Method of Boundary Integral Equations for Analysis of Three Dimensional Crack Problems

Abstract

The solution of spatial problems for finite region with cracks often encounters difficulties which results in the fact that there is a incomparably smaller number of solved spatial problems for crack than that of plane problems. There are almost no exact solutions of this kind at all. Those prevailing are numerical solutions mostly using the finite elements method (PEM). Among the earlier papers these by Tracey [1] and Benzley [2] should be mentioned. The calculations made by this method are rather inefficient and require large computers. It has been shown that the method of boundary integral equations (BIE) is more efficient for these problems not claiming such storage capacities as the finite element method. The BIE method is very well suited to the solution of three-dimensional stress concentration problems reducing the latter to boundary solutions, i.e. requiring only the elements on the boundary to be defined. In contradistinction to them, the finite elements require many interior nodes and approximations involving discontinuity of stresses. The fact that the BIE method allows direct solutions for boundary displacements with no modelling of the internal stresses and stress intensity factor analysis, requiring only crack opening displacements, implies that there is no need to determine the stress inside the body, near the crack tip [3].