-slider nonlinear spring element are compared with the results from a series of dynamic cracked pipe system experiments from the International Piping Integrity Research Group (IPIRG) program
Friction welding; Magnesium; Finite element; Shear test.
Leonardo Contri Campanelli
2013-06-01
Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.
Adaptive finite element method for shape optimization
Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco
2012-01-01
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Finite element simulation of asphalt fatigue testing
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value...... damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...... three point and four point fatigue test on different mixes. It is shown that the same damage law, based on energy density, may be used to explain the gradual deterioration under constant stress as well as under constant strain testing.Some of the advantages of using this method for interpreting fatigue...
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Finite element program Lamcal. (User's manual)
Lamain, L.G.; Blanckenburg, J.F.G.
1982-01-01
The present user's manual gives the input formats, job control and an input example for the finite element part of the Lamcal program. The input data have been organized in a more or less self explaining way, using keywords and standard input formats and is printed at the beginning of every run. To simplify the use of the whole program and to avoid unecessary data handling, all three parts of the Lamcal program, meshgeneration, plotting and, FE, are combined into one load module. This setup allows to do all calculations in one single run. However, preprocessing, postprocessing and restarts can be made in separate runs as well. The same reserved space for the dynamic core storage is used in all three parts, if the available space is not sufficient the FE program will stop
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Chiang, C. K.; Xue, David Y.; Mei, Chuh
1993-04-01
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Finite groups with three conjugacy class sizes of some elements
Conjugacy class sizes; p-nilpotent groups; finite groups. 1. Introduction. All groups ... group G has exactly two conjugacy class sizes of elements of prime power order. .... [5] Huppert B, Character Theory of Finite Groups, de Gruyter Exp. Math.
The finite element analysis program MSC Marc/Mentat a first introduction
Öchsner, Andreas
2016-01-01
Based on simple examples, this book offers a short introduction to the general-purpose finite element program MSC Marc, a specialized program for non-linear problems (implicit solver) distributed by the MSC Software Corporation, which is commonly used in academia and industry. Today the documentation of all finite element programs includes a variety of step-by-step examples of differing complexity, and in addition, all software companies offer professional workshops on different topics. As such, rather than competing with these, the book focuses on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. This makes it an ideal companion book to classical introductory courses on the finite element method.
Finite difference techniques for nonlinear hyperbolic conservation laws
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
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
Finite element formulation for dynamics of planar flexible multi-beam system
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
Impact of new computing systems on finite element computations
Noor, A.K.; Fulton, R.E.; Storaasi, O.O.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Application of viscoplastic constitutive equations in finite element programs
Hornberger, K.; Stamm, H.
1987-04-01
The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de
Finite element analysis of elasto-plastic tee joints
Powell, G.H.
1974-09-01
The theory and computational procedures used in the computer program B169TJ/EP for the analysis of elasto-plastic tee joints are described, and detailed user's guide is presented. The program is particularly applicable to joints conforming to the ANSI B16.9 Manufacturing Standard, but can also be applied to other joint geometries. The joint may be loaded by internal pressure and by arbitrary combinations of applied forces and moments at the ends of the branch and run pipes, and the loading sequence may be arbitrary. The joint material is assumed to yield according to the von Mises criterion, and to exhibit either linear kinematic hardening or nonlinear isotropic hardening after yield. The program makes use of the finite element and mesh generation procedures previously applied in the elastic stress analysis program B16.9TJ/ SA, with minor modifications. (U.S.)
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette
2010-02-23
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.
Contribution to finite element modelling of airfoil aeroelastic instabilities
Horáček J.
2007-10-01
Full Text Available Nonlinear equations of motion for a flexibly supported rigid airfoil with additional degree of freedom for controlling of the profile motion by a trailing edge flap are derived for large vibration amplitudes. Preliminary results for numerical simulation of flow-induced airfoil vibrations in a laminar incompressible flow are presented for the NACA profile 0012 with three-degrees of freedom (vertical translation, rotation around the elastic axis and rotation of the flap. The developed numerical solution of the Navier – Stokes equations and the Arbitrary Eulerian-Lagrangian approach enable to consider the moving grid for the finite element modelling of the fluid flow around the oscillating airfoil. A sequence of numerical simulation examples is presented for Reynolds numbers up to about Re~10^5, when the system loses the aeroelastic stability, and when the large displacements of the profile and a post-critical behaviour of the system take place.
Finite element modeling of Balsa wood structures under severe loadings
Toson, B.; Pesque, J.J.; Viot, P.
2014-01-01
In order to compute, in various situations, the requirements for transporting packages using Balsa wood as an energy absorber, a constitutive model is needed that takes into account all of the specific characteristics of the wood, such as its anisotropy, compressibility, softening, densification, and strain rate dependence. Such a model must also include the treatment of rupture of the wood when it is in traction. The complete description of wood behavior is not sufficient: robustness is also necessary because this model has to work in presence of large deformations and of many other external nonlinear phenomena in the surrounding structures. We propose such a constitutive model that we have developed using the commercial finite element package ABAQUS. The necessary data were acquired through an extensive compilation of the existing literature with the augmentation of personal measurements. Numerous validation tests are presented that represent different impact situations that a transportation cask might endure. (authors)
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models
Quak, W.; Boogaard, A. H. van den
2011-01-01
A successful simulation of a bulk forming process with finite elements can be difficult due to distortion of the finite elements. Nodal smoothed Finite Elements (NSFEM) are an interesting option for such a process since they show good distortion insensitivity and moreover have locking-free behavior and good computational efficiency. In this paper a method is proposed which takes advantage of the nodally smoothed field. This method, named adaptive smoothed finite elements (ASFEM), revises the mesh for every step of a simulation without mapping the history dependent material parameters. In this paper an updated-Lagrangian implementation is presented. Several examples are given to illustrate the method and to show its properties.
Run-up on a body in waves and current. Fully nonlinear and finite-order calculations
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...
Automating the generation of finite element dynamical cores with Firedrake
Ham, David; Mitchell, Lawrence; Homolya, Miklós; Luporini, Fabio; Gibson, Thomas; Kelly, Paul; Cotter, Colin; Lange, Michael; Kramer, Stephan; Shipton, Jemma; Yamazaki, Hiroe; Paganini, Alberto; Kärnä, Tuomas
2017-04-01
The development of a dynamical core is an increasingly complex software engineering undertaking. As the equations become more complete, the discretisations more sophisticated and the hardware acquires ever more fine-grained parallelism and deeper memory hierarchies, the problem of building, testing and modifying dynamical cores becomes increasingly complex. Here we present Firedrake, a code generation system for the finite element method with specialist features designed to support the creation of geoscientific models. Using Firedrake, the dynamical core developer writes the partial differential equations in weak form in a high level mathematical notation. Appropriate function spaces are chosen and time stepping loops written at the same high level. When the programme is run, Firedrake generates high performance C code for the resulting numerics which are executed in parallel. Models in Firedrake typically take a tiny fraction of the lines of code required by traditional hand-coding techniques. They support more sophisticated numerics than are easily achieved by hand, and the resulting code is frequently higher performance. Critically, debugging, modifying and extending a model written in Firedrake is vastly easier than by traditional methods due to the small, highly mathematical code base. Firedrake supports a wide range of key features for dynamical core creation: A vast range of discretisations, including both continuous and discontinuous spaces and mimetic (C-grid-like) elements which optimally represent force balances in geophysical flows. High aspect ratio layered meshes suitable for ocean and atmosphere domains. Curved elements for high accuracy representations of the sphere. Support for non-finite element operators, such as parametrisations. Access to PETSc, a world-leading library of programmable linear and nonlinear solvers. High performance adjoint models generated automatically by symbolically reasoning about the forward model. This poster will present
Probabilistic finite element modeling of waste rollover
Khaleel, M.A.; Cofer, W.F.; Al-fouqaha, A.A.
