Topological Derivatives in Shape Optimization

  • Antonio André Novotny
  • Jan Sokołowski
Part of the Interaction of Mechanics and Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages 1-18
  2. Antonio André Novotny, Jan Sokołowski
    Pages 1-24
  3. Antonio André Novotny, Jan Sokołowski
    Pages 25-45
  4. Antonio André Novotny, Jan Sokołowski
    Pages 47-89
  5. Antonio André Novotny, Jan Sokołowski
    Pages 91-136
  6. Antonio André Novotny, Jan Sokołowski
    Pages 137-180
  7. Antonio André Novotny, Jan Sokołowski
    Pages 181-194
  8. Antonio André Novotny, Jan Sokołowski
    Pages 195-202
  9. Antonio André Novotny, Jan Sokołowski
    Pages 203-223
  10. Antonio André Novotny, Jan Sokołowski
    Pages 225-275
  11. Antonio André Novotny, Jan Sokołowski
    Pages 277-297
  12. Antonio André Novotny, Jan Sokołowski
    Pages 299-324
  13. Back Matter
    Pages 0--1

About this book

Introduction

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.

Keywords

Applied Mathematics Asymptotic Analysis Computational Mechanics Elliptic Boundary Value Shape Optimization Topological Derivative

Authors and affiliations

  • Antonio André Novotny
    • 1
  • Jan Sokołowski
    • 2
  1. 1.Científica LNCC/MCT, Coordenação de Matemática Aplicada eLaboratório Nacional de ComputaçãoPetrópolisBrazil
  2. 2., Institut Élie CartanUniversité de LorraineVandœuvre-Lès-NancyFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-35245-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-35244-7
  • Online ISBN 978-3-642-35245-4
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • About this book