A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry
A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry
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DOI：
10.1002/nme.2147
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发表时间：
2008-04-09
影响因子：
2.9
通讯作者：
Song, Chongmin
中科院分区：
文献类型：
--
作者：
Bazyar, Mohammad Hossein;Song, Chongmin
建立了一个高阶局部传输边界来模拟弹性波在无界域中的传播。该传输边界适用于标量波和矢量波、任意几何形状的无界域和各向异性材料。该公式基于无界域的动刚度矩阵的连续分数解。由动刚度的尺度边界有限元方程递归确定连分式的系数矩阵。随着连分式阶数的增加，解在整个频率范围内迅速收敛。利用连续分式解，引入辅助变量，将高阶局部传输边界表示为对称的、与频率无关的系数矩阵的运动方程。它可以与有限元素无缝耦合。结构动力学中的标准程序直接适用于评估频率和时间域的响应。分析和数值算例表明，这种高阶局部传输边界具有较高的收敛速度和效率。版权所有(C) 2007约翰威利父子有限公司
A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued-fraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary. Copyright (C) 2007 John Wiley & Sons, Ltd.