Finite Element Approximation for Optimal Shape, Material and Topology Design

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.

Preliminaries.

Abstract Setting of the Optimal Shape Design Problem and ItsApproximation.

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

Approximation of the Optimal Shape Design Problems by FiniteElements the Scalar Case.

Numerical Realization of Optimal Shape Design Problems Associatedwith 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 inContact.

Shape Optimization in Problems with Inner Obstacles.

Optimum Composite Material Design.

Topology Optimization in Unilateral Problems.

Appendices.

Bibliography.

Index.