1995-09-01
Stratification of the wastes in many Hanford storage tanks has resulted in sludge layers which are capable of retaining gases formed by chemical and/or radiolytic reactions. As the gas is produced, the mechanisms of gas storage evolve until the resulting buoyancy in the sludge leads to instability, at which point the sludge ''rolls over'' and a significant volume of gas is suddenly released. Because the releases may contain flammable gases, these episodes of release are potentially hazardous. Mitigation techniques are desirable for more controlled releases at more frequent intervals. To aid the mitigation efforts, a methodology for predicting of sludge rollover at specific times is desired. This methodology would then provide a rational basis for the development of a schedule for the mitigation procedures. In addition, a knowledge of the sensitivity of the sludge rollovers to various physical and chemical properties within the tanks would provide direction for efforts to reduce the frequency and severity of these events. In this report, the use of probabilistic finite element analyses for computing the probability of rollover and the sensitivity of rollover probability to various parameters is described
Finite element modelling of composite castellated beam
Frans Richard
2017-01-01
Full Text Available Nowadays, castellated beam becomes popular in building structural as beam members. This is due to several advantages of castellated beam such as increased depth without any additional mass, passing the underfloor service ducts without changing of story elevation. However, the presence of holes can develop various local effects such as local buckling, lateral torsional buckling caused by compression force at the flange section of the steel beam. Many studies have investigated the failure mechanism of castellated beam and one technique which can prevent the beam fall into local failure is the use of reinforced concrete slab as lateral support on castellated beam, so called composite castellated beam. Besides of preventing the local failure of castellated beam, the concrete slab can increase the plasticity moment of the composite castellated beam section which can deliver into increasing the ultimate load of the beam. The aim of this numerical studies of composite castellated beam on certain loading condition (monotonic quasi-static loading. ABAQUS was used for finite element modelling purpose and compared with the experimental test for checking the reliability of the model. The result shows that the ultimate load of the composite castellated beam reached 6.24 times than the ultimate load of the solid I beam and 1.2 times compared the composite beam.
Shakedown analysis by finite element incremental procedures
Borkowski, A.; Kleiber, M.
1979-01-01
It is a common occurence in many practical problems that external loads are variable and the exact time-dependent history of loading is unknown. Instead of it load is characterized by a given loading domain: a convex polyhedron in the n-dimensional space of load parameters. The problem is then to check whether a structure shakes down, i.e. responds elastically after a few elasto-plastic cycles, or not to a variable loading as defined above. Such check can be performed by an incremental procedure. One should reproduce incrementally a simple cyclic process which consists of proportional load paths that connect the origin of the load space with the corners of the loading domain. It was proved that if a structure shakes down to such loading history then it is able to adopt itself to an arbitrary load path contained in the loading domain. The main advantage of such approach is the possibility to use existing incremental finite-element computer codes. (orig.)
Finite element simulation for creep crack growth
Miyazaki, Noriyuki; Sasaki, Toru; Nakagaki, Michihiko; Brust, F.W.
1992-01-01
A finite element method was applied to a generation phase simulation of creep crack growth. Experimental data on creep crack growth in a 1Cr-1Mo-1/4V steel compact tension specimen were numerically simulated using a node-release technique and the variations of various fracture mechanics parameters such as CTOA, J, C * and T * during creep crack growth were calculated. The path-dependencies of the integral parameters J, C * and T * were also obtained to examine whether or not they could characterize the stress field near the tip of a crack propagating under creep condition. The following conclusions were obtained from the present analysis. (1) The J integral shows strong path-dependency during creep crack growth, so that it is does not characterize creep crack growth. (2) The C * integral shows path-dependency to some extent during creep crack growth even in the case of Norton type steady state creep law. Strictly speaking, we cannot use it as a fracture mechanics parameter characterizing creep crack growth. It is, however, useful from the practical viewpoint because it correlates well the rate of creep crack growth. (3) The T * integral shows good path-independency during creep crack growth. Therefore, it is a candidate for a fracture mechanics parameter characterizing creep crack growth. (author)
Radu, F.A.; Pop, I.S.; Knabner, P.; Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.
2006-01-01
In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For
Finite element analysis of a fluid-structure interaction in flexible pipe ...
The obtained mathematical system is constituted of four non-linear hyperbolic partial differential equations describing the wave propagation in both pipe wall and liquid flow. The fluid-structure interaction is found to be governed by Poisson's ratio. In this steady finite element method based on Galerkin formulation is applied.
An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering
Sengers, B.G.; Oomens, C.W.J.; Baaijens, F.P.T.
2004-01-01
A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive
Coupled convective and conductive heat transfer by up-wind finite element method
Kushwaha, H.S.
1981-01-01
Some of concepts relating to finite element formulation of the Navier-Stoke's equations using mixed formulation and Penality formulation have been discussed. The two different approaches for solution of nonlinear differential equations for two different types of formulation have been described. Incremental Newton Raphson method can also be applied to mixed formulation. (author)
A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree
Ali R. Soheili
2009-01-01
Full Text Available A gradient weighted moving finite element method (GWMFE based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation.
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2012-01-01
In this study a stochastic approach is conducted to obtain the horizontal and rotational stiffness of an offshore monopile foundation. A nonlinear stochastic p-y curve is integrated into a finite element scheme for calculation of the monopile response in over-consolidated clay having spatial...
Kim, Taeseong; Hansen, Anders Melchior; Branner, Kim
2013-01-01
In this paper a new anisotropic beam finite element for composite wind turbine blades is developed and implemented into the aeroelastic nonlinear multibody code, HAWC2, intended to be used to investigate if use of anisotropic material layups in wind turbine blades can be tailored for improved...
A Finite Element Analysis of Optimal Variable Thickness Sheets
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill ...
Mixed Element Formulation for the Finite Element-Boundary Integral Method
Meese, J; Kempel, L. C; Schneider, S. W
2006-01-01
A mixed element approach using right hexahedral elements and right prism elements for the finite element-boundary integral method is presented and discussed for the study of planar cavity-backed antennas...
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
finite element model for predicting residual stresses in shielded
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This paper investigates the prediction of residual stresses developed ... steel plates through Finite Element Model simulation and experiments. ... The experimental values as measured by the X-Ray diffractometer were of ... Based on this, it can be concluded that Finite Element .... Comparison of Residual Stresses from X.
Parallel direct solver for finite element modeling of manufacturing processes
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...
A geometric toolbox for tetrahedral finite element partitions
Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.
2011-01-01
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis.
A simple finite element method for linear hyperbolic problems
Mu, Lin; Ye, Xiu
2017-01-01
Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.
Finite Element Modelling of Seismic Liquefaction in Soils
Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.
2013-01-01
Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom
Analysis of Tube Drawing Process – A Finite Element Approach ...
In this paper the effect of die semi angle on drawing load in cold tube drawing has been investigated numerically using the finite element method. The equation governing the stress distribution was derived and solved using Galerkin finite element method. An isoparametric formulation for the governing equation was utilized ...
Finite element simulation of laser transmission welding of dissimilar ...
user
materials between polyvinylidene fluoride and titanium ... finite element (FE) thermal model is developed to simulate the laser ... Keywords: Laser transmission welding, Temperature field, Weld dimension, Finite element analysis, Thermal modeling. 1. .... 4) The heating phenomena due to the phase changes are neglected.
