Numerical Solution of Singular Integral Equations of the Body Force Method in Notch Problems (1st Report, Basic Theory and Discussion on the Stress along the Boundary)

In this paper, numerical solutions of singular integral equations of the body force method in notch problems are discussed. The stress field due to a point force in a body is used as a fundamental solution. Then, the problems are formulated as a system of singular integral equations with Cauchy-type singularities. The unknown functions of the body force densities which satisfy the boundary conditions are approximated by means of the products of the fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparison with the results obtained by the previous method where the unknown functions are approximated by the products of the fundamental density functions and stepped functions. The present method is found to give accurate stress distribution along the notch boundary with short CPU time