A 2D wavelet-based spectral finite element method for elastic wave propagation
A 2D wavelet-based spectral finite element method for elastic wave propagation
复制标题
DOI：
10.1080/14786435.2012.685965
复制
发表时间：
2012-10
影响因子：
1.6
通讯作者：
L. Pahlavan;C. Kassapoglou;A. Suiker;Z. Gürdal
中科院分区：
文献类型：
--
作者：
L. Pahlavan;C. Kassapoglou;A. Suiker;Z. Gürdal
提出了一种基于小波变换的谱有限元法，可用于二维（2D）结构中弹性波传播的准确和有效的分析。该方法的特点是由一个时间变换的控制方程的小波域使用小波Galerkin方法，随后进行空间离散化的小波域的有限元法（FEM）。通过将在小波域中计算的节点位移变换回时域来获得最终解。该方法直接消除了离散小波变换产生的人为时间边缘效应，并允许对具有任意几何形状和边界条件的结构进行建模。该方法的准确性和适用性证明通过（i）轴向和弯曲波（兰姆波）在各向同性层中传播的基准问题的分析，和（ii）板的研究受到冲击载荷。的冲击问题的波传播响应进行比较的结果与标准有限元配备了一个直接的时间积分计划。各向异性对响应的影响表明，通过比较各向同性板的正交各向异性板的数值结果，以及由两种不同材料制成的板，在板的一个角部有和没有切口。小波域中的时间离散方程的解耦使得该方法本质上适合于并行计算，从而有效地研究具有大量自由度的工程结构中的高频波传播的有吸引力的候选人。
A wavelet-based spectral finite element method (WSFEM) is presented that may be used for an accurate and efficient analysis of elastic wave propagation in two-dimensional (2D) structures. The approach is characterised by a temporal transformation of the governing equations to the wavelet domain using a wavelet-Galerkin approach, and subsequently performing the spatial discretisation in the wavelet domain with the finite element method (FEM). The final solution is obtained by transforming the nodal displacements computed in the wavelet domain back to the time domain. The method straightforwardly eliminates artificial temporal edge effects resulting from the discrete wavelet transform and allows for the modelling of structures with arbitrary geometries and boundary conditions. The accuracy and applicability of the method is demonstrated through (i) the analysis of a benchmark problem on axial and flexural waves (Lamb waves) propagating in an isotropic layer, and (ii) the study of a plate subjected to impact loading. The wave propagation response for the impact problem is compared to the result computed with standard FEM equipped with a direct time-integration scheme. The effect of anisotropy on the response is demonstrated by comparing the numerical result for an isotropic plate to that of an orthotropic plate, and to that of a plate made of two dissimilar materials, with and without a cut-out at one of the plate corners. The decoupling of the time-discretised equations in the wavelet domain makes the method inherently suitable for parallel computation, and thus an appealing candidate for efficiently studying high-frequency wave propagation in engineering structures with a large number of degrees of freedom.