Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Abstract

SUMMARYThis paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher runtime and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix-vector multiplication are both reduced to O(N ), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples.

A new BEM for solving 2D and 3D elastoplastic problems without initial stresses/strains

“…(38) and (40) we can see that, the domain integral in Eq. (55) is hyper-singular for evaluating stresses of interior points.…”

“…In the application of rolling engineering analysis, Xiao [36,37] applied boundary element method with initial stress to evaluate three dimensional frictional contact problems, and elastoplastic material behavior is taken into account by means of the initial stress formulation. By applying fast multipole method (FMM) to BEM, Wang and Yao [38] proposed a fast multipole boundary element method for the analysis of twodimensional elastoplastic problems.…”