Numerical solution of three-dimensional crack problem by using hypersingular integral equation

Abstract

In this paper, a flat crack with the normal boundary loading on the crack face is embedded in an infinite medium. The relevant problem is called the three-dimensional crack problem hereafter. The hypersingular integral equation is used to solve the mentioned problem. Two innovative points are suggested in this paper: (a) the involved hypersingular integrals are evaluated in a polar coordinate system, and are converted to the repeated integrals; (b) one of the repeated integral is hypersingular, and the involved integrated function is approximated by a product of the weight function and Chebyshev polynomials. The hypersingular integrals can be evaluated numerically by using a known result. Therefore, the hypersingular integral equation for the three-dimensional crack problem can be solved immediately. Finally, numerical examples are given to demonstrate the efficiency of the suggested approach.