Theoretical analysis of elastic singular stress field by use of singular integral equation method

Simultaneous pairs of dual integral equations with trigonometric kernels encountered in the analysis of mixed boundary value problems by Fourier transforms are solved by reduction to a coupled system of singular integral equations. The method of reduction indicated here is based on the relationship between the Fourier transform and the Hilbert transform. The numerical solution of the simultaneous singular integral equations is obtained by using two types of integration formulae. The accuracy and the convergency of the results are examined by examples of crack problems.