Inverse mass matrix via the method of localized lagrange multipliers
Inverse mass matrix via the method of localized lagrange multipliers
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DOI：
10.1002/nme.5613
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发表时间：
2018-01
影响因子：
2.9
通讯作者：
J. A. González;R. Kolman;S. S. Cho-S.;C. Felippa;K. Park
中科院分区：
文献类型：
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作者：
J. A. González;R. Kolman;S. S. Cho-S.;C. Felippa;K. Park
提出了一种生成结构动力学问题的质量矩阵逆的有效方法，可以对其进行定制以提高目标频率范围和/或波内容的准确性。本方法绕过了使用需要针对边界条件和自由边或表面的特殊程序的核逆质量矩阵的双正交构造，并使用标准有限元程序构造了自由逆质量矩阵。各种边界条件通过局部拉格朗日乘子的方法来实现。特别地，本文利用标准有限元单元质量矩阵构造核逆矩阵。结果表明，该逆质量矩阵的精度几乎与传统一致质量矩阵或集总质量矩阵和一致质量矩阵的组合的精度相同。使用所提出的逆质量矩阵进行数值实验，以验证其应用于杆、梁和平面应力问题的振动分析时的有效性。
An efficient method for generating the mass matrix inverse of structural dynamic problems is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free‐free inverse mass matrix using the standard FEM procedure. The various boundary conditions are realized by the the method of localized Lagrange multipliers. In particular, the present paper constructs the kernel inverse matrix by using the standard FEM elemental mass matrices. It is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices. Numerical experiments with the proposed inverse mass matrix are conducted to validate its effectiveness when applied to vibration analysis of bars, beams, and plain stress problems.