Longitudinal Shear of an Infinite Body with a System of Polygonal Cracks

On the basis of singular integral equations, we propose a new method for the solution of antiplane problems of elasticity theory for bodies with a system of polygonal cracks with regard for the singularities of stresses at the corner points. The modified singular integral equations have continuous regular kernels and right-hand sides, i.e., belong to the same type as in the case of smooth boundary contours. A numerical solution of these equations is found by the method of mechanical quadratures. The values of the stress intensity factors at the corner points and tips of both a three-link polygonal crack and a system of two two-link polygonal cracks in an infinite body are presented. The limiting case of two cracks which form a rhombic hole is also analyzed.