Solution of periodic group crack problems by using the Fredholm integral equation approach

Summary Periodic group cracks composed of infinitely many groups numbered from j = -∞,...-2,-1,0,1,2,...to j = ∞ placed periodically in an infinite plate are studied. The same loading condition and the same geometry are assumed for cracks in all groups. The Fredholm integral equation is formulated for the cracks of the central group (or the 0-th group) collecting the influences from the infinite neighboring groups. The influences from many neighboring groups on the central group are evaluated exactly, and those from remote groups approximately summed up into one term. The stress intensity factors can be directly evaluated from the solution of the Fredholm integral equation. Numerical examples show that the suggested technique provides very accurate results. Finally, several numerical examples are presented, and the interaction between the groups is addressed.