Applied Mathematics and Mechanics

, Volume 11, Issue 9, pp 809–820 | Cite as

A potential-hybrid/mixed finite element scheme for analysis of plates and cylindrical shells

  • Chen Da-peing
  • Pan Yi-su


Based on the potential-hybrid/mixed finite element scheme, 4-node quadrilateral plate-bending elements MP4, MP4a and cylindrical shell element MCS4 are derived with the inclusion of splitting rotations. All these elements demonstrate favorable convergence behavior over the existing counterparts, free from spurious kinematic modes and do not exhibit locking phenomenon in thin plate/shell limit. Inter-connections between the existing modified variational functional for the use of formulating C0-and C1-continuous elements are also indicated. Important particularizations of the present scheme include Prathap's consistent field formulation, the RIT/SRIT-compatible displacement model and so on.

Key words

potential-hybrid/mixed F.E. consistent field R. I. T. plate cylindrical shell 


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  1. [1]
    Pian, T. H. H., Derivation of element stiffness matrices by assumed stress distributions,AIAA J.,2 (1964), 1333–1336.Google Scholar
  2. [2]
    Pian, T. H. H., Element stiffness-matrices for boundary compatibility and for prescribed boundary stresses,Proc. Conf. Matrix Methods in Structural Mechanics (1965).Google Scholar
  3. [3]
    Zienkiewicz, O. C., et al., Reduced integration technique in general analysis of plates and shells,Int. J. Num. Eng.,3 (1971), 274–290.Google Scholar
  4. [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.Google Scholar
  5. [5]
    Belyschko, T., et al., Hourglass control in linear and nonlinear problems,Comp. Meth. Appl. Mech. Eng.,43 (1984), 251–276.Google Scholar
  6. [6]
    Spilker, R. L., et al., The hybrid stress model for thin plates,Int. J. Num. Meth. Eng.,15 (1980) 1239–1260.Google Scholar
  7. [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.Google Scholar
  8. [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.Google Scholar
  9. [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.Google Scholar
  10. [10]
    Simodaira, H., Equivalence between mixed models and displacement models using reduced integration,Int. J. Num. Meth. Eng.,21 (1985), 89–104.Google Scholar
  11. [11]
    Lee, S. W., et al., Experience with finite element modelling of thin plate bending,Computers and Structures,19 (1984), 747–755.Google Scholar
  12. [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.Google Scholar
  13. [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.Google Scholar
  14. [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.Google Scholar
  15. [15]
    Pian, T. H. H., et al., A new formulation of hybrid/mixed finite elements,Computers and Structures,16 (1983), 81–87.Google Scholar
  16. [16]
    Chen, D. P. and Y. L. Pei, FECAL-TR-87020-CH-PYL,Southwestern Jiaotong University (1987). (in Chinese)Google Scholar
  17. [17]
    Prathap, G., et al., An optimally integrated 4-node quadrilateral plate bending element,Int. J. Num. Meth. Eng.,19 (1983), 831–840.Google Scholar
  18. [18]
    Prathap, G., A continuous four-noded cylindical shell element,Computers and Structures,21 (1985), 995–999.Google Scholar
  19. [19]
    Bogner, F. K., et al., A cylindrical shell discrete elements,AIAA J.,5 (1967) 745–750.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1990

Authors and Affiliations

  • Chen Da-peing
    • 1
  • Pan Yi-su
    • 1
  1. 1.Southwest Jiaotong UniversityChengdu

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