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 53
... boundary value state problem - scalar case - 3.1 . Existence result Here we shall apply the general theory , presented in Chapter 2 , Section 2.1 , to a case where the state relation is given by a simple unilateral boundary value ...
... boundary value state problem - scalar case - 3.1 . Existence result Here we shall apply the general theory , presented in Chapter 2 , Section 2.1 , to a case where the state relation is given by a simple unilateral boundary value ...
Page 106
... boundary value problem . The moving part of the boundary will need to be designed in such a way that the flux across it attains its minimum . 6.1 . Setting of the problem Let ( a ) C R2 , a € Uad be given by ( 3.1 ) . The partition of ...
... boundary value problem . The moving part of the boundary will need to be designed in such a way that the flux across it attains its minimum . 6.1 . Setting of the problem Let ( a ) C R2 , a € Uad be given by ( 3.1 ) . The partition of ...
Page 333
... boundary 4 Lipschitz condition 3 lower semicontinuous functional 6 material derivative 87 , 280 matrix Gram 66 mass 77 stiffness 77 , 154 membrane 200 minimizing boundary flux 35 , 106 contact stresses 35 displacements 35 sequence 6 ...
... boundary 4 Lipschitz condition 3 lower semicontinuous functional 6 material derivative 87 , 280 matrix Gram 66 mass 77 stiffness 77 , 154 membrane 200 minimizing boundary flux 35 , 106 contact stresses 35 displacements 35 sequence 6 ...
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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algorithm Appendix applied approximation boundary value problem C₁ Céa Computer constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic element method exist a subsequence Figure Find finite element finite element method follows formula given Glowinski Gm(a H¹(Î Haslinger Haug Hlaváček Ir(an ITERATION jEJk ji Eli Komkov Lagrange multipliers Lemma lim inf lim sup linear Lipschitz continuous lower semicontinuous 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 sequence shape design problems Shape optimization Sokolowski solves P(a structural design structural optimization subgradient subset T(Un T₁ Theorem triangulation un(an variational inequality vector w₁ Zolesio г₁