Introduction to Shape Optimization

Shape Sensitivity Analysis

  • Jan Sokolowski
  • Jean-Paul Zolesio

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 16)

Table of contents

  1. Front Matter
    Pages i-4
  2. Jan Sokolowski, Jean-Paul Zolesio
    Pages 5-12
  3. Jan Sokolowski, Jean-Paul Zolesio
    Pages 13-116
  4. Jan Sokolowski, Jean-Paul Zolesio
    Pages 117-162
  5. Jan Sokolowski, Jean-Paul Zolesio
    Pages 163-239
  6. Back Matter
    Pages 240-250

About this book

Introduction

This book is motivated largely by a desire to solve shape optimization prob­ lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Keywords

Elasticity Elastizität Elastizitätstheorie Free Boundary Value Problem Kontrolltheorie Randwertprobleme Shape Optimization Ungleichungen Variational Inequalities Variationsungleichungen algorithm differential equation optimization partial differential equation wave equation

Authors and affiliations

  • Jan Sokolowski
    • 1
  • Jean-Paul Zolesio
    • 2
  1. 1.Systems Research InstitutePolish Academy of SciencesWarszawaPoland
  2. 2.Faculté des SciencesCentre National de la Recherche Scientifique et Institut non Lineaire de NiceNice Cedex 2France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58106-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63471-0
  • Online ISBN 978-3-642-58106-9
  • Series Print ISSN 0179-3632
  • About this book
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