On the elastic potentials at corners

Abstract

The boundary integral method for solving boundary value problems of elastostatics in domains with interface corners leads to a typical asymptotic behaviour of the potential density near the corner. The solution of the boundary value problem is obtained by evaluation of the representing potential. The singular function follows from decompositions of the potential in the sum of a singular and regular part. After reduction to two normal integrals, namely the logarithmic potential and a bipotential on an interval, decompositions were derived for these potentials with densities occurring in the asymptotics. The singular parts are calculated explicitly for real and complex singular exponents as well as for densities with power logarithmic terms. For integer-valued singular exponents explicit expressions were found for the logarithmic and the bipotential on an interval.