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.

中文翻译：

---

二维弹力分析的有限元法和边界元法迭代耦合算法

有限元方法（FEM）和边界元方法（BEM）的耦合算法可以最大程度地利用这两种方法的优点。但是，这种耦合将降低计算效率，因为系统的自由度将急剧增加。因此，需要一种能够实现精度和计算效率的新型耦合算法。这项研究提出了基于纽马克的精确积分有限元法（NBPI-FEM）和基于分析的时域边界元法（ABTD-BEM）耦合算法。在该耦合算法中，通过基于Newmark的精确积分求解FEM的控制方程，并通过解析方法求解BEM的控制方程。首先，给出了NBPI-FEM和ABTD-BEM的过程。然后提供耦合策略，研究了迭代次数与松弛参数之间的关系。最后，选择了两个说明性示例，即一维杆和半无限结构，以验证研究中提出的耦合算法。结果表明，数值解与一维杆实例的解析解吻合得很好，并且与有限元法计算的数值解吻合。因此，可以将NBPI-FEM和ABTD-BEM用于高精度，高效地解决弹性动力学问题。结果表明，数值解与一维杆实例的解析解吻合得很好，并且与有限元法计算的数值解相吻合。因此，可以将NBPI-FEM和ABTD-BEM用于高精度，高效地解决弹性动力学问题。结果表明，数值解与一维杆实例的解析解吻合得很好，并且与有限元法计算的数值解吻合。因此，可以将NBPI-FEM和ABTD-BEM用于高精度，高效地解决弹性动力学问题。