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
CONTENT
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
Physics
System theory
Calculus of variations
Mechanics
Physics
Mechanics
Calculus of Variations and Optimal Control; Optimization
