A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method
A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method
复制标题
DOI：
10.1002/nme.4613
复制
发表时间：
2014-03
影响因子：
2.9
通讯作者：
D. Chen;C. Birk;Chongmin Song;C. Du
中科院分区：
文献类型：
--
作者：
D. Chen;C. Birk;Chongmin Song;C. Du
提出了一种求解有界域和无界域中波传播的高阶时域方法。它以尺度边界有限元为基础，擅长模拟无界域和奇异性。将有界域和无界域动刚度阵表示为连分式展开式，每个波长只需三项左右即可得到精确的结果。提出了一种改进的连分式方法，用于有界域，得到了数值上更健壮的时间域公式。递归地确定相应连分式展开的系数矩阵。所得到的解适用于具有许多自由度的系统，因为它在整个频率范围内收敛，甚至对于高阶展开也是如此。文中还提出了一种将改进的有界域高阶时域公式与高阶传输边界相结合的方案。在时间域上，耦合模型对应于具有对称的、带状的和频率无关的系数矩阵的运动方程，这些系数矩阵可以用标准的时间积分格式有效地求解。数值算例表明，该方法具有较高的稳健性、效率和精度。版权所有©2013 John Wiley&Sons，Ltd.
A high‐order time‐domain approach for wave propagation in bounded and unbounded domains is proposed. It is based on the scaled boundary FEM, which excels in modelling unbounded domains and singularities. The dynamic stiffness matrices of bounded and unbounded domains are expressed as continued‐fraction expansions, which leads to accurate results with only about three terms per wavelength. An improved continued‐fraction approach for bounded domains is proposed, which yields numerically more robust time‐domain formulations. The coefficient matrices of the corresponding continued‐fraction expansion are determined recursively. The resulting solution is suitable for systems with many DOFs as it converges over the whole frequency range, even for high orders of expansion. A scheme for coupling the proposed improved high‐order time‐domain formulation for bounded domains with a high‐order transmitting boundary suggested previously is also proposed. In the time‐domain, the coupled model corresponds to equations of motion with symmetric, banded and frequency‐independent coefficient matrices, which can be solved efficiently using standard time‐integration schemes. Numerical examples for modal and time‐domain analysis are presented to demonstrate the increased robustness, efficiency and accuracy of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.