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke
2001-01-01
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``
Finite Element Analysis of Pipe T-Joint
P.M.Gedkar; Dr. D.V. Bhope
2012-01-01
This paper reports stress analysis of two pressurized cylindrical intersection using finite element method. The different combinations of dimensions of run pipe and the branch pipe are used to investigate thestresses in pipe at the intersection. In this study the stress analysis is accomplished by finite element package ANSYS.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite size effects of a pion matrix element
Guagnelli, M.; Jansen, K.; Palombi, F.; Petronzio, R.; Shindler, A.; Wetzorke, I.
2004-01-01
We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation
A new dedicated finite element for push-over analysis of reinforced concrete shear wall systems
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.
Iancu, Otto Theodor
2014-01-01
The prediction of the plastic collapse load of cylindrical pressure vessels is very often made by using expensive Finite Element computations. The calculation of the collapse load requires an elastic-plastic material model and the consideration of non-linear geometry effects. The plastic collapse load causes overall structural instability and cannot be determined directly from a Finite Element analysis. In the present paper the plastic collapse load for a cylindrical pressure vessel is determined by an analytical method based on a linear elastic perfectly plastic material model. When plasticity occurs the material is considered to be incompressible and the tensor of plastic strains to be parallel to the stress deviator tensor. In this case the finite stress-strain relationships of Henkel can be used for calculating the pressure for which plastic flow occurs. The analytical results are completely confirmed by Finite Element predictions. (orig.)
Static Analysis of Steel Fiber Concrete Beam With Heterosis Finite Elements
James H. Haido
2014-08-01
Full Text Available Steel fiber is considered as the most commonly used constructional fibers in concrete structures. The formulation of new nonlinearities to predict the static performance of steel fiber concrete composite structures is considered essential. Present study is devoted to investigate the efficiency of utilizing heterosis finite elements analysis in static analysis of steel fibrous beams. New and simple material nonlinearities are proposed and used in the formulation of these elements. A computer program coded in FORTRAN was developed to perform current finite element static analysis with considering four cases of elements stiffness matrix determination. The results are compared with the experimental data available in literature in terms of central deflections, strains, and failure form, good agreement was found. Suitable outcomes have been observed in present static analysis with using of tangential stiffness matrix and stiffness matrix in second iteration of the load increment.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-01-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed
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.
Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time
Wang, Yu
1995-08-01
The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.
Dynamic analysis of fast-acting solenoid valves using finite element method
Kwon, Ki Tae; Han, Hwa Taik
2001-01-01
It is intended to develop an algorithm for dynamic simulation of fast-acting solenoid valves. The coupled equations of the electric, magnetic, and mechanical systems should be solved simultaneously in a transient nonlinear manner. The transient nonlinear electromagnetic field is analyzed by the Finite Element Method (FEM), which is coupled with nonlinear electronic circuitry. The dynamic movement of the solenoid valve is analyzed at every time step from the force balances acting on the plunger, which include the electromagnetic force calculated from the finite element analysis as well as the elastic force by a spring and the hydrodynamic pressure force along the flow passage. Dynamic responses of the solenoid valves predicted by this algorithm agree well the experimental results including bouncing effects
Finite element and boundary element applications in quantum mechanics
Ueta, Tsuyoshi
2003-01-01
Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the 'language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schroedinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature formulae and Green's functions, is conveniently described. I recommend this book to those who need to
Lower extremity finite element model for crash simulation
Schauer, D.A.; Perfect, S.A.
1996-03-01
A lower extremity model has been developed to study occupant injury mechanisms of the major bones and ligamentous soft tissues resulting from vehicle collisions. The model is based on anatomically correct digitized bone surfaces of the pelvis, femur, patella and the tibia. Many muscles, tendons and ligaments were incrementally added to the basic bone model. We have simulated two types of occupant loading that occur in a crash environment using a non-linear large deformation finite element code. The modeling approach assumed that the leg was passive during its response to the excitation, that is, no active muscular contraction and therefore no active change in limb stiffness. The approach recognized that the most important contributions of the muscles to the lower extremity response are their ability to define and modify the impedance of the limb. When nonlinear material behavior in a component of the leg model was deemed important to response, a nonlinear constitutive model was incorporated. The accuracy of these assumptions can be verified only through a review of analysis results and careful comparison with test data. As currently defined, the model meets the objective for which it was created. Much work remains to be done, both from modeling and analysis perspectives, before the model can be considered complete. The model implements a modeling philosophy that can accurately capture both kinematic and kinetic response of the lower limb. We have demonstrated that the lower extremity model is a valuable tool for understanding the injury processes and mechanisms. We are now in a position to extend the computer simulation to investigate the clinical fracture patterns observed in actual crashes. Additional experience with this model will enable us to make a statement on what measures are needed to significantly reduce lower extremity injuries in vehicle crashes. 6 refs.
High accuracy 3D electromagnetic finite element analysis
Nelson, E.M.
1996-01-01
A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed
Finite element model for heat conduction in jointed rock masses
Gartling, D.K.; Thomas, R.K.
1981-01-01
A computatonal procedure for simulating heat conduction in a fractured rock mass is proposed and illustrated in the present paper. The method makes use of a simple local model for conduction in the vicinity of a single open fracture. The distributions of fractures and fracture properties within the finite element model are based on a statistical representation of geologic field data. Fracture behavior is included in the finite element computation by locating local, discrete fractures at the element integration points
High accuracy 3D electromagnetic finite element analysis
Nelson, Eric M.
1997-01-01
A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed
Rigid body formulation in a finite element context with contact interaction
Refachinho de Campos, Paulo R.; Gay Neto, Alfredo
2018-03-01
The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear finite element solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a finite element environment. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.
Finite Element Simulation of Blanking Process
Afzal Ahmed
2012-10-01
daya penembusan sebanyak 42%. Daya tebukan yang diukur melalui eksperimen dan simulasi kekal pada kira-kira 90kN melepasi penembusan punch sebanyak 62%. Apabila ketebalan keputusan kunci ditambah, ketinggian retak dikurangkan dan ini meningkatkan kualiti pengosongan.KEYWORDS: simulation; finite element simulation; blanking; computer aided manufacturing
Finite element analysis of prestressed concrete reactor vessels
Smith, P.D.; Cook, W.A.; Anderson, C.A.
1977-01-01
This paper discusses the development of a finite element code suitable for the safety analysis of prestressed concrete reactor vessels. The project has involved modification of a general purpose computer code to handle reinforced concrete structures as well as comparison of results obtained with the code against published experimental data. The NONSAP nonlinear structural analysis program was selected for the ease with which it can be modified to encompass problems peculiar to nuclear reactors. Pre- and post-processors have been developed for mesh generation and for graphical display of response variables. An out-of-core assembler and solver have been developed for the analysis of large three dimensional problems. The constitutive model for short term loads forms an orthotropic stress-strain relationship in which the concrete and the reinforcing steel are treated as a composite. The variation of stiffness and strength of concrete under multiaxial stress states is accounted for. Cracks are allowed to form at element integration points based on a three dimensional failure envelope in stress space. Composite tensile and shear properties across a crack are modified to account for bond degradation and for dowel action of the reinforcement. The constitutive law for creep is base on the expansion of the usual creep compliance function in the form of a Dirichlet exponential series. Empirical creep data are then fit to the Dirichlet series approximation by means of a least squares procedure. The incremental deformation process is subsequently reduced to a series of variable stiffness elasticity problems in which the past stress history is represented by a finite number of hidden material variables
Thermomechanical finite element analysis of hot water boiler structure
Živković Dragoljub S.
