Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity

Abstract

Abstract Both the hypersingular and nearly singular integrals, which appear in the hypersingular boundary integralequations and integral representations of the secondary fields, respectively, are regularized by the application of the superposition principle. Two kinds of the non‐singular formulations, namely, those with the strongly singular and weakly singular kernels, are presented in this paper. The formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible. Two‐ and three‐dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity.