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Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method
Finite Elements in Analysis and Design ( IF 3.5 ) Pub Date : 2022-04-06 , DOI: 10.1016/j.finel.2022.103760 Ramon Codina 1, 2 , Önder Türk 3
中文翻译:
使用压力稳定有限元法对不可压缩材料的弹性振动进行模态分析
更新日期:2022-04-06
Finite Elements in Analysis and Design ( IF 3.5 ) Pub Date : 2022-04-06 , DOI: 10.1016/j.finel.2022.103760 Ramon Codina 1, 2 , Önder Türk 3
Affiliation
This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimate provided.
中文翻译:
使用压力稳定有限元法对不可压缩材料的弹性振动进行模态分析
本文描述了一种模态分析技术,用于使用稳定有限元方法来近似不可压缩弹性固体的振动,以近似相关的特征值问题。解释了为什么基于残差的公式在这种情况下不合适,并且采用了仅涉及压力梯度的公式。与 Galerkin 方法相比,稳定项的影响在近似公式的推导和提供的误差估计中都有详细说明。