Ebook: Topological Derivatives in Shape Optimization
- Tags: Theoretical and Applied Mechanics, Computational Science and Engineering, Mathematical Applications in the Physical Sciences
- Series: Interaction of Mechanics and Mathematics
- Year: 2013
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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, sensitivity analysis in fracture mechanics 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 in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.
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, sensitivity analysis in fracture mechanics 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 in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.
Content:
Front Matter....Pages 1-18
Introduction....Pages 1-24
Domain Derivation in Continuum Mechanics....Pages 25-45
Material and Shape Derivatives for Boundary Value Problems....Pages 47-89
Singular Perturbations of Energy Functionals....Pages 91-136
Configurational Perturbations of Energy Functionals....Pages 137-180
Topological Derivative Evaluation with Adjoint States....Pages 181-194
Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems....Pages 195-202
Topological Derivative for Three-Dimensional Linear Elasticity Problems....Pages 203-223
Compound Asymptotic Expansions for Spectral Problems....Pages 225-275
Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems....Pages 277-297
Topological Derivatives for Unilateral Problems....Pages 299-324
Back Matter....Pages 0--1
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, sensitivity analysis in fracture mechanics 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 in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.
Content:
Front Matter....Pages 1-18
Introduction....Pages 1-24
Domain Derivation in Continuum Mechanics....Pages 25-45
Material and Shape Derivatives for Boundary Value Problems....Pages 47-89
Singular Perturbations of Energy Functionals....Pages 91-136
Configurational Perturbations of Energy Functionals....Pages 137-180
Topological Derivative Evaluation with Adjoint States....Pages 181-194
Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems....Pages 195-202
Topological Derivative for Three-Dimensional Linear Elasticity Problems....Pages 203-223
Compound Asymptotic Expansions for Spectral Problems....Pages 225-275
Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems....Pages 277-297
Topological Derivatives for Unilateral Problems....Pages 299-324
Back Matter....Pages 0--1
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