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 22
Page 11
... satisfy the " cone property " if and only if such that VxE IN EC2 = C ( §x , 0 , h ) , € 3Cr Vy E B ( x , r ) ns the ... satisfying the cone property of Definition 1.5 . Now we have ( Chenais ( 1975 ) ) Theorem 1.10 . Let 0 , h , r be ...
... satisfy the " cone property " if and only if such that VxE IN EC2 = C ( §x , 0 , h ) , € 3Cr Vy E B ( x , r ) ns the ... satisfying the cone property of Definition 1.5 . Now we have ( Chenais ( 1975 ) ) Theorem 1.10 . Let 0 , h , r be ...
Page 190
... satisfying the following conditions ( 8.3 ) u1 = 0 , T2 ( 0 ) = σ2 ; ( u ) n ; = 0 on T1 ; ( 8.4 ) Ti ( o ) = σij ( u ) n ; = P1 , i = 1,2 on гp ; u2 ( x1 , α ( x1 ) ) ≥ -a ( x1 ) Vx1 € ( a , b ) ( 8.5 ) T2 ( 0 ) = 02j ( u ) n ; ≥ 0 ...
... satisfying the following conditions ( 8.3 ) u1 = 0 , T2 ( 0 ) = σ2 ; ( u ) n ; = 0 on T1 ; ( 8.4 ) Ti ( o ) = σij ( u ) n ; = P1 , i = 1,2 on гp ; u2 ( x1 , α ( x1 ) ) ≥ -a ( x1 ) Vx1 € ( a , b ) ( 8.5 ) T2 ( 0 ) = 02j ( u ) n ; ≥ 0 ...
Page 206
... satisfy the same assumptions introduced in Chapter 4. By ( an ) , or shortly Nh , we denote the domain ( a ) with a ... satisfying the inequality constraints at all interior nodes ( the family of which is denoted by Nh ) of T ( h , an ) ...
... satisfy the same assumptions introduced in Chapter 4. By ( an ) , or shortly Nh , we denote the domain ( a ) with a ... satisfying the inequality constraints at all interior nodes ( the family of which is denoted by Nh ) of T ( h , an ) ...
Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
11 other sections not shown
Other editions - View all
Common terms and phrases
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