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

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.


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
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