2012-01-01
Full Text Available The paper presents an application of the Finite Elements Method for stress and strain analysis of the hot water boiler structure. The aim of the research was to investigate the influence of the boiler scale on the thermal stresses and strains of the structure of hot water boilers. Results show that maximum thermal stresses appear in the zone of the pipe carrying wall of the first reversing chamber. This indicates that the most critical part of the boiler are weld spots of the smoke pipes and pipe carrying plate, which in the case of significant scale deposits can lead to cracks in the welds and water leakage from the boiler. The nonlinear effects were taken into account by defining the bilinear isotropic hardening model for all boiler elements. Temperature dependency was defined for all relevant material properties, i. e. isotropic coefficient of thermal expansion, Young’s modulus, and isotropic thermal conductivity. The verification of the FEA model was performed by comparing the measured deformations of the hot water boiler with the simulation results. As a reference object, a Viessmann - Vitomax 200 HW boiler was used, with the installed power of 18.2 MW. CAD modeling was done within the Autodesk Inventor, and stress and strain analysis was performed in the ANSYS Software.
Precise magnetostatic field using the finite element method
Nascimento, Francisco Rogerio Teixeira do
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Finite element formulation for a digital image correlation method
Sun Yaofeng; Pang, John H. L.; Wong, Chee Khuen; Su Fei
2005-01-01
A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust
Review of Tomographic Imaging using Finite Element Method
Mohd Fua’ad RAHMAT
2011-12-01
Full Text Available Many types of techniques for process tomography were proposed and developed during the past 20 years. This paper review the techniques and the current state of knowledge and experience on the subject, aimed at highlighting the problems associated with the non finite element methods, such as the ill posed, ill conditioned which relates to the accuracy and sensitivity of measurements. In this paper, considerations for choice of sensors and its applications were outlined and descriptions of non finite element tomography systems were presented. The finite element method tomography system as obtained from recent works, suitable for process control and measurement were also presented.
Finite element simulation and testing of ISW CFRP anchorage
Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl
2013-01-01
is modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen....... This paper presents a novel mechanical integrated sleeve wedge anchorage which seem very promising when perusing the scope of ultimate utilization of CFRP 8mm rods (with a tension capacity of approximately 140kN). Compression transverse to the CFRP is evaluated to prevent premature failure. The anchorage...
Magnetic materials and 3D finite element modeling
Bastos, Joao Pedro A
2014-01-01
Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering. The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Development of polygon elements based on the scaled boundary finite element method
Chiong, Irene; Song Chongmin
2010-01-01
We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.
Modelling optimization involving different types of elements in finite element analysis
Wai, C M; Rivai, Ahmad; Bapokutty, Omar
2013-01-01
Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer
Finite-element modeling of soft tissue rolling indentation.
Sangpradit, Kiattisak; Liu, Hongbin; Dasgupta, Prokar; Althoefer, Kaspar; Seneviratne, Lakmal D
2011-12-01
We describe a finite-element (FE) model for simulating wheel-rolling tissue deformations using a rolling FE model (RFEM). A wheeled probe performing rolling tissue indentation has proven to be a promising approach for compensating for the loss of haptic and tactile feedback experienced during robotic-assisted minimally invasive surgery (H. Liu, D. P. Noonan, B. J. Challacombe, P. Dasgupta, L. D. Seneviratne, and K. Althoefer, "Rolling mechanical imaging for tissue abnormality localization during minimally invasive surgery, " IEEE Trans. Biomed. Eng., vol. 57, no. 2, pp. 404-414, Feb. 2010; K. Sangpradit, H. Liu, L. Seneviratne, and K. Althoefer, "Tissue identification using inverse finite element analysis of rolling indentation," in Proc. IEEE Int. Conf. Robot. Autom. , Kobe, Japan, 2009, pp. 1250-1255; H. Liu, D. Noonan, K. Althoefer, and L. Seneviratne, "The rolling approach for soft tissue modeling and mechanical imaging during robot-assisted minimally invasive surgery," in Proc. IEEE Int. Conf. Robot. Autom., May 2008, pp. 845-850; H. Liu, P. Puangmali, D. Zbyszewski, O. Elhage, P. Dasgupta, J. S. Dai, L. Seneviratne, and K. Althoefer, "An indentation depth-force sensing wheeled probe for abnormality identification during minimally invasive surgery," Proc. Inst. Mech. Eng., H, vol. 224, no. 6, pp. 751-63, 2010; D. Noonan, H. Liu, Y. Zweiri, K. Althoefer, and L. Seneviratne, "A dual-function wheeled probe for tissue viscoelastic property identification during minimally invasive surgery," in Proc. IEEE Int. Conf. Robot. Autom. , 2008, pp. 2629-2634; H. Liu, J. Li, Q. I. Poon, L. D. Seneviratne, and K. Althoefer, "Miniaturized force indentation-depth sensor for tissue abnormality identification," IEEE Int. Conf. Robot. Autom., May 2010, pp. 3654-3659). A sound understanding of wheel-tissue rolling interaction dynamics will facilitate the evaluation of signals from rolling indentation. In this paper, we model the dynamic interactions between a wheeled probe and a
Complex finite element sensitivity method for creep analysis
Gomez-Farias, Armando; Montoya, Arturo; Millwater, Harry
2015-01-01
The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions
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.
Validation of High Displacement Piezoelectric Actuator Finite Element Models
Taleghani, B. K.
2000-01-01
The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Finite element model updating using bayesian framework and modal properties
Marwala, T
2005-01-01
Full Text Available Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from measured results and therefore need to be updated to match measured results. Some...
Finite Element Crash Simulations and Impact-Induced Injuries
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.
2013-01-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Optical strain measurements and its finite element analysis of cold ...
International Journal of Engineering, Science and Technology ... Online video images of square grid were recorded during the deformation ... Finite element software ANSYS has been applied for the analysis of the upset forming process.
Finite element analyses for RF photoinjector gun cavities
Marhauser, F.
2006-01-01
This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Finite element model to study calcium distribution in oocytes ...
Parvaiz Ahmad Naik
2015-03-20
Mar 20, 2015 ... Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462051 ... finite element method has been employed to obtain the solution. ..... Nelson MT, Cheng H, Rubart M. Relaxation of arterial smooth.
Finite element concept to derive isostatic residual maps ...
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the ... not require explicit assumptions on isostatic models. Besides .... This information is implicit in the Bouguer ...
Finite element analyses for RF photoinjector gun cavities
Marhauser, F. [Berliner Elektronenspeicherring-Gesellschaft fuer Synchrotronstrahlung mbH (BESSY), Berlin (Germany)
2006-07-01
This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)
Implementation of a high performance parallel finite element micromagnetics package
Scholz, W.; Suess, D.; Dittrich, R.; Schrefl, T.; Tsiantos, V.; Forster, H.; Fidler, J.
2004-01-01
A new high performance scalable parallel finite element micromagnetics package has been implemented. It includes solvers for static energy minimization, time integration of the Landau-Lifshitz-Gilbert equation, and the nudged elastic band method
Finite element analysis of thermal stress distribution in different ...
Nigerian Journal of Clinical Practice • Jan-Feb 2016 • Vol 19 • Issue 1. Abstract ... Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ... applications for force analysis and assessment of different.
Finite element analysis of thermal stress distribution in different ...
Nigerian Journal of Clinical Practice. Journal Home ... Von Mises and thermal stress distributions were evaluated. Results: In all ... distribution. Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ...
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Application of Mass Lumped Higher Order Finite Elements
J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau
2005-01-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied
Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction
Kaewunruen, S.; Mirza, O.
2017-10-01
At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
Mathematical aspects of finite element methods for incompressible viscous flows
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Finite element modeling of the filament winding process using ABAQUS
Miltenberger, Louis C.
1992-01-01
A comprehensive stress model of the filament winding fabrication process, previously implemented in the finite element program, WACSAFE, was implemented using the ABAQUS finite element software package. This new implementation, referred to as the ABWACSAFE procedure, consists of the ABAQUS software and a pre/postprocessing routine that was developed to prepare necessary ABAQUS input files and process ABAQUS displacement results for stress and strain computation. The ABWACSAF...
