Singular integral equations in two-dimensional problems of the theory of cracks

We present a brief survey of the results of investigations devoted to the application of the method of singular integral equations to the solution of two-dimensional problems of fracture mechanics and carried out at the Karpenko Physicomechanical Institute of the Ukrainian National Academy of Sciences. Special attention is given to integral equations on piecewise smooth closed or nonclosed contours appearing in the boundary-value problems for domains, with corners, We propose a new method for the solution of equations of this sort taking into account the singularities of stresses at angular points. The modified singular integral equations obtained as a result have continuous kernels and right-hand sides, i.e., belong to the same type of equations as in the case of smooth contours.