Error-controlled Adaptive Finite Elements in Solid Mechanics

This book contains the numerical methods, mathematical analysis, algorithms, software aspects and comparative results of a six year joint project of nine German University institutes, supported by the German National Science Foundation (DFG).

It covers new progress for efficient and reliable error estimates mainly of the Finite Element Method for non-linear problems in solid mechanics, as well as efficient re-meshing techniques and solution algorithms.

Topics covered include:

• Elastoplastic deformations and contact problems

• Shear localization of inelastic deformations

• Thin-walled structures

• Elastodynamics

Table of Contents

Preface.

Introduction (E. Stein).

Error Estimation and Adaptive Mesh Design for FE Models in Elasto-Plasticity Theory (R. Rannacher and F. Suttmeier).

Adaptive FEM for Elasto-plastic Deformations (E. Stein and M. Schmidt).

Numerical Simulation of Localization Phenomena in Geomechanics by Entended Continuum Formulations (W. Wunderlich, et al.).

Adaptive Methods for Contact Problems (A. Rieger, et al.).

An Adaptive Boundary Element Method for Contact Problems (C. Eck, et al.).

Goal-Oriented Error Estimation in Solid Mechanics (H. Steeb, et al.).

The p-version of the Finite Element Method for Structural Problems (E. Rank, et al.).

Adaptive Analysis of Plate and Shell Structures Under Transient Loading (K. Schweizerhof, et al.).

The Application of Adaptive Parallel Multigrid Methods to Problems in Nonlinear Solid Mechanics (S. Lang, et al.).

Benchmarks (E. Stein, et al.).

Index.