Eléments nis tétraédriques pour l'analyse duale
Keywords:
error estimation, 3D dual analysis, equilibrium model, tetrahedral nite elementAbstract
The error estimation by pure dual analysis requires two nite element computations. It is based on the results of displacement and equilibrium approaches of a given problem. It allows to compute the cumulated global discretization error of the two models by a simple comparison of the total energies computed using both methods. This paper presents the development of a new family of equilibrium type tetrahedral nite elements leading to statically admissible solutions of 3D nite element problems. Two examples of dual analysis using these elements are also presented.
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References
[ALM 96] MOITINHO DE ALMEIDA J. P., PEREIRA O. J. B. A., « A set of hybrid equilibrium
nite element models for the analysis of three-dimensional solids », Int. J. Num. Meth.
Engng, vol. 39, 1996, p. 2789-2802.
[BEC 72] BECKERS P., Les fonctions de tension dans la méthode des éléments nis, PhD
thesis, 1972.
[DEB 95] DEBONGNIE J.-F., ZHONG H.-G., BECKERS P., « Dual analysis with general boundary
conditions », Comp. Meth. Appl. Mech. & Engng., vol. 122, 1995, p. 183-192.
[LYN 75] LYNESS J. N., JESPERSEN D., « Moderate degree symmetric quadrature rules for
the triangle », J. Inst. Maths, Applics., vol. 15, 1975, p. 19-32.
[VEU 65] FRAEIJS DE VEUBEKE B., « Displacements and equilibrium models in the nite
elements method », ZIENKIEWICZ O. C., HOLISTER G. S., Eds., Stress analysis, chapitre
, John Wiley & Sons, London, 1965.
[VEU 73] FRAEIJS DE VEUBEKE B., « Diffusive equilibrium models », Lecture notes, Inter.
Research Seminar, University of Calgary, Canada, 1973.
