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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.

MSC:
49Q12Sensitivity analysis
74P05Compliance or weight optimization (solid mechanics)
49Q10Optimization of shapes other than minimal surfaces
74P10Optimization of other properties (solid mechanics)
74P15Topological methods in solid mechanics
35Q72Other PDE from mechanics (MSC2000)
74B05Classical linear elasticity