Domain sensitivity analysis of the elastic far-field patterns in scattering from nonsmooth obstacles

We consider elastic scattering problems described by the Dirichlet or the Neumann boundary value problem for the elastodynamic equation in the exterior of a 2D bounded domain or in the exterior of a crack. The boundary of the domain is assumed to have a finite set of corner points where the scattered wave may have singular behaviour. The paper is concerned with the sensitivity of the far scattered field with respect to small perturbations of the shape of the scatterer. Using a modification of the method of adjoint problems (K. Dems, Z. Mróz, Internat. J. Solids Structures 20 (1984) 527-552) we obtain a representation for the shape derivative which is well suited for a numerical realization with boundary element methods and which shows in some cases directly the influence of the singularities of the solution on the sensitivity of the far-field patterns.