An effective numerical procedure for calculating stress intensity factors (SIF) in plane problems based on a modified boundary element technique not requiring any crack discretization was proposed by Snyder [1]. Instead of the usual fundamental solution, be used Green's function for the problem of a traction-free central crack in an anisotropic plate.
In the first part of the present paper, the corresponding Green's function for the isotropic problem, not explicitly included in [1], is presented. In addition to the central crack, a semi-infinite edge crack is considered. Both Green's functions are given for the case of the anti-plane state of strain as well. In the first step of the proposed procedure, the tractions and displacements along the outer boundary are calculated. In the second step, the SIF for modes 1, II and III are derived in terms of simple boundary integrals over quantities known from the previous step. Contrary to Snyder's derivation, the determination of the SIF is based on the asymptotic displacement field at the crack tip. The method can easily be extended to multiple crack problems by using the subregion technique. Some illustrative examples demonstrate the effectiveness of the method.