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非协调曲边四边形十二自由度平板弯曲单元*

纪振义 叶开沅

纪振义, 叶开沅. 非协调曲边四边形十二自由度平板弯曲单元*[J]. 应用数学和力学, 1993, 14(2): 101-107.
引用本文: 纪振义, 叶开沅. 非协调曲边四边形十二自由度平板弯曲单元*[J]. 应用数学和力学, 1993, 14(2): 101-107.
Ji Zhen-yi, Yeh Kai-yuan. Incompatible Curved Quadrilateral Plate Bending Element with 12 Degrees of Freedom[J]. Applied Mathematics and Mechanics, 1993, 14(2): 101-107.
Citation: Ji Zhen-yi, Yeh Kai-yuan. Incompatible Curved Quadrilateral Plate Bending Element with 12 Degrees of Freedom[J]. Applied Mathematics and Mechanics, 1993, 14(2): 101-107.

非协调曲边四边形十二自由度平板弯曲单元*

基金项目: *国家教委“优教”基金;博士点基金;国家自然科学基金资助的课题

Incompatible Curved Quadrilateral Plate Bending Element with 12 Degrees of Freedom

  • 摘要: 本文利用精确元法[1],给出一个十二自由度曲边四边形板弯曲单元.该方法不需要变分原理,适用于任意正定和非正定偏微分方程.利用这个方法,单元之间的协调条件很容易满足,仅须位移和内力在单元节点上连续,即可保证所得到的解收敛于精确解.利用本文方法所获得的解,无论是位移还是内力可同时有二阶收敛精度.文末给出数值算例.表明了本文所得到的单元有非常好的精度.
  • [1] 叶开沅、纪振义,精确有限元法,应用数学和力学11(11)(1990),1001-1012.
    [2] Mason,V.,Rectangular elements for analysis of plate vibrations,J.Sound Vib.,7,3(1968),437-448
    [3] Gopalacharyulu,S.,A higher order conforming rectangular and triangular plate-bending elements,J.Sound Vib.,19(1971),333-347.
    [4] Bogner,F.K.,R.L.Fox and L.A.Schmit,Jr.,The generation of inter-element compatible stiffness and mass matrices by use of interpolation formulas,Proc.lst conf.on Matrix Methods in Structural Mech.,Ohio(1965).394-443.
    [5] Hermman,L.R.,Finite element bending analysis for plates,Journal of the Engineering Mechanics Division,Proceedings of the ASCE,93,EM5(1967),13.
    [6] Hermman,L.R.,A bending analysis for plates,AD 646300(1966),557.
    [7] Morley,L.S.D.,On the constant moment plate bending element,Journal of Strain Analysis,6,1(1971),20.
    [8] Zienkiewicz,O.C.,The Finite Element Method,McGraw-Hill Book Company,3rd Ed.(1977).
    [9] Irons,B.and S.Ahmad,Techniques of Finite Elements,Ellis Horword,Ltd.,Chinchester,UK(1979).
    [10] Ji Zhen-yi,Yeh Kai-yuan,An exact element method for bending of nonhomogeneous thin plate,Proceedings of the International Conference on Structural Engineering and Computation,Beijing,APRIL(1990).230-234.
    [11] Timoshehko,S.and S.Woinowsky-Krieger,Theory of Plates and Shell,McGraw-Hill Book Company,Inc,2nd Ed.(1959).
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出版历程
  • 收稿日期:  1991-05-21
  • 刊出日期:  1993-02-15

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