Error-controlled Adaptive Finite Elements in Solid Mechanics
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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* ElastodynamicsThe authors, all experts in computational mechanics, provide a wealth of new ideas for the next generation of software for adaptive finite elements, which will be of great interest to industry. Each chapter includes the state of the art, comparisons between different methods and the mechanical and mathematical background of the methods addressed. Practising engineers, researchers and students in engineering, applied mathematicians and computer scientists will find new material for developing, maintaining and applying finite element algorithms which reach new heights of approximation quality.
Preface1Introduction12Error Estimation and Adaptive Mesh Design for FE Models in Elasto-Plasticity Theory53Adaptive FEM for Elasto-plastic Deformations534Numerical Simulation of Localization Phenomena in Geomechanics by Extended Continuum Formulations1095Adaptive Methods for Contact Problems1476An Adaptive Boundary Element Method for Contact Problems1817Goal-Oriented Error Estimation in Solid Mechanics2118The p-version of the Finite Element Method for Structural Problems2639Adaptive Analysis of Plate and Shell Structures Under Transient Loading30910The Application of Adaptive Parallel Multigrid Methods to Problems in Nonlinear Solid Mechanics34711Benchmarks385Index405
