Topological sensitivity and shape optimization for the Stokes equations

被引：82

作者：

Guillaume, P ^{[1
]}

Idris, KS ^{[1
]}

机构：

[1] Inst Natl Sci Appl, Dept Math, UMR 5640, MIP, F-31077 Toulouse 4, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2004年 / 43卷 / 01期

关键词：

topological sensitivity; topological derivative; shape optimization; design sensitivity; Stokes equations;

D O I：

10.1137/S0363012902411210

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 topological sensitivity analysis provides an asymptotic expansion of a shape function with respect to the insertion of a small hole or obstacle inside a domain. This expansion can then be used for shape optimization. In this paper, such an expansion is obtained for the Stokes equations with general shape functions and arbitrarily shaped holes. A numerical example illustrates the use of the topological sensitivity in a shape optimization problem.

引用

页码：1 / 31

页数：31

共 16 条

[1] On some recent advances in shape optimization [J].

Allaire, G ;

Henrot, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II FASCICULE B-MECANIQUE, 2001, 329 (05) :383-396

[2]

Allaire G., 1990, ARCH RATION MECH AN, V113, P209

[3]

[Anonymous], ADV MATH SCI APPL

[4]

BREZIS H, 1993, THEORIE APPL

[5] SHAPE OPTIMIZATION FOR DIRICHLET PROBLEMS - RELAXED FORMULATION AND OPTIMALITY CONDITIONS [J].

BUTTAZZO, G ;

DALMASO, G .

APPLIED MATHEMATICS AND OPTIMIZATION, 1991, 23 (01) :17-49

[6] OPTIMAL-DESIGN OR IDENTIFICATION OF DOMAINS - A QUICK COMPUTATION OF THE DIRECTIONAL DERIVATIVE OF THE COST FUNCTIONAL [J].

CEA, J .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1986, 20 (03) :371-402

[7]

Cea J., 1973, Calcolo, V10, P207

[8]

DAUTRAY R, 1987, INSTN COLLECTION ENS, V1

[9] The topological asymptotic for PDE systems: The elasticity case [J].

Garreau, S ;

Guillaume, P ;

Masmoudi, M .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 39 (06) :1756-1778

[10] The topological asymptotic expansion for the Dirichlet problem [J].

Guillaume, PH ;

Idris, KS .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (04) :1042-1072

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