Variational Methods for Structural Optimization

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

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      Pages 117-141

4. Quasiconvexity and Relaxation

   1. Front Matter

      Pages 143-143

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   2. Quasiconvexity

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      Pages 145-170

   3. Optimal Structures and Laminates

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      Pages 171-212

   4. Lower Bound: Translation Method

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      Pages 213-237

   5. Necessary Conditions and Minimal Extensions

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      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

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      Pages 279-308

   4. Multimaterial Composites

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      Pages 309-342

   5. Supplement: Variational Principles for Dissipative Media

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      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

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.

• Algebra
• Structural Optimization
• algorithm
• algorithms
• calculus
• optimization

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

  Andrej Cherkaev

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