An iterative hybrid version of the boundary element method and the distributed dislocation method was introduced for solving two-dimensional crack problems. The technique decomposed the problem into (n + 1) subsidiary problems, where n was the number of crack branches. The required solution was then the sum of these (n + 1) solutions. The first subsidiary problem was to find the stress distribution, which was induced in the plate in the absence of the crack, using the boundary element method. All of the remaining subsidiary problems, were stress-disturbance ones that could be solved using the distributed dislocation method. The results were added, and compared with the boundary conditions of the original problem. Iteration was performed between the plate boundaries and crack faces until all of the boundary conditions were satisfied.

Analysis of Cracked Plates using an Iterative Hybrid Technique of Boundary Element Method and Distributed Dislocation Method. M.S.Matbuly, S.A.Mohamed, T.Osman: Engineering Fracture Mechanics, 2008, 75[6], 1535-44