Skip to main content
SpringerLink
Log in

Eléments finis raffinés en élasticité bidimensionnelle

  • Articles Originaux
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

This paper deals with the solution of two-dimensional variational problems of first order by the finite element method. The expressions for the basic functions in a triangular or rectangular element are given in a general form which is especially suitable for computation. These finite elements are used for plane elasticity problems, for which the basic functions ensure the continuity of the displacement field or of the displacement and stress fields. It is shown how the change of variables allows to carry out numerical integrations once for all; thus, the computing time depends very little on the choice of the basic functions. The different approximated solutions are numerically compared.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.-J. Goël,Construction of Basic Functions for Numerical Utilisation of Ritz's Method, Numerische Mathematik12, 435–447 (1968).

    Google Scholar 

  2. O. C. Zienkiewicz,The Finite Element Method in Structural and Continuum Mechanics (McGraw-Hill, London 1967).

    Google Scholar 

  3. C. A. Fellipa,Refined Finite Element Analysis of Linear and Nonlinear Two-dimensional Structures, SESM Report No. 66-22 (University of California, Berkley, Califirnia, 1966).

    Google Scholar 

  4. R. W. Clough andJ. L. Tocher,Finite Element Stiffness Matrices for Analysis of Plate Bending, Proc. Conf. Matrix Meth. Struct. Mech. (Wright-Patterson Air Force Base, Dayton, Ohio, 1965).

    Google Scholar 

  5. A. E. Green andW. Zerna,Theoretical Elasticity (Oxford Press, London 1963).

    Google Scholar 

  6. H. Favre,Cours de mécanique, vol. 3, pp. 29–37 (Dunod, Paris 1949).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de mathématiques appliquées, Ecole Polytechnique Fédérale, Lausanne

    Georges Dupuis & Jean-Jacques Goël

Authors
  1. Georges Dupuis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Jacques Goël
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Cette étude a été partiellement supportée par le Fond National de la Recherche Scientifique. Les auteurs expriment leur gratitude au prof. J. Descloux qui dirige leurs recherches et leur prodigue conseils et encouragements.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dupuis, G., Goël, JJ. Eléments finis raffinés en élasticité bidimensionnelle. Journal of Applied Mathematics and Physics (ZAMP) 20, 858–881 (1969). https://doi.org/10.1007/BF01592296

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01592296

Search

Navigation