Finite Element Approximation for Optimal Shape Design: Theory and ApplicationsExplains how to speed the optimal shape design process using a computer. Outlines the problems inherent in optimal shape design and discusses methods of their solution. Concentrates on finite element approximation and describes numerical realization of optimization techniques. Treats optimal design problems via the optimal control theory when the state systems are governed by variational inequalities. Provides useful background information, followed by numerous approaches to optimal shape design, all supported by illustrative examples. Appendices provide algorithms and numerous examples and their calculations are included. |
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Page 106
... cost functional This chapter deals with domain optimization in state problems in which the state is described by a unilateral boundary value problem . The moving part of the boundary will need to be ... cost functional Setting of the problem.
... cost functional This chapter deals with domain optimization in state problems in which the state is described by a unilateral boundary value problem . The moving part of the boundary will need to be ... cost functional Setting of the problem.
Page 123
... cost functional in such a way that we can settle the optimal shape design problem for the unilateral boundary value problem of Chapter 5 . The modification presented here was originally proposed in Neittaanmäki , Sokolowski and Zolesio ...
... cost functional in such a way that we can settle the optimal shape design problem for the unilateral boundary value problem of Chapter 5 . The modification presented here was originally proposed in Neittaanmäki , Sokolowski and Zolesio ...
Page 156
... cost functional ( see also Correa and Seeger ( 1984 ) ) . In other cases of cost functionals the penalty approach can be recommended . Remark 7.1 . We can write E ( a ) = J ( a , x ( a ) ) as well in the form - 1 E ( a ) = ( r ( a ) , x ...
... cost functional ( see also Correa and Seeger ( 1984 ) ) . In other cases of cost functionals the penalty approach can be recommended . Remark 7.1 . We can write E ( a ) = J ( a , x ( a ) ) as well in the form - 1 E ( a ) = ( r ( a ) , x ...
Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
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Common terms and phrases
algorithm Appendix applied approximation boundary value problem C₁ Céa Computer constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic element method exist a subsequence Figure Find finite element finite element method follows formula given Glowinski Gm(a H¹(Î Haslinger Haug Hlaváček Ir(an ITERATION jEJk ji Eli Komkov Lagrange multipliers Lemma lim inf lim sup linear Lipschitz continuous lower semicontinuous matrix minimization Nečas Neittaanmäki nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal design optimal pair optimal shape design parameter Pironneau Proof results for Example Section sequence shape design problems Shape optimization Sokolowski solves P(a structural design structural optimization subgradient subset T(Un T₁ Theorem triangulation un(an variational inequality vector w₁ Zolesio г₁