Topological Sensitivity Analysis in the Context of Ultrasonic Nondestructive Testing

Abstract. The aim of the topological sensitivity analysis is to determine an asymptotic expansion of a shape functional with respect to the variation of the topology of the domain. In this paper, we consider a state equation of the form div (A∇u) + ku = 0 in dimensions 2 and 3. For that problem, the topological asymptotic expansion is obtained for a large class of cost functions and two kinds of topology perturbation: the creation of arbitrary shaped holes and cracks on which a Neumann boundary condition is prescribed. These results are illustrated by some numerical experiments in the context of the detection of defects in metallic plates by means of ultrasonic probing.