| 用对角质量矩阵时有限单元特征值问题的准确度 |
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| 引用本文： | 李原能,王大钧.用对角质量矩阵时有限单元特征值问题的准确度[J].力学学报,1988(3). |
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| 作者姓名： | 李原能 王大钧 |
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| 作者单位： | 华东水利学院力学系
(李原能)，北京大学力学系(王大钧) |
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| 摘 要： | 本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。
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| 关 键 词： | 对角质量矩阵 有限元法 特征值问题 频率的准确度 振型的准确度 |
ACCURACY OF FINITE ELEMENT EIGENPROBLEM BY USING DIAGONAL MASS MATRIX |
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| Li Yuanneng.ACCURACY OF FINITE ELEMENT EIGENPROBLEM BY USING DIAGONAL MASS MATRIX[J].chinese journal of theoretical and applied mechanics,1988(3). |
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| Authors: | Li Yuanneng |
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| Institution: | Li Yuanneng(The East China University of Hydraulic Resources)Wang Dajun(Peking University) |
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| Abstract: | In the present paper the model of diagonalization for mass matrix is used. In the formula of integration for kinetic energy, the integration points are coincident with finite element nodes so that a diagonal mass matrix is obtained and an algebraic eigenvalue problem is constructed. This paper shows how the error estimates of natural frequencies, natural modes and corresponding stresses by using such diagonal mass matrix depends upon the algebraic accuracy of the integration formula for kinetic energy, the number of order of polynomial for interpolation of displacements and the number of highest order of derivative of displace-ments in strain energy. The applicability of diagonal mass matrix is discussed. |
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| Keywords: | diagonal mass matrix finite element method eigenvalue problem ac-curacy of frequencies accuracy of natural modes |
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