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 36
... triangulation of No. In Figure 2.4 we see the final design , which is also the optimum . The value of the cost functional for No is -1.072 and for the final design -1.244 . Figure 2.3 . Figure 2.4 . Example 2.2 . Minimization 36.
... triangulation of No. In Figure 2.4 we see the final design , which is also the optimum . The value of the cost functional for No is -1.072 and for the final design -1.244 . Figure 2.3 . Figure 2.4 . Example 2.2 . Minimization 36.
Page 42
... Figure 2.11 D be the polar region where the magnetic field is desired to be constant . Moreover , NF denotes the ferrous , c the copper and NA the air material . In Figure 2.11 half of the original magnet is shown after a cut through ...
... Figure 2.11 D be the polar region where the magnetic field is desired to be constant . Moreover , NF denotes the ferrous , c the copper and NA the air material . In Figure 2.11 half of the original magnet is shown after a cut through ...
Page 216
... ( No is indicated by a broken line ) . Figure 9.6 shows the contour plot of the obstacle . We find that the equipotential contours of the state and the obstacle coincide in No. Figure 9.4 . 6 E In Figures 9.7 and 9.8 we see the 216.
... ( No is indicated by a broken line ) . Figure 9.6 shows the contour plot of the obstacle . We find that the equipotential contours of the state and the obstacle coincide in No. Figure 9.4 . 6 E In Figures 9.7 and 9.8 we see the 216.
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