Variational Methods for Structural Optimization
By: by Andrej Cherkaev
Series: Applied Mathematical Sciences -- 140; Applied mathematical sciences (Springer-Verlag New York Inc.) -- 140.
Publisher: Springer New York
Published: 2000
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 545
ISBN-13: 9781461270386; 9781461211884
Subjects: Mechanics; Mathematical optimization; Physics; Systems theory
Description: 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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Table of contents: title: I Preliminaries. Introduction. Non-Convex Variational Problems; title: II Optimization of Conducting Composites; title: Conducting Composites. Conducting Composites of Extremal Energy. Optimization of Arbitrary Goal Functional; title: III Quasiconvex Envelope. Quasiconvex Envelope. Lower Bound: Translation Method. Minimizing Sequences. Algebra of Laminates. Upper Bounds and Extensions; title: IV Optimal Design of Elastic Constructions. Elasticity of Inhomogeneous Media. Elastic Mixtures of Extermal Rigidity. Plane Problem. Optimal Design; title: V Gm Closures; title: Bounds On G-Closures.