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 83
... material derivative method We shall introduce a treatment based on a dynamic interpretation of the optimal shape design process . The method presented here is called the ma- terial derivative or shape derivative method . Material ...
... material derivative method We shall introduce a treatment based on a dynamic interpretation of the optimal shape design process . The method presented here is called the ma- terial derivative or shape derivative method . Material ...
Page 264
... material derivative approach ) . As we have seen above ( Chapters 5 and 6 , Appendix II ) , when the material derivative approach is applied to the discrete model obtained by the finite element method ( linear elements or , in general ...
... material derivative approach ) . As we have seen above ( Chapters 5 and 6 , Appendix II ) , when the material derivative approach is applied to the discrete model obtained by the finite element method ( linear elements or , in general ...
Page 279
... Material derivatives We shall shortly introduce the material derivative concept and give some useful formulae . In the next section we apply these results in the case of linear elements for computing sensitivities with respect to design ...
... Material derivatives We shall shortly introduce the material derivative concept and give some useful formulae . In the next section we apply these results in the case of linear elements for computing sensitivities with respect to design ...
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
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