Author(s)

V. V. Zozulya

Abstract

This article considers the hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve fracture mechanics problems . The methodology of hypersingular integral regularization developed in our previous publications is based on theory of distribution and Green’s theorems. In the case of piecewise constant and piecewise linear approximations the hypersingular integrals are transformed into the regular contour integrals that can be easily calculated analytically or numerically. Keywords: weakly singular, singular, hypersingular integrals, boundary integral equations, fracture mechanics. 1 Introduction A huge amount of publications is devoted to the boundary integral equation methods (BEM) and its application science and engineering. One of the main problems arising in numerical solution of the BIE by the BEM is a calculation of the divergent integrals. Different methods have been developed for regularization of the divergent integrals [7]. The hypersingular integrals had been considered by Hadamard in the sense of finite part (FP) in [4]. The theory of distributions allows us to study the divergent integrals and integral operators with kernels containing different kind of singularities in the same way as the regular integrals. Analysis of the most known methods used for treatment of the different divergent integrals has been done in our previous publications. It was shown that theory of distributions provides a unified approach for the study of the divergent integrals and integral operators with kernels containing different kind of singularities. We applied the theory of distribution approach for the first time in [8], then it was further developed in [9–11] and was applied for static and

Keywords

weakly singular, singular, hypersingular integrals, boundary integral equations, fracture mechanics.