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Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd Edition

ISBN: 978-0-471-95850-5
442 pages
August 1996
Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd Edition (0471958506) cover image


This book addresses the formulation, approximation and numerical solution of optimal shape design problems: from the continuous model through its discretization and approximation results, to sensitivity analysis and numerical realization. Shape optimization of structures is addressed in the first part, using variational inequalities of elliptic type. New results, such as contact shape optimization for bodies made of non-linear material, sensitivity analysis based on isoparametric technique, and analysis of cost functionals related to contact stress distribution are included. The second part presents new concepts of shape optimization based on a fictitious domain approach. Finally, the application of the shape optimization methodology in the material design is discussed. This second edition is a fully revised and up-dated version of Finite Element Method for Optimal Shape Design. Numerous numerical examples illustrate the theoretical results, and industrial applications are given.
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Table of Contents


Abstract Setting of the Optimal Shape Design Problem and Its Approximation.

Optimal Shape Design of Systems Governed by a Unilateral Boundary Value State Problem the Scalar Case.

Approximation of the Optimal Shape Design Problems by Finite Elements the Scalar Case.

Numerical Realization of Optimal Shape Design Problems Associated with a Unilateral Boundary Value Problem the Scalar Case.

Shape optimization in Unilateral Boundary Value Problems with a "Flux" Cost Functional.

Optimal Shape Design Contact Problems the Elastic Case.

Shape Optimization of Materially Non-linear Bodies in Contact.

Shape Optimization in Problems with Inner Obstacles.

Optimum Composite Material Design.

Topology Optimization in Unilateral Problems.



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