Numerical determination of a class of generalized stress intensity factors

A modification of the collocation method for the numerical solution of Cauchy‐type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A ( x − c ) α + B ( x − c ) β , where α < 0, 0 < β − α < 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.