A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems

A new fast multipole boundary element method (BEM) is presented in this paper for large-scale analysis of two-dimensional (2-D) elastostatic problems based on the direct boundary integral equation (BIE) formulation. In this new formulation, the fundamental solution for 2-D elasticity is written in a complex form using the two complex potential functions in 2-D elasticity. In this way, the multipole and local expansions for 2-D elasticity BIE are directly linked to those for 2-D potential problems. Furthermore, their translations (moment to moment, moment to local, and local to local) turn out to be exactly the same as those in the 2-D potential case. This formulation is thus very compact and more efficient than other fast multipole approaches for 2-D elastostatic problems using Taylor series expansions of the fundamental solution in its original form. Several numerical examples are presented to study the accuracy and efficiency of the developed fast multipole BEM formulation and code. BEM models with more than one million equations have been solved successfully on a laptop computer. These results clearly demonstrate the potential of the developed fast multipole BEM for solving large-scale 2-D elastostatic problems.