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Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics

  • Erwin Stein

Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 416)

Table of contents

About this book

Introduction

This course with 6 lecturers intends to present a systematic survey of recent re­ search results of well-known scientists on error-controlled adaptive finite element methods in solid and structural mechanics with emphasis to problem-dependent concepts for adaptivity, error analysis as well as h- and p-adaptive refinement techniques including meshing and remeshing. Challenging applications are of equal importance, including elastic and elastoplastic deformations of solids, con­ tact problems and thin-walled structures. Some major topics should be pointed out, namely: (i) The growing importance of goal-oriented and local error estimates for quan­ tities of interest—in comparison with global error estimates—based on dual finite element solutions; (a) The importance of the p-version of the finite element method in conjunction with parameter-dependent hierarchical approximations of the mathematical model, for example in boundary layers of elastic plates; (Hi) The choice of problem-oriented error measures in suitable norms, consider­ ing residual, averaging and hierarchical error estimates in conjunction with the efficiency of the associated adaptive computations; (iv) The importance of implicit local postprocessing with enhanced test spaces in order to get constant-free, i. e. absolute-not only relative-discretizati- error estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat­ ical modeling in related subdomains, such as boundary layers. The main goals of adaptivity are reliability and efficiency, combined with in­ sight and access to controls which are independent of the applied discretization methods. By these efforts, new paradigms in Computational Mechanics should be realized, namely verifications and even validations of engineering models.

Keywords

behavior computational mechanics control elasticity finite element method mechanics model modeling numerical analysis solid structural mechanics theoretical mechanics

Editors and affiliations

  • Erwin Stein
    • 1
  1. 1.University of HannoverGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-211-38060-4
  • Copyright Information CISM, Udine 2005
  • Publisher Name Springer, Vienna
  • eBook Packages Engineering
  • Print ISBN 978-3-211-26975-6
  • Online ISBN 978-3-211-38060-4
  • Series Print ISSN 0254-1971
  • Series Online ISSN 2309-3706
  • Buy this book on publisher's site
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