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Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory. (English) Zbl 0489.73057

MSC:
74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
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[1] Ciarlet, P.G.; Kesavan, S., Approximation bidimensionnelle du problème de valeurs propres pour une plaque, C.R. acad. sci. Paris, 289, 579-582, (1979) · Zbl 0416.73051
[2] Ciarlet, P.G.; Destuynder, P., A justification of the two-dimensional linear plate model, J. Mécanique, 18, 315-344, (1979) · Zbl 0415.73072
[3] Ciarlet, P.G.; Destuynder, P., A justification of a nonlinear model in plate theory, Comput. meths. appl. mech. engrg., 17/18, 227-258, (1979) · Zbl 0405.73050
[4] Ciarlet, P.G., A justification of the von Kármán equations, Arch. rational mech. anal., 73, 349-389, (1980) · Zbl 0443.73034
[5] Destuynder, P., Sur une justification mathématique des théories de plaques et de coques en élasticité linéaire, ()
[6] Lions, J.L., Perturbations singulières dans LES problèmes aux limites et en contrôle optimal, () · Zbl 0268.49001
[7] Kesavan, S., Sur l’approximation de problèmes linéaires et non-linéaires de valeurs propres, ()
[8] Kesavan, S., Homogeneization of eigenvalue problems: part 1, Appl. math. optim., 5, 153-167, (1979)
[9] D. Caillerie, The effect of a thin inclusion of high rigidity in an elastic body, Math. Meths. Appl. Sci., to appear. · Zbl 0446.73014
[10] Rigolot, A., Approximation asymptotique des vibrations de flexion des poutres droites élastiques, J. Mécanique, 16, 493-529, (1977) · Zbl 0403.73067
[11] Babus̆ka, I.; Aziz, A.K., Survey lectures on the mathematical foundations of the finite element method, (), 3-359
[12] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
[13] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs · Zbl 0278.65116
[14] Duvaut, G.; Lions, J.L., LES inéquations en Mécanique et en physique, (1972), Dunod Paris · Zbl 0298.73001
[15] Landau, L.; Lifchitz, E., Théorie de l’elasticité, (1967), Mir Moscow · Zbl 0166.43101
[16] Fichera, G., Existence theorems in elasticity-boundary value problems of elasticity with unilateral constraints, (), 347-424, a/2
[17] Taylor, A.E., Introduction to functional analysis, (1958), Wiley New York · Zbl 0081.10202
[18] Courant, R.; Hilbert, D., ()
[19] de Veubeke, B.Fraeijs, A course in elasticity, () · Zbl 0245.73031
[20] Lions, J.L.; Magenes, E., ()
[21] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Varangian multipliers, Rev. française automat. informat. recherche opérationnelle Sér. rouge anal. numér. R-2, 129-151, (1974) · Zbl 0338.90047
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