Variational Methods for Structural Optimization

By: Andrej Cherkaev

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Hardcover | 1 January 2000

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580 Pages

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23.39 x 15.6 x 3.18

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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.

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List of Figures
Preface
Relaxation of One-Dimensional Variational Problems	p. 3
Conducting Composites	p. 35
Bounds and G-Closures	p. 59
Domains of Extremal Conductivity	p. 81
Optimal Conducting Structures	p. 117
Quasiconvexity	p. 145
Optimal Structures and Laminates	p. 171
Lower Bound: Translation Method	p. 213
Necessary Conditions and Minimal Extensions	p. 239
Obtaining G-Closures	p. 261
Examples of G-Closures	p. 279
Multimaterial Composites	p. 309
Supplement: Variational Principles for Dissipative Media	p. 343
Elasticity of Inhomogeneous Media	p. 359
Elastic Composites of Extremal Energy	p. 393
Bounds on Effective Properties	p. 419
Some Problems of Structural Optimization	p. 459
References	p. 495
Author/Editor Index	p. 525
Subject Index	p. 533
Table of Contents provided by Blackwell. All Rights Reserved.

Variational Methods for Structural Optimization

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