Variational Methods for Structural Optimization

This book treats two sets of mathematical problems that are closely related to each other. The first kind is structural optimization problems which asks about inner structure of an inhomogeneous body which is designed to be optimal in some sense. The description of optimal microstructures is the second topic of this book.

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This book bridges 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 sufficiently simple form as to make them available for practical use.

Contenu
I Preliminaries.- 1 Relaxation of One-Dimensional Variational Problems.- 2 Conducting Composites.- 3 Bounds and G-Closures.- II Optimization of Conducting Composites.- 4 Domains of Extremal Conductivity.- 5 Optimal Conducting Structures.- III Quasiconvexity and Relaxation.- 6 Quasiconvexity.- 7 Optimal Structures and Laminates.- 8 Lower Bound: Translation Method.- 9 Necessary Conditions and Minimal Extensions.- IV G-Closures.- 10 Obtaining G-Closures.- 11 Examples of G-Closures.- 12 Multimaterial Composites.- 13 Supplement: Variational Principles for Dissipative Media.- V Optimization of Elastic Structures.- 14 Elasticity of Inhomogeneous Media.- 15 Elastic Composites of Extremal Energy.- 16 Bounds on Effective Properties.- 17 Some Problems of Structural Optimization.- References.- Author/Editor Index.