Variational Methods for Structural Optimization

  • Andrej┬áCherkaev

Part of the Applied Mathematical Sciences book series (AMS, volume 140)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Andrej Cherkaev
      Pages 35-58
    3. Andrej Cherkaev
      Pages 59-77
  3. Optimization of Conducting Composites

    1. Front Matter
      Pages 79-79
    2. Andrej Cherkaev
      Pages 81-116
    3. Andrej Cherkaev
      Pages 117-141
  4. Quasiconvexity and Relaxation

    1. Front Matter
      Pages 143-143
    2. Andrej Cherkaev
      Pages 145-170
    3. Andrej Cherkaev
      Pages 171-212
    4. Andrej Cherkaev
      Pages 213-237
    5. Andrej Cherkaev
      Pages 239-258
  5. G-Closures

    1. Front Matter
      Pages 259-259
    2. Andrej Cherkaev
      Pages 261-277
    3. Andrej Cherkaev
      Pages 279-308
    4. Andrej Cherkaev
      Pages 309-342
  6. Optimization of Elastic Structures

    1. Front Matter
      Pages 357-357
    2. Andrej Cherkaev
      Pages 359-391

About this book

Introduction

In recent decades, it has become possible to turn the design process into computer algorithms. By applying different computer oriented methods the topology and shape of structures can be optimized and thus designs systematically improved. These possibilities have stimulated an interest in the mathematical foundations of structural optimization. The challenge of this book is to bridge a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in a sufficiently simple form to make them available for practical use and to allow their critical appraisal for improving and adapting these results to specific models. Special attention is to pay to the description of optimal structures of composites; to deal with this problem, novel mathematical methods of nonconvex calculus of variation are developed. The exposition is accompanied by examples.

Keywords

Algebra Structural Optimization algorithm algorithms calculus optimization

Authors and affiliations

  • Andrej┬áCherkaev
    • 1
  1. 1.Department of MathematicsThe University of UtahSalt Lake CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1188-4
  • Copyright Information Springer-Verlag New York, Inc 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7038-6
  • Online ISBN 978-1-4612-1188-4
  • Series Print ISSN 0066-5452
  • About this book
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