Hypersingular integral equation method for three-dimensional crack problem in shear mode

摘要

This paper presents the use of the hypersingular integral equation method for solving the flat crack problem in shear mode. In the method, the crack opening displacement (COD) functions are assumed to be polynomials with several undetermined coefficients. The involved hypersingular integral can be reduced into a repeat integral in a particular polar co-ordinate, and further integrated by a known quadrature rule. This technique considerably reduces the effort of derivation and computation to obtain the final solution. The undetermined coefficients in the COD functions are obtained from an algebraic equation. The stress intensity factors (SIF) along the boundary of the flat crack can then be easily calculated. Numerical examples are given to demonstrate the efficiency of the proposed method.