## 留言板

 引用本文: 钱源耀. 中厚板特征值问题的杂交/混合有限元分析[J]. 应用数学和力学, 1987, 8(8): 733-742.
Qian Yuan-yao. A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates[J]. Applied Mathematics and Mechanics, 1987, 8(8): 733-742.
 Citation: Qian Yuan-yao. A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates[J]. Applied Mathematics and Mechanics, 1987, 8(8): 733-742.

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

• 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。
•  [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．

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

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