Thermal stresses in rectangular plates: variational and finite element solutions
Laura, P.A.A.; Gutierrez, R.H.; Sanchez Sarmiento, G.; Basombrio, F.G.
1978-01-01
This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach. (Auth.)
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
A finite element solution method for quadrics parallel computer
Zucchini, A.
1996-08-01
A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem
3D finite element modelling of sheet metal blanking process
Bohdal, Lukasz; Kukielka, Leon; Chodor, Jaroslaw; Kulakowska, Agnieszka; Patyk, Radoslaw; Kaldunski, Pawel
2018-05-01
The shearing process such as the blanking of sheet metals has been used often to prepare workpieces for subsequent forming operations. The use of FEM simulation is increasing for investigation and optimizing the blanking process. In the current literature a blanking FEM simulations for the limited capability and large computational cost of the three dimensional (3D) analysis has been largely limited to two dimensional (2D) plane axis-symmetry problems. However, a significant progress in modelling which takes into account the influence of real material (e.g. microstructure of the material), physical and technological conditions can be obtained by using 3D numerical analysis methods in this area. The objective of this paper is to present 3D finite element analysis of the ductile fracture, strain distribution and stress in blanking process with the assumption geometrical and physical nonlinearities. The physical, mathematical and computer model of the process are elaborated. Dynamic effects, mechanical coupling, constitutive damage law and contact friction are taken into account. The application in ANSYS/LS-DYNA program is elaborated. The effect of the main process parameter a blanking clearance on the deformation of 1018 steel and quality of the blank's sheared edge is analyzed. The results of computer simulations can be used to forecasting quality of the final parts optimization.
Fluid-film bearings: a finite element method of analysis
Pururav, T.; Soni, R.S.; Kushwaha, H.S.; Mahajan, S.C.
1995-01-01
Finite element method (FEM) has become a very popular technique for the analysis of fluid-film bearings in the last few years. These bearings are extensively used in nuclear industry applications such as in moderator pumps and main coolant pumps. This report gives the methodology for the solution of Reynold's equation using FEM and its implementation in FE software LUBAN developed in house. It also deals with the mathematical basis and algorithm to account for the cavitation phenomena which makes these problems non-linear in nature. The dynamic coefficients of bearings are evaluated by one-step approach using variational principles. These coefficients are useful for the dynamic characterisation of fluid-film bearings. Several problems have been solved using this code including two real life problems, a circumferentially grooved journal bearing for which experimental results are available and the bearing of moderator pump of 500 MWe PHWR, have been solved. The results obtained for sample problems are in good agreement with the published literature. (author). 9 refs., 14 figs., 5 tabs., 2 ills
Finite Element Analysis of Saferooms Subjected to Tornado Impact Loads
Parfilko, Y.; Amaral de Arruda, F.; Varela, B.
2017-10-01
A Tornado is one of the most dreadful and unpredictable events in nature. Unfortunately, weather and geographic conditions make a large portion of the United States prone to this phenomenon. Tornado saferooms are monolithic reinforced concrete protective structures engineered to guard against these natural disasters. Saferooms must withstand impacts and wind loads from EF-5 tornadoes - where the wind speed reaches up to 150 m/s (300 mph) and airborne projectiles can reach up to 50 m/s (100 mph). The objective of this work is to evaluate the performance of a saferoom under impact from tornado-generated debris and tornado-dragged vehicles. Numerical simulations were performed to model the impact problem using explicit dynamics and energy methods. Finite element models of the saferoom, windborne debris, and vehicle models were studied using the LS-DYNA software. RHT concrete material was used to model the saferoom and vehicle models from NCAC were used to characterize damage from impacts at various speeds. Simulation results indicate good performance of the saferoom structure at vehicle impact speeds up to 25 meters per second. Damage is more significant and increases nonlinearly starting at impact velocities of 35 m/s (78 mph). Results of this study give valuable insight into the dynamic response of saferooms subjected to projectile impacts, and provide design considerations for civilian protective structures. Further work is being done to validate the models with experimental measurements.
A 3D Finite Element Method for Flexible Multibody Systems
Gerstmayr, Johannes; Schoeberl, Joachim
2006-01-01
An efficient finite element (FE) formulation for the simulation of multibody systems is derived from Hamilton's principle. According to the classical assumptions of multibody systems, a large rotation formulation has been chosen, where large rotations and large displacements, but only small deformations of the single bodies are taken into account. The strain tensor is linearized with respect to a co-rotated frame. The present approach uses absolute coordinates for the degrees of freedom and forms an alternative to the floating frame of reference formulation that is based on relative coordinates and describes deformation with respect to a co-rotated frame. Due to the modified strain tensor, the present formulation distinguishes significantly from standard nodal based nonlinear FE methods. Constraints are defined in integral form for every pair of surfaces of two bodies. This leads to a small number of constraint equations and avoids artificial stress singularities. The resulting mass and stiffness matrices are constant apart from a transformation based on a single rotation matrix for each body. The particular structure of this transformation allows to prevent from the usually expensive factorization of the system Jacobian within implicit time--integration methods. The present method has been implemented and tested with the FE-package NGSolve and specific 3D examples are verified with a standard beam formulation
FEMA: a Finite Element Model of Material Transport through Aquifers
Yeh, G.T.; Huff, D.D.
1985-01-01
This report documents the construction, verification, and demonstration of a Finite Element Model of Material Transport through Aquifers (FEMA). The particular features of FEMA are its versatility and flexibility to deal with as many real-world problems as possible. Mechanisms included in FEMA are: carrier fluid advection, hydrodynamic dispersion and molecular diffusion, radioactive decay, sorption, source/sinks, and degradation due to biological, chemical as well as physical processes. Three optional sorption models are embodied in FEMA. These are linear isotherm and Freundlich and Langmuir nonlinear isotherms. Point as well as distributed source/sinks are included to represent artificial injection/withdrawals and natural infiltration of precipitation. All source/sinks can be transient or steady state. Prescribed concentration on the Dirichlet boundary, given gradient on the Neumann boundary segment, and flux at each Cauchy boundary segment can vary independently of each other. The aquifer may consist of as many formations as desired. Either completely confined or completely unconfined or partially confined and partially unconfined aquifers can be dealt with effectively. FEMA also includes transient leakage to or from the aquifer of interest through confining beds from or to aquifers lying below and/or above
FEMA: a Finite Element Model of Material Transport through Aquifers
Yeh, G.T.; Huff, D.D.
1985-01-01
This report documents the construction, verification, and demonstration of a Finite Element Model of Material Transport through Aquifers (FEMA). The particular features of FEMA are its versatility and flexibility to deal with as many real-world problems as possible. Mechanisms included in FEMA are: carrier fluid advection, hydrodynamic dispersion and molecular diffusion, radioactive decay, sorption, source/sinks, and degradation due to biological, chemical as well as physical processes. Three optional sorption models are embodied in FEMA. These are linear isotherm and Freundlich and Langmuir nonlinear isotherms. Point as well as distributed source/sinks are included to represent artificial injection/withdrawals and natural infiltration of precipitation. All source/sinks can be transient or steady state. Prescribed concentration on the Dirichlet boundary, given gradient on the Neumann boundary segment, and flux at each Cauchy boundary segment can vary independently of each other. The aquifer may consist of as many formations as desired. Either completely confined or completely unconfined or partially confined and partially unconfined aquifers can be dealt with effectively. FEMA also includes transient leakage to or from the aquifer of interest through confining beds from or to aquifers lying below and/or above.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-01-01
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research
Comparison of 3-D finite elements for incompressible fluid flow
Robichaud, M.; Tanguy, P.A.
