Computational Mechanics

, Volume 13, Issue 5, pp 332–342 | Cite as

A mixed 3D finite element for modelling thick plates

  • Mark Asch
  • Michel Bercovier


Based on the Hellinger-Reissner variational principle, we formulate a mixed 3-d finite element for plate bending. This element is used to model thick plates and alleviates the problem of shear-locking in plates with large length/thickness ratios. The computer code which was used here, is available.


Thick Plate Plate Theory Uniform Mesh Mixed Finite Element Rank Deficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Asch, M.; Bercovier, M.: Mixed finite elements with optimal order projections. In preparationGoogle Scholar
  2. [2]
    Asch, M.; Bercovier, M. (1993): Mix-3d—a mixed finite element code for modelling thick plates. Technical Report 6 (February), Leibniz Institute of Computer Science, Hebrew University of Jerusalem, Givat-Ram, IsraelGoogle Scholar
  3. [3]
    Bercovier, M.; Engelman, M.; Gresho, P.; Sani, R. (1982): Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements. Int. J. Numer. Meth. Fluids 2, 25–42MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Ciarlet, P. G.; Destuynder, Ph. (1979): A justification of the two-dimensional linear plate model. J. Mécanique 18, 315–344MATHMathSciNetGoogle Scholar
  5. [5]
    Ciarlet, P. G.; Destuynder, Ph. (1981): A justification of a nonlinear model in plate theory. Comp. Methods Appl. Mech. Engrg., 26, 145–172MATHCrossRefGoogle Scholar
  6. [6]
    Bathe, K. J.; Brezzi, F. and Fortin, M. (1989): Mixed-interpolated elements for Reissner/Mindlin plates. Int. Journal for Numerical Methods in Engineering, 28, 1787–1801MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Harder, R. L. (1985): Review of the MacNeil-Harder linear static test problems. Finite Elements in Analysis and Design, 1(1)Google Scholar
  8. [8]
    Hughes, T. J. R. (1987): The finite element method: Linear static and dynamic finite element analysis Prentice-Hall, New YorkGoogle Scholar
  9. [9]
    Timoshenko, S.; Woinowsky-Krieger, S. (1959): Theory of plates and shells. McGraw-Hill, New YorkMATHGoogle Scholar
  10. [10]
    Washizu, K. (1974): Variational methods in elasticity and plasticity. Pergamon Press, New YorkMATHGoogle Scholar
  11. [11]
    Weissman, S. L.; Taylor, R. L. (1992): Mixed formulations for plate bending elements. Comput. Meth. Appl; Mech. Engng. 94, 391–427MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    Zienkiewicz, O. C. (1977): The Finite Element Method, 3rd edition. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Mark Asch
    • 1
  • Michel Bercovier
    • 2
  1. 1.Laboratoire d'Analyse NumériqueUniversité Paris XIOrsayFrance
  2. 2.Hebrew University of JerusalemGivat-RamIsrael

Personalised recommendations