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

计量
- 文章访问数: 1874
- HTML全文浏览量: 120
- PDF下载量: 541
- 被引次数: 0
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.

HTML全文

参考文献(12)

[1]	Hughes,T.J.R.and T.E.Tezduyar,Finite element based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element,Journal of Applied Mechanics,48,Sept.(1981),587.
[2]	钱伟长,《变分法及有限元》,科学出版社(1980),
[3]	胡海昌,《弹性力学的变分原理及其应用》,科学出版社(1981).
[4]	Allman,D.J.,Finite element analysis of plate buckling using a mixed variational principle,Proc.3rd Conf Matrix Meth.Struct.Mech.(1971),683.
[5]	Tabarrok,B.and A.Simpson,An equilibrium finite element model for buckling analysis of plates,Int.J.Num.Meth.,Eng.,11 (1977),1733.
[6]	Reddy,J.N.and C.S.Tsay,Stability and vibration of thin rectangular plates by simplified mixed finite elements,Journal of Sound and Vibration,55,2(1977),289.
[7]	Venkateswara Rao,G.,J.Venkataramana and K.Kanaka Raju,Stability of moderately thick rectangular plates using a high precision triangular finite element,Comp.and Struct.,5(1975),257.
[8]	罗继伟,中厚板屈曲的平衡模型有限元分析,固体力学学报,2 (1983),177
[9]	Rock,T.A.and E.Hinton,A finite element method for the free vibration of plates allowing for transverse shear deformation,Comp.and Struct.,6(1976),37.
[10]	Hinton,E.,and N.Bićanić,A comparison of Lagrange and Serendipity Mindlin plate elements for free vibration analysis,Comp.and Struct.,10(1979),483.
[11]	铁摩辛柯,S.P.J.M.盖菜,《单性稳定理论》,第二版,科学出版社(1965).
[12]	Srinivas,S.and A.K.Rao.Buckling of thick rectangular plate,AIAAJ.,7(1969),1645．