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 37
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 hand ... results for Examples 6.5-6.8 . In Figures 6.8-6.11 we see the numerical ... Example 6.5 ; f = 4 sin 2x2 . 0.0207 1 $ ( ak ) 0.015 0.010 0.005 0.000 130.
Theory and Applications J. Haslinger, Pekka Neittaanmäki. Value of I Example Right hand ... results for Examples 6.5-6.8 . In Figures 6.8-6.11 we see the numerical ... Example 6.5 ; f = 4 sin 2x2 . 0.0207 1 $ ( ak ) 0.015 0.010 0.005 0.000 130.
Page 240
... example y = 2 1 , B = 1 , b = 1 , r = and € = 10-4 . β 10 100 and the initial guess was up B , which does not ... results for Example 10.2 ; n ( h ) B = 1.0 , 2.0 , r = 0.01 , ε = 10-4 . y = = 31 , a = 0.1 , In the second example y = 10 ...
... example y = 2 1 , B = 1 , b = 1 , r = and € = 10-4 . β 10 100 and the initial guess was up B , which does not ... results for Example 10.2 ; n ( h ) B = 1.0 , 2.0 , r = 0.01 , ε = 10-4 . y = = 31 , a = 0.1 , In the second example y = 10 ...
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