Ebook: Variational Methods for Structural Optimization

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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Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Relaxation of One-Dimensional Variational Problems....Pages 3-33
Conducting Composites....Pages 35-58
Bounds and G-Closures....Pages 59-77
Front Matter....Pages 79-79
Domains of Extremal Conductivity....Pages 81-116
Optimal Conducting Structures....Pages 117-141
Front Matter....Pages 143-143
Quasiconvexity....Pages 145-170
Optimal Structures and Laminates....Pages 171-212
Lower Bound: Translation Method....Pages 213-237
Necessary Conditions and Minimal Extensions....Pages 239-258
Front Matter....Pages 259-259
Obtaining G-Closures....Pages 261-277
Examples of G-Closures....Pages 279-308
Multimaterial Composites....Pages 309-342
Supplement: Variational Principles for Dissipative Media....Pages 343-355
Front Matter....Pages 357-357
Elasticity of Inhomogeneous Media....Pages 359-391
Elastic Composites of Extremal Energy....Pages 393-420
Bounds on Effective Properties....Pages 421-460
Some Problems of Structural Optimization....Pages 461-496
Back Matter....Pages 497-547

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Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Relaxation of One-Dimensional Variational Problems....Pages 3-33
Conducting Composites....Pages 35-58
Bounds and G-Closures....Pages 59-77
Front Matter....Pages 79-79
Domains of Extremal Conductivity....Pages 81-116
Optimal Conducting Structures....Pages 117-141
Front Matter....Pages 143-143
Quasiconvexity....Pages 145-170
Optimal Structures and Laminates....Pages 171-212
Lower Bound: Translation Method....Pages 213-237
Necessary Conditions and Minimal Extensions....Pages 239-258
Front Matter....Pages 259-259
Obtaining G-Closures....Pages 261-277
Examples of G-Closures....Pages 279-308
Multimaterial Composites....Pages 309-342
Supplement: Variational Principles for Dissipative Media....Pages 343-355
Front Matter....Pages 357-357
Elasticity of Inhomogeneous Media....Pages 359-391
Elastic Composites of Extremal Energy....Pages 393-420
Bounds on Effective Properties....Pages 421-460
Some Problems of Structural Optimization....Pages 461-496
Back Matter....Pages 497-547
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