Finite and spectral cell method for wave propagation in heterogeneous materials
Finite and spectral cell method for wave propagation in heterogeneous materials
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DOI：
10.1007/s00466-014-1019-z
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发表时间：
2014-09
影响因子：
4.1
通讯作者：
Meysam Joulaian;S. Duczek;U. Gabbert;A. Düster
中科院分区：
文献类型：
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作者：
Meysam Joulaian;S. Duczek;U. Gabbert;A. Düster
在本文中，我们提出了一种快速，可靠的技术来模拟波在复杂结构的非均匀材料。所提出的方法，谱单元法，是有限单元法和谱单元法的组合，显着降低预处理和计算费用。谱单元法利用显式时间积分方案和对角质量矩阵，减少了求解方程组的时间。通过采用虚拟域方法，该方法还有助于消除与网格生成相关的一些困难。除了介绍一个适当的，具体的质量集总技术，我们还研究了这种方法的低阶和高阶版本的性能的基础上，几个数值例子。我们的研究结果表明，高阶版本的谱单元方法一起需要更少的内存存储和更少的CPU时间比其他可能的版本，同时结合显式时间积分算法。此外，由于所提出的方法在可用的有限元程序中的实现是简单的，这些属性使该方法成为实际应用的可行工具，例如结构健康监测[1-3]，定量超声应用[4]或振动和噪声的主动控制[5，6]。
In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1–3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].