Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis
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Finite element method and boundary element method iterative coupling algorithm for 2‑D elastodynamic analysis Duofa Ji1,2 · Weidong Lei3 · Zhijian Liu3 Received: 1 December 2018 / Revised: 1 December 2018 / Accepted: 20 June 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
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 Newmarkbased 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. Keywords Elastodynamic analysis · Finite element method · Time domain boundary element method · Newmark method · Analytical solution Mathematics Subject Classification 45Exx
Communicated by Baisheng Yan. * Weidong Lei [email protected] 1
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
2
Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China
3
Shenzhen Graduate School, Harbin institute of Technology, Shenzhen 518055, China
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D. Ji et al.
1 Introduction Computer-based simulations play an important role in the fields of engineering, in which the finite element method (FEM) is the most widely adopted computer method. Currently, FEM can work with many types of problems. For example, many researchers have adopted FEM to simulate structural responses under natural hazards (e.g., earthquakes(Jankowski 2005, 2009), tsunamis (Grilli et al. 2013; Romano et al. 2014), fires (Landesmann et al. 2005; Kodur et al. 2009) and explosions (Wang et al. 2005; Lu et al. 2005)). FEM can also be applied to heat transfer (Sheikholeslami et al. 2015; Sheikholeslami and Vajravelu 2017), fluid mechanics (Donea et al. 1982; Hughes et al. 1989), fracture mechanics (Sukumar et al. 2015; Ferté e
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