## 留言板

 引用本文: 陈大鹏, 潘亦甦. 用于平板和圆柱壳分析的势能～杂交/混合分离位移有限元格式*[J]. 应用数学和力学, 1990, 11(9): 761-770.
Chen Da-peng, Pan Yi-su. A Potential-Hybrid/Mixed Finite Element Scheme for Analysis of Plates and Cylindrical Shells[J]. Applied Mathematics and Mechanics, 1990, 11(9): 761-770.
 Citation: Chen Da-peng, Pan Yi-su. A Potential-Hybrid/Mixed Finite Element Scheme for Analysis of Plates and Cylindrical Shells[J]. Applied Mathematics and Mechanics, 1990, 11(9): 761-770.

## A Potential-Hybrid/Mixed Finite Element Scheme for Analysis of Plates and Cylindrical Shells

• 摘要: 本文基于势能～杂交/混合有限元格式,导出了具有分离转动变量的4节点四边形Reissner-Mindlin板元MP4、MP4a和圆柱壳元MCS4.所有这些单元都显示了良好的收敛性;不含有多余机动模式;当趋于薄板/壳极限时,不存在“自锁”现象.本文还指明了在C0和C1连续的单元列式中使用的修正泛函,存在相互联系.本文的方法可导出Prathap的一致场列式,也可导出RIT/SRIT的位移协调模型.
•  [1] Pian,T.H.H.,Derivation of element stiffness matrices by assumed stress distributions,AIAA J.,2(1964),1333-1336. [2] Pian,T.H.H.,Element stiffness-matrices for boundary compatibility and for prescribed boundary stresses,Proc.Conf.Matrix Methods in Structural Mechanics(1965). [3] Zienkiewicz,O.C.,et al.,Reduced integration technique in general analysis of plates and shells,Int.J.Num.Eng.,3(1971),274-290. [4] Belytschko,T.,et al.,A Consistant control of spurious singular models in the 9-node Lagrange element for the Laplace and Mindlin plate equations,Comp.Meth.Appl.Mech Eng.,44(1984),269-295. [5] Belyschko,T.,et al.,Hourglass control in linear and nonlinear problems,Comp.Meth.Appl.Mech.Eng.,43(1984),251-276. [6] Spilker,R.L.,et al.,The hybrid stress model for thin plates,Int.J.Num.Meth.Eng.,15(1980)1239-1260. [7] Spilker,R.L.,et al.,A serendipity cubic displacement hybrid stress element for thin and moderately thick plates,Int.J.Num.Meth.Eng.,15(1980),1261-1278. [8] Lee,S.W.and T.H.H.Pian,Improvement of plate and shell finite element by mixed formulations,AIAA J.,16(1978),29-34. [9] Malkus,D.S.,et al.Mixed finite element methods-reduced and selective integration techniques:a unification,Comp.Meth.Appl.Mech.Eng.,15(1978),63-81. [10] Simodaira,H.,Equivalence between mixed models and displacement models using reduced integration,Int.J.Num.Meth.Eng.,21(1985),89-104. [11] Lee,S.W.,et al.,Experience with finite element modelling of thin plate bending,Computers and Structures,19(1984),747-755. [12] Lee,S.W.,and J.C.Zhang,A six-node finite element for plate bending,Int.J.Nume.Meth.Eng.,21(1985),131-143. [13] Lee,S.W.and S.C.Wang,Mixed formulation finite elements for Mindlin theory plate bending,Int.J.Num.Meth.Eng.,18(1982),1297-1311. [14] Pian,T.H.H.and D.P.Chen,Alternative ways for formulation of hybrid stress element,Int.J.Num.Meth.Eng.,18(1983),1679-1684. [15] Pian,T.H.H.,et al.,A new formulation of hybrid/mixed finite elements,Computers and Structures,16(1983),81-87. [16] 陈大鹏、裴亚玲C1类薄板杂交应力法与杂交/混合法列式,FECAL-TR-87020,西南交通大学(1987). [17] Prathap,G.,et al.,An optimally integrated 4-node quadrilateral plate bending element,Int.J.Num.Meth.Eng.,19(1983),831-840. [18] Prathap,G.,A continuous four-noded cylindical shell element,Computers and Structures,21(1985).995-999. [19] Bogner,F.K.,et al.,A cylindrical shell discrete elements,AIAA J.,5(1967)745-750.

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##### 出版历程
• 收稿日期:  1989-06-29
• 刊出日期:  1990-09-15

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