Approximate Determination of Stresses near Notches and Corners in Elastic Media by an Integral Equation Method

摘要

A numerical method for determining stresses near corners and cracks in two-dimensional elastic bodies is presented. The method is based on an integral equation formulation which uses the character of the displacements near such irregular boundary points. Kernels for the integral equations at points along smooth portions of the boundary are obtained from the solutions to concentrated force problems in the usual manner. The most significant part of the study consists of the development of convenient new kernels for the integral equations written at the irregular boundary points. Suitable numerical techniques are used to convert the set of integral equations to a set of linear algebraic equations which involve the boundary values as unknowns. Accurate results are obtained for three sample problems using a relatively small number of simultaneous equations. Moreover, the results are stable with respect to the number and distribution of boundary points. (Author)