| 基于Maxwell模型的线性粘弹性波传播问题的质量集中杂交应力有限元法 |
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| 引用本文： | 周亚婧,陈豫眉. 基于Maxwell模型的线性粘弹性波传播问题的质量集中杂交应力有限元法[J]. 四川大学学报(自然科学版), 2021, 58(6): 061001 |
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| 作者姓名： | 周亚婧 陈豫眉 |
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| 作者单位： | 四川大学,西华师范大学 |
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| 摘 要： | 在有限元方法求解偏微分方程的过程中，时常涉及对质量矩阵的求逆. “质量集中”是一种利用特殊数值积分将质量矩阵对角化以提高计算效率的技术. 本文针对一类求解二维线性粘弹性固体介质波传(播问题的全离散杂交应力四边形有限元方法，研究其质量集中格式，利用位移插值节点为求积节点的Gauss-Lobatto 数值积分实现质量矩阵的对角化. 用数值算例验证了该质量集中格式的性能.
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| 关 键 词： | Maxwell模型 粘弹性波传导问题 杂交应力有限元 全离散 质量集中 |
| 收稿时间： | 2021-03-05 |
| 修稿时间： | 2021-04-16 |
A hybrid stress finite element method with mass lumping for Maxwell elastodynamic problems of wave propagation |
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| ZHOU Ya-Jing,CHEN Yu-Mei. A hybrid stress finite element method with mass lumping for Maxwell elastodynamic problems of wave propagation[J]. Journal of Sichuan University (Natural Science Edition), 2021, 58(6): 061001 |
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| Authors: | ZHOU Ya-Jing CHEN Yu-Mei |
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| Affiliation: | Sichuan University,China West Normal University |
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| Abstract: | The inversion of a mass matrix is often involved in solving partial differential equations by finite element method. Mass lumping can be used to improve the computational efficiency by diagonalizing mass matrix withspecial numerical integration. In this paper, a fully discrete hybrid stress quadrilateral finite element method for the wave propagation in viscoelastic solid media is presented. To realize the diagonalization of the mass matrix, the Gauss-Lobatto numerical integration with displacement interpolation nodes as quadrature nodes is used. A numerical examples is given to verify the performance of the method. |
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| Keywords: | Maxwell model viscoelastic wave propagation hybrid stress finite element fully discrete mass lumping |
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