An alternative fredholm integral equation approach for multiple crack problem and multiple rigid line problem in plane elasticity

Abstract

An alternative Fredholm integral equation approach for the multiple crack problem and the multiple rigid line problem in plane elasticity is suggested in this paper. After using some operators on both sides of the singular integral equation for the relevant problem, an alternative Fredholm integral equation is obtainable. The solutions of the suggested integral equations satisfy the single-valuedness condition of displacement (for the multiple crack problem) and the zero resultant force condition (for the multiple rigid line problem), respectively. The obtained integral equation is compact in form and easy for computation. A technique for evaluating the rotation in the multiple rigid line problem is also proposed. Numerical examples are given to demonstrate the efficiency of the proposed approach.