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Elastoplastic Problems (elastoplastic + problem)

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Engineering100%

Selected Abstracts

Fast multipole boundary element analysis of two-dimensional elastoplastic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007
P. B. Wang
Abstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Three-dimensional elastoplastic analysis by triple-reciprocity boundary element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2007
Yoshihiro Ochiai
Abstract In general, internal cells are required to solve elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is ease of data preparation, is lost. Triple-reciprocity BEM can be used to solve two-dimensional elastoplasticity problems with a small plastic deformation. In this study, it is shown that three-dimensional elastoplastic problems can be solved, without the use of internal cells, by the triple-reciprocity BEM. An initial strain formulation is adopted and the initial strain distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solving several problems. Copyright © 2006 John Wiley & Sons, Ltd. [source]

An objective incremental formulation for the solution of anisotropic elastoplastic problems at finite strain

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2001
S. Chatti
Abstract This paper presents an objective formulation for the anisotropic elastic,plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame. The multiplicative decomposition of the deformation gradient is adopted and the formulation is hyperelastic based. Since no stress rates are present and the incremental constitutive law was formulated in a rotating frame, the formulation is numerically objective in the time integration. Explicit algorithm was proposed and has been optimized with regard to stability and accuracy. The incremental law was integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic,plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Numerical analysis of Augmented Lagrangian algorithms in complementary elastoplasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004
L. Contrafatto
The main subject of the paper is the investigation of Augmented Lagrangian algorithms and update formulas in the solution of elastoplastic problems. A stress rate formulation for elastoplastic models with internal variables and its finite increment form is employed to state the mechanical problem. In this formulation the Augmented Lagrangian is used to enforce the constraint of plastic admissibility directly on the stresses and thermodynamic forces. This is not a limitation of the Augmented Lagrangian approach, and the same framework can be built on more classical displacement formulations as well. The meaning and the derivation of various first and second order Lagrangian multipliers update formulas and iterative schemes is shown. A new diagonal iteration algorithm and the introduction of a scale factor for the Augmented Lagrangian term are proposed. Numerical examples compare the efficiency of several forms of Augmented Lagrangian algorithms and illustrate the influence of the scale factor and of the penalty parameter. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Adaptive finite element procedures for elastoplastic problems at finite strains

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
A. Koch Dipl.-Ing.
A major difficulty in the context of adaptive analysis of geometrically nonlinear problems is to provide a robust remeshing procedure that accounts both for the error caused by the spatial discretization and for the error due to the time discretization. For stability problems, such as strain localization and necking, it is essential to provide a step,size control in order to get a robust algorithm for the solution of the boundary value problem. For this purpose we developed an easy to implement step,size control algorithm. In addition we will consider possible a posteriori error indicators for the spatial error distribution of elastoplastic problems at finite strains. This indicator is adopted for a density,function,based adaptive remeshing procedure. Both error indicators are combined for the adaptive analysis in time and space. The performance of the proposed method is documented by means of representative numerical examples. [source]