1985-01-01
In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)
Numerical experiment on finite element method for matching data
Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.
1993-03-01
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
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.
MESHREF, Finite Elements Mesh Combination with Renumbering
1973-01-01
1 - Nature of physical problem solved: The program can assemble different meshes stored on tape or cards. Renumbering is performed in order to keep band width low. Voids and/ or local refinement are possible. 2 - Method of solution: Topology and geometry are read according to input specifications. Abundant nodes and elements are eliminated. The new topology and geometry are stored on tape. 3 - Restrictions on the complexity of the problem: Maximum number of nodes = 2000. Maximum number of elements = 1500
An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials
Lee Hae Sung.
1991-01-01
This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions
Vibration study of a vehicle suspension assembly with the finite element method
Cătălin Marinescu, Gabriel; Castravete, Ştefan-Cristian; Dumitru, Nicolae
2017-10-01
The main steps of the present work represent a methodology of analysing various vibration effects over suspension mechanical parts of a vehicle. A McPherson type suspension from an existing vehicle was created using CAD software. Using the CAD model as input, a finite element model of the suspension assembly was developed. Abaqus finite element analysis software was used to pre-process, solve, and post-process the results. Geometric nonlinearities are included in the model. Severe sources of nonlinearities such us friction and contact are also included in the model. The McPherson spring is modelled as linear spring. The analysis include several steps: preload, modal analysis, the reduction of the model to 200 generalized coordinates, a deterministic external excitation, a random excitation that comes from different types of roads. The vibration data used as an input for the simulation were previously obtained by experimental means. Mathematical expressions used for the simulation were also presented in the paper.
Ochoa-Avendaño, J.; Garzon-Alvarado, D. A.; Linero, Dorian L.; Cerrolaza, M.
2017-01-01
This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending...
A Finite Element Model for convection-dominatel transport problems
Carmo, E.G.D. do; Galeao, A.C.N.R.
1987-08-01
A new Protev-Galerkin Finite Element Model which automatically incorporates the search for the appropriate upwind direction is presented. It is also shown that modifying the Petrov-Galerkin weightin functions associated with elements adjascent to downwing boudaries effectively eliminates numerical oscillations normally obtained near boundary layers. (Author) [pt
Stress distributions in finite element analysis of concrete gravity dam ...
Gravity dams are solid structures built of mass concrete material; they maintain their stability against the design loads from the geometric shape, the mass, and the strength of the concrete. The model was meshed with an 8-node biquadratic plane strain quadrilateral (CPE8R) elements, using ABAQUS, a finite element ...
Finite element stress analysis of brick-mortar masonry under ...
Stress analysis of a brick-mortar couplet as a substitute for brick wall structure has been performed by finite element method, and algorithm for determining the element stiffness matrix for a plane stress problem using the displacement approach was developed. The nodal displacements were derived for the stress in each ...
Behaviour of Lagrangian triangular mixed fluid finite elements
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a ...
Modelling Convergence of Finite Element Analysis of Cantilever Beam
Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution ...
Coupling of smooth particle hydrodynamics with the finite element method
Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.
1994-01-01
A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))
A cohesive finite element formulation for modelling fracture and ...
cohesive elements experience material softening and lose their stress carrying capacity. A few simple ..... In the present work, a Lagrangian finite element procedure is employed. In this formu clation ...... o, is related to 'c o by,. 't o='c o ¼ 1 ہ. 1.
Finite element prediction of the swift effect based on Taylor-type polycrystal plasticity models
Duchene, Laurent; Delannay, L.; Habraken, Anne
2004-01-01
This paper describes the main concepts of the stress-strain interpolation model that has been implemented in the non-linear finite element code Lagamine. This model consists in a local description of the yield locus based on the texture of the material through the full constraints Taylor’s model. The prediction of the Swift effect is investigated: the influence of the texture evolution is shown up. The LAMEL model is also investigated for the Swift effect prediction. Peer reviewed
Finite element simulation of the welding process and structural behaviour of welded components
Locci, J.M.; Rouvray, A. de; Barbe, B.; Poirier, J.
1977-01-01
In the field of inelastic analysis of nuclear metal structures, the computation of residual stresses in welds, and their effects on the strength of welded components is of major importance. This paper presents an experimentally checked finite element simulation with the general nonlinear program PAM NEP-D, of the electron beam welding of two thick hemispherical shells, and the behaviour of the welded sphere under various additional thermomechanical sollicitations. (Auth.)
High accuracy 3D electromagnetic finite element analysis
Nelson, E.M.
1997-01-01
A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed. copyright 1997 American Institute of Physics
Finite element approximation to the even-parity transport equation
Lewis, E.E.
1981-01-01
This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions
Linear finite element method for one-dimensional diffusion problems
Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica
2011-07-01
We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)
Finite element analysis of beam-to-column joints in steel frames under cyclic loading
Elsayed Mashaly
2011-03-01
Full Text Available The aim of this paper is to present a simple and accurate three-dimensional (3D finite element model (FE capable of predicting the actual behavior of beam-to-column joints in steel frames subjected to lateral loads. The software package ANSYS is used to model the joint. The bolted extended-end-plate connection was chosen as an important type of beam–column joints. The extended-end-plate connection is chosen for its complexity in the analysis and behavior due to the number of connection components and their inheritable non-linear behavior. Two experimental tests in the literature were chosen to verify the finite element model. The results of both the experimental and the proposed finite element were compared. One of these tests was monotonically loaded, whereas the second was cyclically loaded. The finite element model is improved to enhance the defects of the finite element model used. These defects are; the long time need for the analysis and the inability of the contact element type to follow the behavior of moment–rotation curve under cyclic loading. As a contact element, the surface-to-surface element is used instead of node-to-node element to enhance the model. The FE results show good correlation with the experimental one. An attempt to improve a new technique for modeling bolts is conducted. The results show that this technique is supposed to avoid the defects above, give much less elements number and less solution time than the other modeling techniques.
Xiao Xuejian; Chen Ruxin
1995-02-01
Based on the R. Hills incremental virtual power principle and the elasto-plastic constitution equation for large deformation and by considering physical nonlinear, geometric nonlinear and thermal effects, a plane and axisymmetric finite element equation for thermal large elasto-plastic deformation has been established in the Euler description. The corresponding analysis program ATLEPD has been also complied for thermal large elasto-plastic deformation process of O-ring in RPV. The variations of stress, strain, contact specific pressure, mesh deformation and the aspects of spring back in upsetting and spring back process have been also investigated. Numerical results are fairly consistent with experimental ones. (5 figs., 4 tabs.)
Finite bandwidth, nonlinear convective flow in a mushy layer
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)
On Using Particle Finite Element for Hydrodynamics Problems Solving
E. V. Davidova
2015-01-01
Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \
Finite Element Analysis of Circular Plate using SolidWorks
Kang, Yeo Jin; Jhung, Myung Jo
2011-01-01
Circular plates are used extensively in mechanical engineering for nuclear reactor internal components. The examples in the reactor vessel internals are upper guide structure support plate, fuel alignment plate, lower support plate etc. To verify the structural integrity of these plates, the finite element analyses are performed, which require the development of the finite element model. Sometimes it is very costly and time consuming to make the model especially for the beginners who start their engineering job for the structural analysis, necessitating a simple method to develop the finite element model for the pursuing structural analysis. Therefore in this study, the input decks are generated for the finite element analysis of a circular plate as shown in Fig. 1, which can be used for the structural analysis such as modal analysis, response spectrum analysis, stress analysis, etc using the commercial program Solid Works. The example problems are solved and the results are included for analysts to perform easily the finite element analysis of the mechanical plate components due to various loadings. The various results presented in this study would be helpful not only for the benchmark calculations and results comparisons but also as a part of the knowledge management for the future generation of young designers, scientists and computer analysts
Two-dimensional isostatic meshes in the finite element method
Martínez Marín, Rubén; Samartín, Avelino
2002-01-01
In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...
