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 96
... results for Example 5.1 a - c : in- cluding the decrease of I ; versus iteration as well as the spline - smoothed FE ... results obtained for Examples 5.2 a - c . Figures 5.15-5.17 show the numerical results for Examples 5.3 a - c ...
... results for Example 5.1 a - c : in- cluding the decrease of I ; versus iteration as well as the spline - smoothed FE ... results obtained for Examples 5.2 a - c . Figures 5.15-5.17 show the numerical results for Examples 5.3 a - c ...
Page 130
Theory and Applications J. Haslinger, Pekka Neittaanmäki. Value of I Example Right ... results for Examples 6.5-6.8 . In Figures 6.8-6.11 we see the numerical ... Example 6.5 ; f = 4 sin 27x2 . 0.02077 ( ak ) 0.015 0.010 0.005 0.000 1 2 130.
Theory and Applications J. Haslinger, Pekka Neittaanmäki. Value of I Example Right ... results for Examples 6.5-6.8 . In Figures 6.8-6.11 we see the numerical ... Example 6.5 ; f = 4 sin 27x2 . 0.02077 ( ak ) 0.015 0.010 0.005 0.000 1 2 130.
Page 240
... example y = 2 and the initial guess was up ẞ , which does not violate the state constraint . After 18 SQP - iterations the initial weight 1.00 was reduced to 0.514 . The optimal shape is shown in Figure ... results for Example 10.2 ; n. 240.
... example y = 2 and the initial guess was up ẞ , which does not violate the state constraint . After 18 SQP - iterations the initial weight 1.00 was reduced to 0.514 . The optimal shape is shown in Figure ... results for Example 10.2 ; n. 240.
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