Showing papers on "Finite element limit analysis published in 2004"
25 Mar 2004
TL;DR: The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Bending Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Non-linear Analysis of Time-Dependent Problems 9. Finite Elements Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems as mentioned in this paper
Abstract: 1. Introduction 2. The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Heat Transfer and other Field Problems in Two Dimensions 6. Nonlinear Bending of Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Nonlinear Analysis of Time-Dependent Problems 9. Finite Element Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems A1 Solution Procedures for Nonlinear Equations A2 Banded Symmetric and Unsymmetric Solvers
896 citations
TL;DR: In this article, a combination of discrete element method (DEM) and finite element method for dynamic analysis of geomechanics problems is presented, which can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system.
252 citations
TL;DR: Investigation of the influence of the material mapping algorithm on the results predicted by the finite element analysis showed that the choice of the mapping algorithm influences the material distribution, but this did not always propagate into the finiteelement results.
249 citations
TL;DR: This paper explains how the evaluation of integrals and the transfer between arbitrary finite element spaces can be implemented easily and computed efficiently.
Abstract: The basis of mapped finite element methods are reference elements where the components of a local finite element are defined. The local finite element on an arbitrary mesh cell will be given by a map from the reference mesh cell. This paper describes some concepts of the implementation of mapped finite element methods. From the definition of mapped finite elements, only local degrees of freedom are available. These local degrees of freedom have to be assigned to the global degrees of freedom which define the finite element space. We will present an algorithm which computes this assignment. The second part of the paper shows examples of algorithms which are implemented with the help of mapped finite elements. In particular, we explain how the evaluation of integrals and the transfer between arbitrary finite element spaces can be implemented easily and computed efficiently.
171 citations
TL;DR: The method involves a simple shift of the integration points to locations away from conventional Gauss or Gauss–Lobatto integration points, which results in fourth-order accuracy with respect to dispersion error (error in wavelength), as opposed to the second- order accuracy resulting from conventional integration.
156 citations
TL;DR: In this paper, a partial mixed layerwise finite element model for adaptive plate structures is presented by considering a Reissner mixed variational principle, and the mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables.
148 citations
TL;DR: A unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques to introduce a generic tool for the study of in vivo knee joint behavior.
137 citations
15 Nov 2004
TL;DR: The goals of the present chapter are to sketch out that several physical problems share such an algebraic structure once a discretization is introduced, and to present a simple, algebraic version of the abstract theory that rules most applications of mixed finite element methods.
Abstract: Within the well-known and highly effective finite element method for the computation of approximate solutions of complex boundary value problems, we focus on the often-called mixed finite element methods, where in our terminology the word ‘mixed’ indicates the fact that the problem discretization typically results in a linear algebraic system characterized by a null matrix on the main diagonal.
Accordingly, the goals of the present chapter are: (1) to sketch out that several physical problems share such an algebraic structure once a discretization is introduced; (2) to present a simple, algebraic version of the abstract theory that rules most applications of mixed finite element methods; (3) to give several examples of efficient mixed finite element methods; (4) finally, to give some hints on how to perform a stability and error analysis, focusing on a representative problem.
Keywords:
mixed finite elements;
potential energy;
Hellinger-Reissner;
Hu-Washizu;
thermal diffusion;
stokes;
nearly incompressible elasticity;
stability conditions
124 citations
TL;DR: In this paper, the vector form intrinsic finite element is extended to formulate plane solid elements, a three-node triangular element and a four-node isoparametric element, and conceptual differences of the intrinsic element and traditional element based on variational formulation are discussed.
Abstract: In the second article of the series, the vector form intrinsic finite element is extended to formulate plane solid elements, a three-node triangular element and a four-node isoparametric element. Also, conceptual differences of the intrinsic element and traditional element based on variational formulation are discussed.
93 citations
Patent•
11 Nov 2004TL;DR: In this article, a method for automatic evaluation of a finite element simulation for an industrial system such as a motor vehicle body includes predefining an electronic design model of the industrial system and generating finite elements for the model.
Abstract: A method for automatic evaluation of a finite element simulation for an industrial system such as a motor vehicle body includes predefining an electronic design model of the industrial system and generating finite elements for the model. The stresses occurring in the finite elements are determined using a finite element simulation. Each finite element, which is a two-dimensional element and not a rigid object element and whose stress exceeds a predefined stress limiting value, is determined. For each determined two-dimensional element which is not a triangle, an element limiting value is determined on the basis of the stress limiting value. Each determined two-dimensional element is classified as critical if its computed stress exceeds the established element limiting value. The method enables identification of areas of the industrial system having a high stress and reduces the effect of inaccuracies that occur on the evaluation of the finite element simulation due to the approximation of the vehicle body by finite elements.
91 citations
TL;DR: The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively, however modifications to the basic idea are vital to meet the particular needs of the analysis.
Abstract: Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.
TL;DR: In this paper, a finite element formulation for the non-linear analysis of two-layer composite planar frames with an interlayer slip is presented, where the geometrically nonlinear Reissner's beam theory is assumed.
TL;DR: In this article, analytical and finite element models are used to study the modal interactions in both planar and spatial responses to harmonic in-plane and out-of-plane loads.
