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. |
From inside the book
Results 1-3 of 16
Page 10
... Nečas ( 1967 ) , Nečas and Hlavá- ček ( 1981 ) , Leis ( 1986 ) , Nitsche ( 1981 ) . 1Summation convention is used . 1.6 . Uniform extension property Let NE Co , 1 10.
... Nečas ( 1967 ) , Nečas and Hlavá- ček ( 1981 ) , Leis ( 1986 ) , Nitsche ( 1981 ) . 1Summation convention is used . 1.6 . Uniform extension property Let NE Co , 1 10.
Page 27
... Nečas and Lovíšek ( 1988 ) , Nečas and Hlaváček ( 1981 ) , Oden and Carey ( 1982 , 1984 ) , Owen and Hinton ( 1980 ) , Reddy ( 1986 ) , Wait and Mitchell ( 1985 ) , White ( 1985 ) . Abstract setting of optimal shape design problem and ...
... Nečas and Lovíšek ( 1988 ) , Nečas and Hlaváček ( 1981 ) , Oden and Carey ( 1982 , 1984 ) , Owen and Hinton ( 1980 ) , Reddy ( 1986 ) , Wait and Mitchell ( 1985 ) , White ( 1985 ) . Abstract setting of optimal shape design problem and ...
Page 262
... Nečas and Lovíšek ( 1988 ) , Oden and Carey ( 1982 , 1984 ) and Wait and Michell ( 1985 ) ) . The asymptotic relation between solutions for discretized optimal shape prob- lems and continuous ones has not been very widely studied until ...
... Nečas and Lovíšek ( 1988 ) , Oden and Carey ( 1982 , 1984 ) and Wait and Michell ( 1985 ) ) . The asymptotic relation between solutions for discretized optimal shape prob- lems and continuous ones has not been very widely studied until ...
Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
10 other sections not shown
Other editions - View all
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