Sensitivity analysis of 2D elastic structures in presence of stress singularities

Abstract

The object of this paper is the investigation of the influence of stress singularities on the sensitivity of two-dimensional linearized elastic fields and the corresponding functionals under a variation of the domain. This requires a detailed study of the local behaviour of the material and of the shape derivatives of the displacement field in the vicinity of boundary corner points. Using these regularity results, we apply the method of adjoint problems to express the shape derivatives of the functionals as boundary integrals and give precise conditions under which this approach can be justified. It turns out that in case of elastic structures with cracks, the sensitivity of the functionals depends also on the stress intensity factors of the solution of the adjoint problem.