OPTIMAL SHAPE DESIGN SUBJECT TO ELLIPTIC VARIATIONAL INEQUALITIES

被引：33

作者：

Hintermueller, M. ^{[1
,2
]}

Laurain, A. ^{[2
]}

机构：

[1] Humboldt Univ, Dept Math, Berlin, Germany

[2] Graz Univ, Dept Math & Sci Comp, Graz, Austria

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 03期

关键词：

asymptotic analysis; elliptic variational inequality; free boundary problem; level set method; obstacle problem; shape and topology optimization; LEVEL SET METHOD; OPTIMIZATION; SENSITIVITY; TOPOLOGY; SYSTEMS; DOMAIN;

D O I：

10.1137/080745134

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The shape of the free boundary arising from the solution of a variational inequality is controlled by the shape of the domain where the variational inequality is defined. Shape and topological sensitivity analysis is performed for the obstacle problem and for a regularized version of its primal-dual formulation. The shape derivative for the regularized problem can be defined and converges to the solution of a linear problem. These results are applied to an inverse problem and to the electrochemical machining problem.

引用

页码：1015 / 1047

页数：33

共 35 条

[1] Allaire G, 2005, CONTROL CYBERN, V34, P59
[2] [Anonymous], 1996, MATH PROGRAMS EQUILI, DOI DOI 10.1017/CBO9780511983658
[3] [Anonymous], 1996, FINITE ELEMENT APPRO
[4] OPTIMAL-DESIGN OF DOMAINS WITH FREE-BOUNDARY PROBLEMS
BARBU, V
FRIEDMAN, A
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1991, 29 (03) : 623 - 637
[5] ELLIOTT CM, 1980, J I MATH APPL, V25, P121
[6] BUBBLE METHOD FOR TOPOLOGY AND SHAPE OPTIMIZATION OF STRUCTURES
ESCHENAUER, HA
KOBELEV, VV
SCHUMACHER, A
[J]. STRUCTURAL OPTIMIZATION, 1994, 8 (01): : 42 - 51
[7] The topological asymptotic for PDE systems: The elasticity case
Garreau, S
Guillaume, P
Masmoudi, M
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 39 (06) : 1756 - 1778
[8] Glowinski R., 2007, LECT NOTES PURE APPL, V252
[9] HACKBUSCH W, 1992, SPRINGER SER COMPUT, V18
[10] HASLINGER J, 2003, ADV DES CONTROL SIAM, V7

← 1 2 3 4 →