Direct stiffness matrices of BEs in the Galerkin BEM formulation

In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/r2, r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartzʹs distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.