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 vii
... present various tech- niques for carrying out design sensitivity analysis . Furthermore , we give a procedure for solving optimal shape design problems by applying nonlinear programming algorithms . Several numerical examples are ...
... present various tech- niques for carrying out design sensitivity analysis . Furthermore , we give a procedure for solving optimal shape design problems by applying nonlinear programming algorithms . Several numerical examples are ...
Page 184
Theory and Applications J. Haslinger, Pekka Neittaanmäki. Figures 7.16 and 7.17 present the analogues to Figure 7.15 , 6 , in the case of Examples 7.7.b and 7.7.c ( i.e. g 30. , 50. , respectively ) . = -80 59 78 CONTACT STRESSES Figure ...
Theory and Applications J. Haslinger, Pekka Neittaanmäki. Figures 7.16 and 7.17 present the analogues to Figure 7.15 , 6 , in the case of Examples 7.7.b and 7.7.c ( i.e. g 30. , 50. , respectively ) . = -80 59 78 CONTACT STRESSES Figure ...
Page 302
... present general results concerning the differentiability of a projection in a Hilbert space onto its closed convex subset . For more detailed analysis see Mignot ( 1976 ) and Haraux ( 1977 ) . Let us begin with some notation . Let H be ...
... present general results concerning the differentiability of a projection in a Hilbert space onto its closed convex subset . For more detailed analysis see Mignot ( 1976 ) and Haraux ( 1977 ) . Let us begin with some notation . Let H be ...
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 Find finite element follows formula given Gm(a H¹(Î Haslinger Haug Hlaváček Ir(an jEJk Komkov Lagrange multipliers least one solution Lemma lim inf lim sup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative 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 sensitivity analysis sequence shape design problems Shape optimization Sokolowski solves P(a subgradient subset T(Un T₁ Theorem triangulation triangulation T(h un(an unilateral boundary value variational inequality vector w₁ Zolesio г₁ дп