TL;DR: In this paper, a thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin-walled structures.
Abstract: A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin-walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature-dependent elastic–plastic model with a non-linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one-sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters is presented, which is based on the general so-called direct differentiation method (DDM).
Abstract: This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in the number of elements required for a given level of accuracy in the computed response of the finite element model. This advantage of force-based elements is of even more interest in structural reliability analysis, which requires accurate and efficient computation of structural response and structural response sensitivities. This paper focuses on material non-linearities in the context of both static and dynamic response analysis. The formulation presented herein assumes the use of a general-purpose non-linear finite element analysis program based on the direct stiffness method. It is based on the general so-called direct differentiation method (DDM) for computing response sensitivities. The complete analytical formulation is presented at the element level and details are provided about its implementation in a general-purpose finite element analysis program. The new formulation and its implementation are validated through some application examples, in which analytical response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The force-based finite element methodology augmented with the developed procedure for analytical response sensitivity computation offers a powerful general tool for structural response sensitivity analysis.
TL;DR: In this article, a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle was proposed to create a stable finite element method in the context of nearly incompressible behavior.
Abstract: Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finiteelement method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm.
TL;DR: An improved finite element model for the linear analysis of anisotropic and laminated doubly curved, moderately thick composite shells/shell-panels is presented in this article, where the extensional and flexural stresses are regularized by least square smoothing technique.
TL;DR: In this paper, a voxel-transformation model and algorithm have been developed to allow accurate representation of cutting through the part voxels intersected by the tool volume.
TL;DR: In this paper, a study on the dynamic response of flexible massive strip-foundations embedded in layered soils is presented, where the foundation is treated with a finite element formulation, while the difficulty in modeling the infinite extent of the soil is overcome by a boundary element formulation.
TL;DR: By passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained, and strong a priori estimates for the finiteelement solutions are derived.
Abstract: Semidiscrete finite element approximations of a linear fluid-structure interaction problem are studied. First, results concerning a divergence-free weak formulation of the interaction problem are reviewed. Next, semidiscrete finite element approximations are defined, and the existence of finite element solutions is proved with the help of an auxiliary, discretely divergence-free formulation. A discrete inf-sup condition is verified, and the existence of a finite element pressure is established. Strong a priori estimates for the finite element solutions are also derived. Then, by passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained.
TL;DR: In this paper, two recently proposed formulations to couple mesh-free and finite element methods are discussed and compared.
01 Jan 2004
TL;DR: This book discusses one-Dimensional Shape Functions, Isoparametric Elements, Gradient-Based Methods, and more.
Abstract: Preface Notation Introduction One-Dimensional Shape Functions One-Dimensional Second-Order Equations One-Dimensional Fourth-Order Equations Two-Dimensional Elements Two-Dimensional Problems More Two-Dimensional Problems Axisymmetric Heat Transfer Transient Problems Single Nonlinear One-Dimensional Equations Plane Elasticity Stokes Equations and Penalty Method Vibration Analysis Computer Codes: Mathematica Codes, Ansys Codes, MatLab Codes, Fortran Codes Appendix A: Integration Formulas Appendix B: Special Cases Appendix C: Temporal Approximations Appendix D: Isoparametric Elements Appendix E: Green's Identities Appendix F: Gaussian Quadrature Appendix G: Gradient-Based Methods Bibliography Index
TL;DR: In this article, a micromechanical layered model is proposed for the finite element analysis of the quasi-static collapse of foam-filled ultralight aluminium box sections, which allows for the local penetration of the folds and shearing of the foam, thus avoiding the commonly adopted approximations in which the foam must undergo global deformation to accommodate the externally applied loads.
TL;DR: In this paper, a multi-level computational procedure that leads to optimum wall ply thickness and geometric shapes for areas such as door and window openings is investigated. And the optimisation procedures are extensively automated whereby iterative finite element solutions are executed under the control of a software suite containing information on the optimization parameters, objective functions and constraints.
01 Sep 2004
TL;DR: In this article, the authors used an extended form of the finite element method to study failure in polycrystalline microstructures, and they used the framework of partition of unity to enrich the classical finite element approximation with a discontinuous function.
Abstract: In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.
TL;DR: In this paper, the sequential limit analysis (SFA) procedure is used to estimate the structural response of a rigid-plastic shell element to a single-shell failure in the presence of a single shell element.
06 Jun 2004
TL;DR: The standard FEM is improved with techniques needed to efficiently capture growth and fractures and makes it possible to synthesize patterns of fractures induced by growth or shrinkage of one layer with respect to another.
Abstract: We present a model of fracture formation on surfaces of bi-layered materials. The model makes it possible to synthesize patterns of fractures induced by growth or shrinkage of one layer with respect to another. We use the finite element methods (FEM) to obtain numerical solutions. This paper improves the standard FEM with techniques needed to efficiently capture growth and fractures.
TL;DR: In this article, a finite element analysis was carried out to achieve the multistage deep drawing of a rectangular configuration with an extreme aspect ratio, focusing on the process design, and the analysis incorporated brick elements in a rigid-plastic finite element method with an explicit time integration scheme using LS-DYNA3D software.