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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*

陈大鹏 潘亦甦

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.
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.

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*

基金项目: * 国家自然科学基金资助项目

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.
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    [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.
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    [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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