The Topological Asymptotic for PDE Systems: The Elasticity Case

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.

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