Numerical solutions of singular integral equations having Cauchy-type singular kernel by means of expansion method

This paper is concerned with numerical solutions of singular integral equations with Cauchy-type singular kernel. It is well-known that this type of singular integral equations appears in the analysis of crack problems using the continuously distributed dislocation method. In addition, it also appears in the analysis of notch problems using the body force method. In the present analysis, the unknown function of densities of dislocations and body forces are approximated by the product of the fundamental density functions and polynomials. The accuracy of stress intensity factors and stress concentration factors obtained by the present method is verified through the comparison with the exact solution and the reliable numerical solution obtained by other researchers. The present method is found to give good convergency of the numerical results for notch problem as well as internal and edge crack problems.