A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements

Abstract

A fast multipole boundary element method (BEM) for solving 2-D multiple crack problems in linear elastic fracture mechanics is presented in this paper. For multiple crack problems, both the degrees of freedom (DOFs) and the size of system matrices increase quickly as the number of cracks increases, and the conventional BEM cannot support such large systems. Instead of using the singular quarter-point boundary elements at the crack tips, constant line elements are applied to symmetrically discretize the outer boundaries and crack surfaces in the present approach. In order to keep the accuracy within a limited acceptable range, a relatively large number of constant elements are required to discretize the crack surfaces. The crack opening displacement (COD) fields of the multiple crack problems are obtained by the fast multipole BEM. Stress intensity factors (SIFs) are extracted from the obtained displacement fields near the crack tip by using one point COD formula. Comparison of the CODs between the fast multipole BEM and a finite element method using ANSYS are illustrated to show the feasibility of the proposed approach. With the acceleration of fast multipole technique, multi-crack problems can be dealt with desktop PCs. Several numerical examples are presented for computing the SIFs of cracks to study the effectiveness and the efficiency of the proposed approach. The numerical results clearly demonstrate the potentials of the fast multipole BEM for solving 2-D large-scale multi-crack problems by using constant elements.