Introduction to Shape Optimization: Shape Sensitivity Analysis (Springer Series in Computational Mathematics)

Sokolowski, Jan; Zolesio, Jean-Paul

ISBN 10: 3642634710 ISBN 13: 9783642634710

Editorial: Springer, 2012

Idioma: Ingl�s

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Detalles bibliogr�ficos

T�tulo

Introduction to Shape Optimization: Shape Sensitivity Analysis (Springer Series in Computational Mathematics)

Editor

Springer

Fecha de publicaci�n

2012

Idioma

Ingl�s

ISBN 10

3642634710

ISBN 13

9783642634710

Encuadernaci�n

Encuadernaci�n de tapa blanda

Estado

New

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Sinopsis

Shape Optimization is a classical field of the calculus of variations, optimal control theory and structural optimization. In this book the authors discuss the shape calculus introduced by J. Hadamard and extend it to a broad class of free boundary value problems. The approach is functional analytic throughout and will serve as an excellent basis for the development of numerical algorithms for the solution of shape optimization problems.

Rese�a del editor

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.

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