Topological Derivative in Shape Optimization
Author(s)
Bibliographic Information
Topological Derivative in Shape Optimization
(Interaction of mechanics and mathematics)
Springer, c2013
Available at 2 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
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  United States of America
Note
Include bibliographical references (p. [397]-408) and index
Description and Table of Contents
Description
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.
Table of Contents
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.
by "Nielsen BookData"