Implementation and computational aspects of a 3D elastic wave modelling by PUFEM
Implementation and computational aspects of a 3D elastic wave modelling by PUFEM
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DOI：
10.1016/j.apm.2017.05.013
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发表时间：
2017-09
影响因子：
5
通讯作者：
M. Mahmood;O. Laghrouche;J. Trevelyan;A. Kacimi
中科院分区：
文献类型：
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作者：
M. Mahmood;O. Laghrouche;J. Trevelyan;A. Kacimi
本文提出了频域中三维弹性波问题的丰富有限元模型，每个节点间距能够包含多个波长。这是通过将平面波基分解应用于三维 (3D) 弹性波方程并将位移场表示为压力 (P) 和剪切 (S) 平面波之和来实现的。与 2D 模型相比，该模型在 3D 中的实现存在许多问题，特别是关于如何在每个节点的基础中使用 S 波以及如何在近似空间中选择 P 波和 S 波之间的平衡。还总结并使用了可用于选择 3D 波方向的各种建议技术。所开发的元素使我们能够放宽传统的要求，即考虑每个波长的许多节点，与基于低阶多项式的有限元一起使用，因此可以解决弹性波问题，而无需细化每个频率的计算域的网格。该技术的有效性是通过将选定问题的解决方案与可用分析模型或使用传统有限元的高分辨率数值结果进行比较，并考虑网格尺寸和丰富的 3D 平面波数量的影响来确定的。研究了结构化网格上空间平面波方向的平衡和不平衡选择，以评估弹性波 3D PUFEM 模型的准确性和条件。
This paper presents an enriched finite element model for three dimensional elastic wave problems, in the frequency domain, capable of containing many wavelengths per nodal spacing. This is achieved by applying the plane wave basis decomposition to the three-dimensional (3D) elastic wave equation and expressing the displacement field as a sum of both pressure (P) and shear (S) plane waves. The implementation of this model in 3D presents a number of issues in comparison to its 2D counterpart, especially regarding how S-waves are used in the basis at each node and how to choose the balance between P and S-waves in the approximation space. Various proposed techniques that could be used for the selection of wave directions in 3D are also summarised and used. The developed elements allow us to relax the traditional requirement which consists to consider many nodal points per wavelength, used with low order polynomial based finite elements, and therefore solve elastic wave problems without refining the mesh of the computational domain at each frequency. The effectiveness of the proposed technique is determined by comparing solutions for selected problems with available analytical models or to high resolution numerical results using conventional finite elements, by considering the effect of the mesh size and the number of enriching 3D plane waves. Both balanced and unbalanced choices of plane wave directions in space on structured mesh grids are investigated for assessing the accuracy and conditioning of this 3D PUFEM model for elastic waves.