General case of multiple crack problems in an infinite plate

Abstract

General case of multiple crack problems in an infinite plate is a case that the tractions applied on two edges of each crack are arbitrary, generally, are not in equilibrium. Two elementary solutions are present to solve the proposed problem. The first (second) elementary solution is defined as a solution that two pairs of normal and tangential concentrated forces are applied at a point of both edges of a single crack in an infinite isotropic elastic medium, with same magnitude and opposite direction (with same magnitude and same direction). Using the two elementary solutions and the principle of superposition, we found the proposed problem can be converted into a system of Fredholm integral equations. Finally, the system is solved numerically and SIF values at the crack tips can be easily calculated. In order to explain our study, one numerical example is given in this paper.