Regularized computation of interior displacements and stresses by BEM

Summary The computation of interior displacements and stresses with the boundary element method (BEM) often requires the evaluation of nearly singular integrals. These integrals arise from the singular behaviour of the kernel functions in the Somigliana identity and the Somigliana stress identity. Treating them numerically in a standard way leads to inaccuracy near the boundary. This effect is always present in the calculation of field variables near the boundary and is called boundary layer effect. In this paper regularization procedures are proposed which consist of an indirect evaluation of singular integrals and a special coordinate transformation. The proposed procedures eliminate the boundary layer effect for both, the calculation of displacements and stresses. In a numerical example of elastostatics the developed strategies are shown to work. Due to the generality of the proposed procedures they can be extended to any standard boundary element formulation for problems with bounded domains.