The topological asymptotic for PDE systems: The elasticity case. (English) Zbl 0990.49028

Garreau, Stéphane; Guillaume, Philippe; Masmoudi, Mohamed

SIAM J. Control Optimization 39, No. 6, 1756-1778 (2001).

Summary: The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole. In this paper, such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique. The method is general and can be easily adapted to other linear PDEs and other types of boundary conditions.

MSC:

49Q12	Sensitivity analysis for optimization problems on manifolds
74P05	Compliance or weight optimization in solid mechanics
49Q10	Optimization of shapes other than minimal surfaces
74P10	Optimization of other properties in solid mechanics
74P15	Topological methods for optimization problems in solid mechanics
35Q72	Other PDE from mechanics (MSC2000)
74B05	Classical linear elasticity

Keywords:

topological sensitivity; topological derivative; shape optimization; design sensitivity; elasticity; compliance