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Variational Methods for Structural Optimization

  • Book
  • © 2000

Overview

Authors:
  1. Andrej Cherkaev

    1. Department of Mathematics, The University of Utah, Salt Lake City, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxvi
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  2. Preliminaries

    1. Front Matter

      Pages 1-1
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    2. Relaxation of One-Dimensional Variational Problems

      • Andrej Cherkaev
      Pages 3-33

    3. Conducting Composites

      • Andrej Cherkaev
      Pages 35-58

    4. Bounds and G-Closures

      • Andrej Cherkaev
      Pages 59-77

  3. Optimization of Conducting Composites

    1. Front Matter

      Pages 79-79
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    2. Domains of Extremal Conductivity

      • Andrej Cherkaev
      Pages 81-116

    3. Optimal Conducting Structures

      • Andrej Cherkaev
      Pages 117-141

  4. Quasiconvexity and Relaxation

    1. Front Matter

      Pages 143-143
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    2. Quasiconvexity

      • Andrej Cherkaev
      Pages 145-170

    3. Optimal Structures and Laminates

      • Andrej Cherkaev
      Pages 171-212

    4. Lower Bound: Translation Method

      • Andrej Cherkaev
      Pages 213-237

    5. Necessary Conditions and Minimal Extensions

      • Andrej Cherkaev
      Pages 239-258

  5. G-Closures

    1. Front Matter

      Pages 259-259
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    2. Obtaining G-Closures

      • Andrej Cherkaev
      Pages 261-277

    3. Examples of G-Closures

      • Andrej Cherkaev
      Pages 279-308

    4. Multimaterial Composites

      • Andrej Cherkaev
      Pages 309-342

    5. Supplement: Variational Principles for Dissipative Media

      • Andrej Cherkaev
      Pages 343-355

  6. Optimization of Elastic Structures

    1. Front Matter

      Pages 357-357
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    2. Elasticity of Inhomogeneous Media

      • Andrej Cherkaev
      Pages 359-391
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, The University of Utah, Salt Lake City, USA

    Andrej Cherkaev

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