Comparaison entre les modeles tridimensionnels et bidimensionnels de plaques en élasticité. (French) Zbl 0479.73042


74K20 Plates
Full Text: DOI EuDML


[1] P. G. CIARLET, Ph. DESTUYNDER, Ajustification of the two espace dimensional linear late model, J. de Mécanique, 18 (1979), 315-344. Zbl0415.73072 MR533827 · Zbl 0415.73072
[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 · Zbl 0118.41603 · doi:10.1016/0021-8928(62)90161-2
[3] A. RIGOLOT, Sur une théorie asymptotique des poutres droites, Thèse d’état, Paris, 1973. MR368552 · Zbl 0257.73013
[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. Zbl0338.90047 MR365287 · Zbl 0338.90047
[5] [5] I. BABUšKA, Error bounds for finite element method, Numer. Math., 16 (1971), 323-333. Zbl0214.42001 MR288971 · Zbl 0214.42001 · doi:10.1007/BF02165003
[6] Ph. DESTUYNDER, Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques, Thèse d’état, Paris, 1979.
[7] J. NECAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. Zbl1225.35003 MR227584 · Zbl 1225.35003
[8] G. DUVAUT, J. L. LIONS, Les inéquations en mécanique et en physique, Dunod, Paris, 1973. Zbl0298.73001 MR464857 · Zbl 0298.73001
[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. Zbl0268.49001 MR600331 · Zbl 0268.49001
[10] H. BREZIS, Opérateurs maximaux monotones, Mathematics Studies N^\circ 5, Nort Holland Amsterdam and New York, 1952.
[11] J. L. LIONS, E. MAGENES, Problèmes aux limites non homogènes et applications, T. 1, Dunod, Paris, 1968. Zbl0165.10801 · Zbl 0165.10801
[12] N. BOURBAKI, Éléments de mathématiques, Livre VI : Intégration, Actualités Scienti-fiques et Industrielles, 1175, Hermann, Paris, 1952. Zbl0115.04903 · Zbl 0115.04903
[13] K. YOSEDA, Functional Analysis, Springer Verlag, Berlin 1975 (4e ed.).
[14] R. ADAMS, Sobolev spaces, Academic Press, New York, 1976. Zbl0314.46030 MR450957 · Zbl 0314.46030
[15] A. E. GREEN, W. ZERNA, Theoretical elasticity, Oxford Press, 1975. Zbl0155.51801 MR64598 · Zbl 0155.51801
[16] G. GEYMONAT, Sui problemi ai limiti per i systemi lineari ellitici, Annali di Matematica Pura e Applicata, LXIX (1965), 207-284. Zbl0152.11102 MR196262 · Zbl 0152.11102 · doi:10.1007/BF02414374
[17] K. O. FRIEDRICHS, R. F. DRESSLER, A boundary layer theory for elastic plates, C.P.A.M., XIV, 1961, 1-33. Zbl0096.40001 MR122117 · Zbl 0096.40001 · doi:10.1002/cpa.3160140102
[18] P. G. CIARLET, S. KESAVAN, Two-dimensional appproximations of three-dimansional eigenvalue problems in plate theory, Comput. Meth. Appl. Mech. Engrg. (1981). Zbl0489.73057 MR626720 · Zbl 0489.73057 · doi:10.1016/0045-7825(81)90091-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.