Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

Abstract

The coupling algorithm of the finite element method (FEM) and boundary element method (BEM) can make maximal use of both methods’ advantages. However, such coupling will reduce the computational efficiency because the systems’ degrees of freedom will increase sharply. Thus, a new coupling algorithm that achieves accuracy and computational efficiency is necessary. This study proposes the Newmark-based precise integration FEM (NBPI-FEM) and analytical-based time domain BEM (ABTD-BEM) coupling algorithm. In this coupling algorithm, the governing equation of the FEM is solved by Newmark-based precise integration, and the governing equation of the BEM is solved by the analytical method. First, the procedures of NBPI-FEM and ABTD-BEM are given. The coupling strategy is then provided, and the relationship between the iteration numbers and the relaxation parameter is investigated. Finally, two illustrative examples—i.e., 1-D rod and a semi-infinite structure—are selected to verify the coupling algorithm proposed in the study. The results show that the numerical solutions agree well with the analytical solutions for the 1-D rod example and coincide with the numerical solutions calculated by FEM. Thus, NBPI-FEM and ABTD-BEM can be applied for solving elastodynamic problems with high accuracy and efficiency.