Regularization of the hypersingular integrals in 3-D fracture mechanics. Rectangular BE and piecewise linear approximations

摘要

This paper deals with the hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used for solution of fracture mechanics problems. For hypersingular integral regularization the methodology based on theory of distribution and Green's theorems have bean used. This methodology is applied for regularization of the hypersingular integrals over rectangular boundary elements (BE) for 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.