Variational Methods for Structural Optimization
Search in google:
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.
List of FiguresPreface1Relaxation of One-Dimensional Variational Problems32Conducting Composites353Bounds and G-Closures594Domains of Extremal Conductivity815Optimal Conducting Structures1176Quasiconvexity1457Optimal Structures and Laminates1718Lower Bound: Translation Method2139Necessary Conditions and Minimal Extensions23910Obtaining G-Closures26111Examples of G-Closures27912Multimaterial Composites30913Supplement: Variational Principles for Dissipative Media34314Elasticity of Inhomogeneous Media35915Elastic Composites of Extremal Energy39316Bounds on Effective Properties41917Some Problems of Structural Optimization459References495Author/Editor Index525Subject Index533
