A Fast Multipole Dual Boundary Element Method for the Three-dimensional Crack Problems

A fast boundary element solver for the analysis of three-dimensional general crack problems is presented. In order to effectively model the embedded or edge cracked structures a dual boundary integral equation (BIE) formulation is used. By implementing the fast multipole method (FMM) to the discretized BIE, structures containing a large number of three-dimensional cracks can be readily simulated on one personal computer. In the FMM framework, a multipole expansion formulation is derived for the hyper-singular integral in order that the multipole moments of the dual BIEs containing the weakly-, strongly- and hyper-singular kernels are collected and translated with a unified form. In the numerical examples, the accuracy of the proposed method for the evaluations of both the crack opening displacement (COD) and stress intensity factor (SW) is tested, and its performance in both the memory consumption and solution time in comparison with several other algorithms is investigated. The results are shown to demonstrate the effectiveness of this method for large-scale crack problems.