Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité

Ph. Destuynder

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 4, page 331-369
  • ISSN: 0764-583X

How to cite

top

Destuynder, Ph.. "Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.4 (1981): 331-369. <http://eudml.org/doc/193386>.

@article{Destuynder1981,
author = {Destuynder, Ph.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {compare solutions of three-dimensional linear plate models and two- dimensional ones; thickness becomes infinitely small; convergence results; error estimates; influence of boundary conditions},
language = {fre},
number = {4},
pages = {331-369},
publisher = {Dunod},
title = {Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité},
url = {http://eudml.org/doc/193386},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Destuynder, Ph.
TI - Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 4
SP - 331
EP - 369
LA - fre
KW - compare solutions of three-dimensional linear plate models and two- dimensional ones; thickness becomes infinitely small; convergence results; error estimates; influence of boundary conditions
UR - http://eudml.org/doc/193386
ER -

References

top
  1. [1] P. G. CIARLET, Ph. DESTUYNDER, Ajustification of the two espace dimensional linear late model, J. de Mécanique, 18 (1979), 315-344. Zbl0415.73072MR533827
  2. [2] A. L. GOL'DEVEIZER, Derivation of an approximate theory of bending of a plate by a method of asymptotic integration of the equations in the theory of elasticity, J. App. Math, 19 (1963), 1000-1025. Zbl0118.41603
  3. [3] A. RIGOLOT, Sur une théorie asymptotique des poutres droites, Thèse d'état, Paris, 1973. MR368552
  4. [4] F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O., R2 (1974), 129-151. Zbl0338.90047MR365287
  5. [5] I. BABUšKA, Error bounds for finite element method, Numer. Math., 16 (1971), 323-333. Zbl0214.42001MR288971
  6. [6] Ph. DESTUYNDER, Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques, Thèse d'état, Paris, 1979. 
  7. [7] J. NECAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
  8. [8] G. DUVAUT, J. L. LIONS, Les inéquations en mécanique et en physique, Dunod, Paris, 1973. Zbl0298.73001MR464857
  9. [9] J. L. LIONS. Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lectures Notes in Mathematics, Vol. 323, Springer Verlag, Berlin, 1973. Zbl0268.49001MR600331
  10. [10] H. BREZIS, Opérateurs maximaux monotones, Mathematics Studies N° 5, Nort Holland Amsterdam and New York, 1952. 
  11. [11] J. L. LIONS, E. MAGENES, Problèmes aux limites non homogènes et applications, T. 1, Dunod, Paris, 1968. Zbl0165.10801
  12. [12] N. BOURBAKI, Éléments de mathématiques, Livre VI : Intégration, Actualités Scienti-fiques et Industrielles, 1175, Hermann, Paris, 1952. Zbl0115.04903
  13. [13] K. YOSEDA, Functional Analysis, Springer Verlag, Berlin 1975 (4e ed.). 
  14. [14] R. ADAMS, Sobolev spaces, Academic Press, New York, 1976. Zbl0314.46030MR450957
  15. [15] A. E. GREEN, W. ZERNA, Theoretical elasticity, Oxford Press, 1975. Zbl0155.51801MR64598
  16. [16] G. GEYMONAT, Sui problemi ai limiti per i systemi lineari ellitici, Annali di Matematica Pura e Applicata, LXIX (1965), 207-284. Zbl0152.11102MR196262
  17. [17] K. O. FRIEDRICHS, R. F. DRESSLER, A boundary layer theory for elastic plates, C.P.A.M., XIV, 1961, 1-33. Zbl0096.40001MR122117
  18. [18] P. G. CIARLET, S. KESAVAN, Two-dimensional appproximations of three-dimansional eigenvalue problems in plate theory, Comput. Meth. Appl. Mech. Engrg. (1981). Zbl0489.73057MR626720

Citations in EuDML Documents

top
  1. Isabelle Gruais, Modélisation de la jonction entre une plaque et une poutre en élasticité linéarisée
  2. L. J. Alvarez-Vásquez, J. M. Viaño, Modeling and optimization of non-symmetric plates
  3. J.-C. Paumier, Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
  4. Stéphane Busse, Philippe G. Ciarlet, Bernadette Miara, Justification d'un modèle linéaire bi-dimensionnel de coques «faiblement courbées» en coordonnées curvilignes

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.