Finite element modeling of fluid/thermal/structural interaction for a gas-cooled fast reactor core
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
Hualien forced vibration calculation with a finite element model
Wang, F.; Gantenbein, F.; Nedelec, M.; Duretz, Ch.
1995-01-01
The forced vibration tests of the Hualien mock-up were useful to validate finite element models developed for soil-structure interaction. In this paper the two sets of tests with and without backfill were analysed. the methods used are based on finite element modeling for the soil. Two approaches were considered: calculation of soil impedance followed by the calculation of the transfer functions with a model taking into account the superstructure and the impedance; direct calculation of the soil-structure transfer functions, with the soil and the structure being represented in the same model by finite elements. Blind predictions and post-test calculations are presented and compared with the test results. (author). 4 refs., 8 figs., 2 tabs
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Analytical and finite element modeling of grounding systems
Luz, Mauricio Valencia Ferreira da [University of Santa Catarina (UFSC), Florianopolis, SC (Brazil)], E-mail: mauricio@grucad.ufsc.br; Dular, Patrick [University of Liege (Belgium). Institut Montefiore], E-mail: Patrick.Dular@ulg.ac.be
2007-07-01
Grounding is the art of making an electrical connection to the earth. This paper deals with the analytical and finite element modeling of grounding systems. An electrokinetic formulation using a scalar potential can benefit from floating potentials to define global quantities such as electric voltages and currents. The application concerns a single vertical grounding with one, two and three-layer soil, where the superior extremity stays in the surface of the soil. This problem has been modeled using a 2D axi-symmetric electrokinetic formulation. The grounding resistance obtained by finite element method is compared with the analytical one for one-layer soil. With the results of this paper it is possible to show that finite element method is a powerful tool in the analysis of the grounding systems in low frequencies. (author)
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Finite element simulation of ironing process under warm conditions
Swadesh Kumar Singh
2014-01-01
Full Text Available Metal forming is one of the most important steps in manufacturing of a large variety of products. Ironing in deep drawing is done by adjusting the clearance between the punch and the die and allow the material flow over the punch. In the present investigation effect of extent of ironing behavior on the characteristics of the product like thickness distribution with respect to temperature was studied. With the help of finite element simulation using explicit finite element code LS-DYNA the stress in the drawn cup were predicted in the drawn cup. To increase the accuracy in the simulation process, numbers of integration points were increased in the thickness direction and it was found that there is very close prediction of finite element results to that of experimental ones.
The Finite Element Numerical Modelling of 3D Magnetotelluric
Ligang Cao
2014-01-01
Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.
Adaptive finite-element ballooning analysis of bipolar ionized fields
Al-Hamouz, Z.M.
1995-01-01
This paper presents an adaptive finite-element iterative method for the analysis of the ionized field around high-voltage bipolar direct-current (HVDC) transmission line conductors without resort to Deutsch's assumption. A new iterative finite-element ballooning technique is proposed to solve Poisson's equation wherein the commonly used artificial boundary around the transmission line conductors is simulated at infinity. Unlike all attempts reported in the literature for the solution of ionized field, the constancy of the conductors' surface field at the corona onset value is directly implemented in the finite-element formulation. In order to investigate the effectiveness of the proposed method, a laboratory model was built. It has been found that the calculated V-I characteristics and the ground-plane current density agreed well with those measured experimentally. The simplicity in computer programming in addition to the low number of iterations required to achieve convergence characterize this method of analysis
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
Stochastic Finite Elements in Reliability-Based Structural Optimization
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....
FINITE ELEMENT MODELING OF THIN CIRCULAR SANDWICH PLATES DEFLECTION
K. S. Kurachka
2014-01-01
Full Text Available A mathematical model of a thin circular sandwich plate being under the vertical load is proposed. The model employs the finite element method and takes advantage of an axisymmetric finite element that leads to the small dimension of the resulting stiffness matrix and sufficient accuracy for practical calculations. The analytical expressions for computing local stiffness matrices are found, which can significantly speed up the process of forming the global stiffness matrix and increase the accuracy of calculations. A software is under development and verification. The discrepancy between the results of the mathematical model and those of analytical formulas for homogeneous thin circularsandwich plates does not exceed 7%.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim; Xue, Guangri
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Finite element solution of two dimensional time dependent heat equation
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
Stress analysis of heated concrete using finite elements
Majumdar, P.; Gupta, A.; Marchertas, A.
1994-01-01
Described is a finite element analysis of concrete, which is subjected to rapid heating. Using thermal mass transport calculation, the moisture content, temperature and pore pressure distribution over space and time is obtained first. From these effects, stress at various points of the concrete are computed using the finite element method. Contribution to the stress formulation comes from three components, namely the thermal expansion, pore pressure, and the shrinkage of concrete due to moisture loss (from dehydration). The material properties of concrete are assumed to be homogeneous, elastic, and cracking is not taken into consideration. (orig.)
COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER
Khomchenko A.
2017-12-01
Full Text Available The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.
Stochastic Finite Elements in Reliability-Based Structural Optimization
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Finite element analyses for seismic shear wall international standard problem
Park, Y.J.; Hofmayer, C.H.
1998-04-01
Two identical reinforced concrete (RC) shear walls, which consist of web, flanges and massive top and bottom slabs, were tested up to ultimate failure under earthquake motions at the Nuclear Power Engineering Corporation's (NUPEC) Tadotsu Engineering Laboratory, Japan. NUPEC provided the dynamic test results to the OECD (Organization for Economic Cooperation and Development), Nuclear Energy Agency (NEA) for use as an International Standard Problem (ISP). The shear walls were intended to be part of a typical reactor building. One of the major objectives of the Seismic Shear Wall ISP (SSWISP) was to evaluate various seismic analysis methods for concrete structures used for design and seismic margin assessment. It also offered a unique opportunity to assess the state-of-the-art in nonlinear dynamic analysis of reinforced concrete shear wall structures under severe earthquake loadings. As a participant of the SSWISP workshops, Brookhaven National Laboratory (BNL) performed finite element analyses under the sponsorship of the U.S. Nuclear Regulatory Commission (USNRC). Three types of analysis were performed, i.e., monotonic static (push-over), cyclic static and dynamic analyses. Additional monotonic static analyses were performed by two consultants, F. Vecchio of the University of Toronto (UT) and F. Filippou of the University of California at Berkeley (UCB). The analysis results by BNL and the consultants were presented during the second workshop in Yokohama, Japan in 1996. A total of 55 analyses were presented during the workshop by 30 participants from 11 different countries. The major findings on the presented analysis methods, as well as engineering insights regarding the applicability and reliability of the FEM codes are described in detail in this report. 16 refs., 60 figs., 16 tabs
Numerical analysis of creep brittle rupture by the finite element method
Goncalves, O.J.A.; Owen, D.R.J.
1983-01-01
In this work an implicit algorithm is proposed for the numerical analysis of creep brittle rupture problems by the finite element method. This kind of structural failure, typical in components operating at high temperatures for long periods of time, is modelled using either a three dimensional generalization of the Kachanov-Rabotnov equations due to Leckie and Hayhurst or the Monkman-Grant fracture criterion together with the Linear Life Fraction Rule. The finite element equations are derived by the displacement method and isoparametric elements are used for the spatial discretization. Geometric nonlinear effects (large displacements) are accounted for by an updated Lagrangian formulation. Attention is also focussed on the solution of the highly stiff differential equations that govern damage growth. Finally the numerical results of a three-dimensional analysis of a pressurized thin cylinder containing oxidised pits in its external wall are discussed. (orig.)
