Boundary integral equations in three-dimensional elastostatics using the Boussinesq-Cerruti fundamental solution

Abstract

A so-called traction-free fundamental solution rather than the conventional Kelvin fundamental solution is used to formulate the boundary integral equations for problems in three-dimensional elastostatics. For an isotropic material, the traction-free fundamental solution is a combination of the Boussinesq and Cerruti solutions. This formulation has two advantages over the conventional one. The first is that the boundary integral equations are less singular than the conventional formulation and converge in the normal sense rather than in the Cauchy principal value sense. The second is that a formal differentiation of the boundary integral representation for displacement leads to a valid integral representation for the in-plane stress components on the boundary in terms of the boundary displacements and tractions only. The analogous representation obtained from the conventional boundary integral equations does not converge.