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 45
... Initial data for the problem . The FE - mesh of N = NFUNCUNA can be seen in Figure 2.14 . The shaded domains indicate NF and D respectively . We use a triangulation of Л with 267 elements and 158 nodes . Figure 2.15 shows the initial ...
... Initial data for the problem . The FE - mesh of N = NFUNCUNA can be seen in Figure 2.14 . The shaded domains indicate NF and D respectively . We use a triangulation of Л with 267 elements and 158 nodes . Figure 2.15 shows the initial ...
Page 95
... initial design and for final design , information about the decrease in criterion func- tion , etc. 5.7 . Numerical examples In this section we study the performance of a gradient algorithm used for solving optimal design problems ...
... initial design and for final design , information about the decrease in criterion func- tion , etc. 5.7 . Numerical examples In this section we study the performance of a gradient algorithm used for solving optimal design problems ...
Page 119
... initial design was the same as in previous chapters : a ; = 1 , i = 0 , 1 , 2 , ... , D ( h ) . Value of E Example Right hand side f for initial Value of E for final design 6.1 4 sin 2πx2 1.976 design 1.185.10-9 6.2 4 sin ( 2π ( x1 - x2 ...
... initial design was the same as in previous chapters : a ; = 1 , i = 0 , 1 , 2 , ... , D ( h ) . Value of E Example Right hand side f for initial Value of E for final design 6.1 4 sin 2πx2 1.976 design 1.185.10-9 6.2 4 sin ( 2π ( x1 - x2 ...
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