Simulation of Effective Elastic Moduli of Plate with Randomly Distributed Holes Based on Fast Multipole Virtual Boundary Element Method

Abstract:

The main idea of fast multipole virtual boundary element method (VBEM) presented in the paper is that generalized minimal residual algorithm (GMRES) and fast multipole method (FMM) are integrated with the solution of VBEM equations.In virtue of the combined scheme of multipole expansion at the collocation point and local expansion at the integration point,the complexities of operation and memory about solution of the equations are made to be linearly proportional to the freedoms of the problem.As an application of the method,the effective elastic moduli of a plate containing randomly distributed circular holes are analyzed and the results are compared with one of other numerical methods.And the feasibility,accuracy and efficiency of this method are fully demonstrated.

Key words:fast multipole method(FMM); generalized minimal residual algorithm(GMRES); effective elastic moduli; virtual boundary element method(VBEM); elastic body