The finite and spectral cell methods for smart structure applications: transient analysis
The finite and spectral cell methods for smart structure applications: transient analysis
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DOI：
10.1007/s00707-014-1227-9
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发表时间：
2015-03
期刊：
影响因子：
2.7
通讯作者：
S. Duczek;S. Liefold;U. Gabbert
中科院分区：
文献类型：
--
作者：
S. Duczek;S. Liefold;U. Gabbert
本文介绍了一种强大而高效的数值工具，非常适合于超声导波的模拟，在处理非均匀材料时特别有用。所提出的方法是基于高阶有限元法（FEM）和虚拟域的概念相结合。如果部署了从p-版本的有限元法（p-FEM）中熟悉的分层形函数，则该方法被称为有限单元法（FCM）。在使用通过Gaussian-Lobatto-Legendre点的拉格朗日多项式的情况下，我们将其称为谱单元法（SCM）。这个名字，SCM，来自于这样一个事实，即部署的形状函数通常用于谱元素方法。为了模拟智能结构应用，如形状控制问题，噪声消除设备和超声导波的激励/传感，电气和机械变量之间的耦合也被考虑在内。在这方面，我们专注于包括压电的线性理论的变分制定的FCM和SCM，分别。几个数值基准问题，然后用来验证所提出的方法。仿真结果表明，该方法的准确性和计算工作量方面有前途的结果。我们观察到类似的收敛性能与“传统”高阶有限元方法的建议高阶虚拟域方法。此外，在现有的有限元软件中实施所提出的方法是一个简单的过程。这些特性使得该方法在结构健康监测问题和智能结构应用中的实际应用中成为一种有效的工具。
This article introduces a robust and efficient numerical tool that is well suited for the simulation of ultrasonic guided waves and can be especially helpful when dealing with heterogeneous materials. The proposed method is based on a combination of high-order finite element methods (FEM) and the fictitious domain concept. If hierarchic shape functions, which are familiar from thep-version of the finite element method (p-FEM), are deployed the method is referred to as the finite cell method (FCM). Where Lagrange polynomials through Gauß–Lobatto–Legendre points are used, we refer to it as the spectral cell method (SCM). The name, SCM, derives from the fact that the deployed shape functions are commonly utilized in the spectral element method. To model smart structure applications such as shape control problems, noise cancelation devices and the excitation/sensing of ultrasonic guided waves, a coupling between electrical and mechanical variables is also taken into account. In this context, we focus on including the linear theory of piezoelectricity in the variational formulation of the FCM and the SCM, respectively. Several numerical benchmark problems are then used to validate the proposed approach. The simulations show promising results with respect to the accuracy of the method and the computational effort. We observe similar convergence properties for the proposed high-order fictitious domain methods as with “conventional” high-order finite element approaches. Implementing the proposed method in existing finite element software is, moreover, a straightforward process. These properties make the method an efficient tool for practical applications in structural health monitoring problems and smart structure applications in general.