Advanced finite element simulation with MSC Marc application of user subroutines
Javanbakht, Zia
2017-01-01
This book offers an in-depth insight into the general-purpose finite element program MSC Marc, which is distributed by MSC Software Corporation. It is a specialized program for nonlinear problems (implicit solver) which is common in academia and industry. The primary goal of this book is to provide a comprehensive introduction to a special feature of this software: the user can write user-subroutines in the programming language Fortran, which is the language of all classical finite element packages. This subroutine feature allows the user to replace certain modules of the core code and to implement new features such as constitutive laws or new elements. Thus, the functionality of commercial codes (‘black box’) can easily be extended by linking user written code to the main core of the program. This feature allows to take advantage of a commercial software package with the flexibility of a ‘semi-open’ code. .
Determination of the ultimate load in concrete slabs by the yield line finite element method
Vaz, L.E.; Feijo, B.; Martha, L.F.R.; Lopes, M.M.
1984-01-01
A method for calculating the ultimate load in reinforced concrete slabs is proposed. The method follows the finite element aproach representating the continuum slab as an assembly of rigid triangular plates connected along their sides through yield line elements. This approach leads to the definition of the displacement configuration of the plate only as a function of the transversal displacement at the nodes of the mesh (1 DOF per node) reducing significantly the number of DOF's in relation to the conventional formulation by means of the finite element method (minimum of 3 DOF per node). Nonlinear behaviour of the reinforced concrete section is considered in the definition of the moment rotation curve of the yield lines. The effect of the in plane forces acting in the middle surface of the plate is also taken into account. The validity of the model is verified comparing the numerical solutions with the results of the classical yield line theory. (Author) [pt
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Second-order wave diffraction by a circular cylinder using scaled boundary finite element method
Song, H; Tao, L
2010-01-01
The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.
A finite element field solver for dipole modes
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
Finite elements for the thermomechanical calculation of massive structures
Argyris, J.H.; Szimmat, J.; Willam, K.J.
1978-01-01
The paper examines the fine element analysis of thermal stress and deformation problems in massive structures. To this end compatible idealizations are utilized for heat conduction and static analysis in order to minimize the data transfer. For transient behaviour due to unsteady heat flow and/or inelastics material processes the two computational parts are interwoven in form of an integrated software package for finite element analysis of thermomechanical problems in space and time. (orig.) [de
Liu, P.F.; Zheng, J.Y.; Zhang, B.J.; Shi, P.
2010-01-01
A 3D parametric finite element model of the pipeline and soil is established using finite element method to perform the failure analysis of natural gas buried X65 steel pipeline under deflection load. The pipeline is assumed to be loaded in a parabolic deflection displacement along the axial direction. Based on the true stress-strain constitutive relationship of X65 steel, the elastic-plastic finite element analysis employs the arc-length algorithm and non-linear stabilization algorithm respectively to simulate the strain softening properties of pipeline after plastic collapse. Besides, effects of the soil types and model sizes on the maximum deflection displacement of pipeline are investigated. The proposed finite element method serves as a base available for the safety design and evaluation as well as engineering acceptance criterion for the failure of pipeline due to deflection.
Crack modeling of rotating blades with cracked hexahedral finite element method
Liu, Chao; Jiang, Dongxiang
2014-06-01
Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.
Piezoelectric Accelerometers Modification Based on the Finite Element Method
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
Optimization of forging processes using finite element simulations
Bonte, M.H.A.; Fourment, Lionel; Do, Tien-tho; van den Boogaard, Antonius H.; Huetink, Han
2010-01-01
During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to the design of feasible forming processes. Coupling FEM to mathematical optimization algorithms offers a promising opportunity to design optimal metal forming processes rather than
Finite element method for solving neutron transport problems
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
Finite element concept to derive isostatic residual maps
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual ...
Total hip reconstruction in acetabular dysplasia : a finite element study
Schüller, H.M.; Dalstra, M.; Huiskes, H.W.J.; Marti, R.K.
1993-01-01
In acetabular dysplasia, fixation of the acetabular component of a cemented total hip prosthesis may be insecure and superolateral bone grafts are often used to augment the acetabular roof. We used finite element analysis to study the mechanical importance of the lateral acetabular roof and found
A mixed finite element method for particle simulation in lasertron
Le Meur, G.
1987-03-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Steam generator tube rupture simulation using extended finite element method
Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken
2016-08-15
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
FINELM: a multigroup finite element diffusion code. Part II
Davierwalla, D.M.
1981-05-01
The author presents the axisymmetric case in cylindrical coordinates for the finite element multigroup neutron diffusion code, FINELM. The numerical acceleration schemes incorporated viz. the Lebedev extrapolations and the coarse mesh rebalancing, space collapsing, are discussed. A few benchmark computations are presented as validation of the code. (Auth.)
A particle finite element method for machining simulations
Sabel, Matthias; Sator, Christian; Müller, Ralf
2014-07-01
The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.
Possibilities of Particle Finite Element Methods in Industrial Forming Processes
Oliver, J.; Cante, J. C.; Weyler, R.; Hernandez, J.
2007-04-01
The work investigates the possibilities offered by the particle finite element method (PFEM) in the simulation of forming problems involving large deformations, multiple contacts, and new boundaries generation. The description of the most distinguishing aspects of the PFEM, and its application to simulation of representative forming processes, illustrate the proposed methodology.
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Design, development and use of the finite element machine
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
Aranha: a 2D mesh generator for triangular finite elements
Fancello, E.A.; Salgado, A.C.; Feijoo, R.A.
1990-01-01
A method for generating unstructured meshes for linear and quadratic triangular finite elements is described in this paper. Some topics on the C language data structure used in the development of the program Aranha are also presented. The applicability for adaptive remeshing is shown and finally several examples are included to illustrate the performance of the method in irregular connected planar domains. (author)
3D finite element simulation of optical modes in VCSELs
Rozova, M.; Pomplun, J.; Zschiedrich, L.; Schmidt, F.; Burger, S.
2011-01-01
We present a finite element method (FEM) solver for computation of optical resonance modes in VCSELs. We perform a convergence study and demonstrate that high accuracies for 3D setups can be attained on standard computers. We also demonstrate simulations of thermo-optical effects in VCSELs.
Finite element analysis of tubular joints in offshore structures ...
... representing a 2-D model of the joint between the brace and the chord walls. This was subsequently followed but finite element analysis of six tubular joints. A global analysis was initially undertaken, then the submodel analysis carried in the areas of stress concentration. Journal of Civil Engineering, JKUAT (2001) Vol 6, ...
A mixed finite element method for particle simulation in Lasertron
Le Meur, G.
1987-01-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Steam generator tube rupture simulation using extended finite element method
Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken
2016-01-01
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
Can finite element models detect clinically inferior cemented hip implants?
Stolk, J.; Maher, S.A.; Verdonschot, N.J.J.; Prendergast, P.J.; Huiskes, R.
2003-01-01
Rigorous preclinical testing of cemented hip prostheses against the damage accumulation failure scenario will reduce the incidence of aseptic loosening. For that purpose, a finite element simulation is proposed that predicts damage accumulation in the cement mantle and prosthetic migration. If the
a finite element model for the analysis of bridge decks
Dr Obe
A FINITE ELEMENT MODEL FOR THE ANALYSIS OF BRIDGE DECKS. NIGERIAN JOURNAL OF TECHNOLOGY, VOL. 27 NO.1, MARCH 2008. 59. (a) Beam-plate system. (b) T-beam structural model. Fig. 1 Beam-plate structure idealisations. The matrix displacement method of analysis is used. The continuum structure is.