Error indicators and adaptive remeshing in large deformation finite element analysis

Abstract We present and use a system of adaptive procedures for large-deformation finite element analysis of elastic and elastoplastic problems using the h -refinement approach. The procedures include a pointwise indicator for error in stresses, a pointwise indicator for error in plastic strain increments, a quadrilateral element mesh generator for generating completely new meshes on the deformed configuration of the body, and several mapping schemes for transferring state variables and history-dependent variables accurately across models. These procedures constitute the ingredients of a proposed adaptive scheme that is demonstrated to be effective in solutions of two-dimensional stress analysis problems including contact conditions. An important observation is that with coarse finite element meshes and no error indicator used, crucial physical phenomena may be completely missed in the analysis.

[1]  Richard H. Crawford,et al.  Mesh rezoning of 2D isoparametric elements by inversion , 1989 .

[2]  John S. Campbell,et al.  Local and global smoothing of discontinuous finite element functions using a least squares method , 1974 .

[3]  Nam-Sua Lee,et al.  On the use of hierartchical models in engineering analyqiq , 1990 .

[4]  I. Babuska,et al.  Rairo Modélisation Mathématique Et Analyse Numérique the H-p Version of the Finite Element Method with Quasiuniform Meshes (*) , 2009 .

[5]  K. Bathe,et al.  The inf-sup test , 1993 .

[6]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[7]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[8]  Mark S. Shephard,et al.  Automated metalforming modeling utilizing adaptive remeshing and evolving geometry , 1988 .

[9]  Jung-Ho Cheng,et al.  Automatic adaptive remeshing for finite element simulation of forming processes , 1988 .

[10]  Henry T. Y. Yang,et al.  Adaptive 2D finite element simulation of metal forming processes , 1989 .

[11]  S. A. Coons SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS , 1967 .

[12]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[13]  W. A. Cook Body oriented (natural) co-ordinates for generating three-dimensional meshes , 1974 .

[14]  B. Guo,et al.  The hp version of the finite element method Part 1 : The basic approximation results , 2022 .

[15]  O. C. Zienkiewicz,et al.  Adaptive FEM computation of forming processes—Application to porous and non‐porous materials , 1990 .

[16]  W. Rheinboldt,et al.  Error Estimates for Adaptive Finite Element Computations , 1978 .

[17]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[18]  Klaus-Jürgen Bathe,et al.  A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures , 1990 .

[19]  K. Bathe,et al.  Effects of element distortions on the performance of isoparametric elements , 1993 .

[20]  K. Bathe,et al.  Studies of finite element procedures—stress band plots and the evaluation of finite element meshes , 1986 .

[21]  Noboru Kikuchi,et al.  A mesh re-zoning technique for finite element simulations of metal forming processes , 1986 .

[22]  Barna A. Szabó,et al.  Estimation and Control Error Based on P-Convergence, , 1984 .

[23]  Richard H. Gallagher,et al.  A general two‐dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings , 1981 .

[24]  Klaus-Jürgen Bathe,et al.  Adaptive finite element analysis of large strain elastic response , 1993 .

[25]  K. Bathe,et al.  A finite element formulation for nonlinear incompressible elastic and inelastic analysis , 1987 .

[26]  J. Z. Zhu,et al.  Effective and practical h–p‐version adaptive analysis procedures for the finite element method , 1989 .

[27]  J. Oden,et al.  Toward a universal h - p adaptive finite element strategy: Part 2 , 1989 .

[28]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[29]  Mark S. Shephard,et al.  Automated adaptive two-dimensional system for the hp-version of the finite element method , 1991 .

[30]  F. Brezzi,et al.  A discourse on the stability conditions for mixed finite element formulations , 1990 .

[31]  Ivo Babuška,et al.  On the Rates of Convergence of the Finite Element Method , 1982 .

[32]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[33]  V. Murti,et al.  Numerical inverse isoparametric mapping in remeshing and nodal quantity contouring , 1986 .

[34]  Miguel Luiz Bucalem,et al.  On the use of hierarchical models in engineering analysis , 1990 .