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 50
From the principle of minimum potential energy , the displacement field u of the
contact problem is the field that solves ... Since the constraint function is linear in
the displacement fields , the subset K of K defined as În = { 1 ( u ) < 0 and u € K }
is ...
From the principle of minimum potential energy , the displacement field u of the
contact problem is the field that solves ... Since the constraint function is linear in
the displacement fields , the subset K of K defined as În = { 1 ( u ) < 0 and u € K }
is ...
Page 190
Let us assume that there exists a displacement field u = ( ul , u2 ) sufficiently
smooth and satisfying the following conditions ( 8 . 3 ) ( 8 . 4 ) on li ; on Гр ; Uj = 0
, T2 ( 0 ) = 02 ; ( u ) n ; = 0 T : ( 0 ) = 0 ; j ( u ) n ; = Pi , i = 1 , 2 U2 ( x1 , a ( x1 ) ) > -
a ...
Let us assume that there exists a displacement field u = ( ul , u2 ) sufficiently
smooth and satisfying the following conditions ( 8 . 3 ) ( 8 . 4 ) on li ; on Гр ; Uj = 0
, T2 ( 0 ) = 02 ; ( u ) n ; = 0 T : ( 0 ) = 0 ; j ( u ) n ; = Pi , i = 1 , 2 U2 ( x1 , a ( x1 ) ) > -
a ...
Page 332
... 200 displacement field 50 domain 28 stress field 189 a . e . = almost
everywhere 9 algorithm CG 270 CG - SSOR 271 MG 271 nonlinear SOR 278
SOR 269 SOR with projection 272 subgradient 295 , 298 approximation of
contact problems ...
... 200 displacement field 50 domain 28 stress field 189 a . e . = almost
everywhere 9 algorithm CG 270 CG - SSOR 271 MG 271 nonlinear SOR 278
SOR 269 SOR with projection 272 subgradient 295 , 298 approximation of
contact problems ...
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Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
14 other sections not shown
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Common terms and phrases
algorithm Appendix applied approach approximation associated assume assumptions Banach space body boundary bounded called Chapter closed compute Consequently consider constant constraints contains continuous convex corresponding cost functional defined definition denote depend derivative described differentiable direction discrete displacement domain elastic element equivalent Example exist a subsequence exists field Figure Finally Find fixed follows formula function give given hand holds initial ITERATION Lemma linear mapping material matrix means method minimize Moreover moving nodes nonlinear numerical Numerical results obtain optimal shape design parameter positive presented programming Proof prove reads refer relation Remark respect results for Example satisfying sensitivity analysis sequence shape design problems solution solves space Step stress structural sufficiently suppose Table term Theorem triangulation unique variational inequality vector write
Bibliographic information
| Title | Finite Element Approximation for Optimal Shape Design: Theory and Applications |
| Authors | J. Haslinger, Pekka Neittaanmäki |
| Publisher | Wiley, 1988 |
| Original from | the University of Michigan |
| Digitized | 28 Nov 2007 |
| ISBN | 0471920797, 9780471920793 |
| Length | 335 pages |
| Subjects | › Technology & Engineering / Drafting & Mechanical Drawing Technology & Engineering / Manufacturing |
| Export Citation | BiBTeX EndNote RefMan |