The computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local coordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solving of the hypersingular integral equation, the so called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a lot of problems. In this paper the limiting procedure in taking the load point to the boundary is carried out and the contributions of all different types of singularity to the boundary integral equation is studied in detail. The hypersingular statement is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended to be applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied detailed. A numerical example of elastostatics confirms the validity of the proposed method.

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