Numerical analysis of Lamb waves using the finite and spectral cell methods
Numerical analysis of Lamb waves using the finite and spectral cell methods
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DOI：
10.1002/nme.4663
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发表时间：
2014-07-06
影响因子：
2.9
通讯作者：
Gabbert, U.
中科院分区：
文献类型：
--
作者：
Duczek, S.;Joulaian, M.;Gabbert, U.
波浪传播现象的准确模拟在不同的工程学科中起着重要作用。例如，在结构性健康监测中，超声波引导波用于检测和定位损害，并评估所考虑的组件部分的结构完整性。由于实际结构的复杂性，结构健康监测系统的数值模拟是一项计算要求的任务。因此，为了促进对波传播现象的分析，作者建议将有限的细胞方法与光谱元素方法相结合。随后的新方法称为光谱细胞方法。由于它不依赖身体构成的网格，因此所得的方法消除了在常规有限元方法中遇到的所有离散困难。此外，借助质量大块，它为使用显式时间整合算法铺平了道路。在本文的第一部分中，我们表明，使用一个集团的质量基质而不是一致的矩阵对光谱元素方法的准确性没有不利影响。我们在第二部分中引入了光谱细胞方法，表明当应用于波传播分析时，光谱细胞方法产生的结果可与其他标准高阶有限元方法相媲美。
An accurate and efficient simulation of wave propagation phenomena plays an important role in different engineering disciplines. In structural health monitoring, for example, ultrasonic guided waves are used to detect and localize damage and to assess the structural integrity of the component part under consideration. Because of the complexity of real structures, the numerical simulation of structural health monitoring systems is a computationally demanding task. Therefore, to facilitate the analysis of wave propagation phenomena, the authors propose to combine the finite cell method with the spectral element method. The ensuing novel method is referred to as the spectral cell method. Because it does not rely on body-fitted meshes, the resulting approach eliminates all discretization difficulties encountered in conventional finite element methods. Moreover, with the aid of mass lumping, it paves the way for the use of explicit time-integration algorithms. In the first part of the paper, we show that using a lumped mass matrix instead of the consistent one has no detrimental effect on the accuracy of the spectral element method. We introduce the spectral cell method in the second part, showing that, when applied to wave propagation analysis, the spectral cell method yields results comparable with other standard higher order finite element approaches.Copyright (c) 2014 John Wiley & Sons, Ltd.