Solution of integral equation in curve crack problem by using curve length coordinate

Abstract

This paper describes a new numerical method for the solution of the profoundly curved crack in plane elasticity. In the method, the length of the curved crack is taken as the coordinate in the singular integral equation of curve crack problem. The crack configuration maps onto the real axis with interval (− a, a), where 2 a is the curve length of the crack. The original singular integral equation is converted into other singular integral equation which is formulated in the curve length coordinate. The singular integral equation is solved numerically by using the Gauss integration rule. Numerical examples indicate that higher efficiency can be achieved with the suggested method.