中厚板特征值问题的杂交/混合有限元分析

钱源耀

中厚板特征值问题的杂交/混合有限元分析

钱源耀

上海市应用数学和力学研究所

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出版历程
- 收稿日期: 1985-06-30
- 刊出日期: 1987-08-15

A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates

Qian Yuan-yao

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要

摘要: 本文采用杂交/混合有限元对中厚板的屈曲问题和自由振动问题进行了分析,首先推导了一个修正的Reissner变分原理,它仅要求构造C⁰类场变量,避免了闭锁现象的产生。所有的场变量皆采用线性插值。最后得到一个矩阵型的位移广义本征值方程,刚度矩阵对称、正定。计算结果表明本文采用的方法简单、可靠,较为令人满意。

Abstract: The buckling and free vibration problems of moderately thick plate are considered in this paper by using the hybrid/mixed finite element model. A modified Reissner principle which only requires C⁰ continuity is derived. No lockling phenomenon is observed. Linear interpolation is used for all independent unknown function. Finally a displacement generalized eigenvalue equation is obtained, in which the stiffness matrix is symmetric and positively definite. The calculated results show that the method proposed is simple, reliable and satisfactory.

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参考文献(12)

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