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Crack detection by the topological gradient method. (English) Zbl 1167.74437

Summary: The topological sensitivity analysis consists in studying the behavior of a shape functional when modifying the topology of the domain. In general, the perturbation under consideration is the creation of a small hole. In this paper, the topological asymptotic expansion is obtained for the Laplace equation with respect to the insertion of a short crack inside a plane domain. This result is illustrated by some numerical experiments in the context of crack detection.

MSC:

74G75 Inverse problems in equilibrium solid mechanics
49K40 Sensitivity, stability, well-posedness
49Q10 Optimization of shapes other than minimal surfaces
35J25 Boundary value problems for second-order elliptic equations
35Q72 Other PDE from mechanics (MSC2000)
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
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