A. Dias, E. Albuquerque, L. Campos, P. Sollero, A. Júnior
This paper presents a two-dimensional fast multipole boundary element method for large-scale analysis of anisotropic elastic problems. The expansions and fast multipole operations it uses are similar to those in formulations of fast multipole boundary element method already presented for potential and isotropic elastostatic problems. The anisotropic fundamental solutions used in here are based on the Lekhnitskii formalism. They are expanded in order to allow the development of fast multipole operations. To assess the accuracy of the expansions, the fundamental solutions and some terms of the boundary element influence matrices obtained by direct integration of kernels are compared to those obtained by the fast multipole expansion. Moreover, to validate the method, numerical solutions are compared to analytical solutions. The proposed formulation has quasi-linear complexity that is ideal for solving large scale problems. The main conclusion of this paper is that the proposed formulation is more effective than the conventional boundary element method. It is faster and uses less memory, allowing the analysis of larger problems in less time.
Published on 22/05/19Submitted on 14/05/19
Licence: CC BY-NC-SA license
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