Topological Derivatives in Shape Optimization

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Sprache: Englisch

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Beschreibung

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.

Zusammenfassung

First monograph describing in details the new developments in shape optimization for elliptic boundary value problems

Presents a wide spectrum of examples and techniques for

learning how to use the modern mathematics in applied shape optimization of structures

Makes this important field of research accessible for the students of mathematics and of mechanics

Inhaltsverzeichnis

Domain Derivation in Continuum Mechanics.- Material and Shape Derivatives for Boundary Value Problems.- Singular Perturbations of Energy Functionals.- Configurational Perturbations of Energy Functionals.- Topological Derivative Evaluation with Adjoint States.- Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems.- Topological Derivative for Three-Dimensional Linear Elasticity Problems.- Compound Asymptotic Expansions for Spectral Problems.- Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems.- Topological Derivatives for Unilateral Problems.

Details

Erscheinungsjahr:	2012
Fachbereich:	Fertigungstechnik
Genre:	Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	436
Reihe:	Interaction of Mechanics and Mathematics
Inhalt:	xii 324 S. 68 s/w Illustr. 324 p. 68 illus.
ISBN-13:	9783642352447
ISBN-10:	3642352448
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Soko¿owski, Jan Novotny, Antonio André
Auflage:	2013
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Interaction of Mechanics and Mathematics
Maße:	235 x 155 x 24 mm
Von/Mit:	Jan Soko¿owski (u. a.)
Erscheinungsdatum:	14.12.2012
Gewicht:	0,657 kg

preigu-id: 106093916