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 50
... field u of the contact problem is the field that solves the following problem ( 2.42 ) min J ( u ) uEK subject to ( u ) ≤0 , where K is defined as the convex set of functions u and u satisfying bilateral kinematic boundary conditions ...
... field u of the contact problem is the field that solves the following problem ( 2.42 ) min J ( u ) uEK subject to ( u ) ≤0 , where K is defined as the convex set of functions u and u satisfying bilateral kinematic boundary conditions ...
Page 279
... field ( velocity field ) and Nt CR2 a domain with a Lipschitz boundary . We denote by N , the image of N in the mapping Ft : nt = F ( N ) . In formula ( 5.18 ) several useful properties of the mapping F , were given . t It , 2 St Xt , 1 ...
... field ( velocity field ) and Nt CR2 a domain with a Lipschitz boundary . We denote by N , the image of N in the mapping Ft : nt = F ( N ) . In formula ( 5.18 ) several useful properties of the mapping F , were given . t It , 2 St Xt , 1 ...
Page 332
... field 50 stress field 189 a.e. almost everywhere 9 algorithm CG 270 CG - SSOR 271 MG 271 nonlinear SOR 278 SOR 269 SOR with projection 272 subgradient 295 , 298 approximation of contact problems without friction . 145-151 with friction ...
... field 50 stress field 189 a.e. almost everywhere 9 algorithm CG 270 CG - SSOR 271 MG 271 nonlinear SOR 278 SOR 269 SOR with projection 272 subgradient 295 , 298 approximation of contact problems without friction . 145-151 with friction ...
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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adjoint algorithm Appendix applied approximation boundary value problem C₁ Céa compute constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic exist a subsequence Figure Find finite element follows formula given Gm(a H¹(Î Haslinger Haug Hlaváček I₁ Ir(an ITERATION jEJk Komkov Lagrange multipliers least one solution Lemma lim inf lim sup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative matrix method minimization Nečas Neittaanmäki nodes nonlinear nonlinear programming nonsmooth Numerical results obtain optimal control optimal design optimal pair optimal shape design parameter Pironneau Proof results for Example Section sensitivity analysis sequence shape design problems Shape optimization Sokolowski solves P(a subgradient subset T₁ Theorem triangulation un(an unilateral boundary value variational inequality vector w₁ Zolesio г₁