Ciarlet, P. G.; Kesavan, S. Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory. (English) Zbl 0489.73057 Comput. Methods Appl. Mech. Eng. 26, 145-172 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 43 Documents MSC: 74K20 Plates 74H45 Vibrations in dynamical problems in solid mechanics 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions Keywords:eigenvalues; eigenfunctions; three-dimensional equations; linear elastic equilibrium; clamped plate; converge to eigenvalues and eigenfunctions of two-dimensional biharmonic operator; limit eigenvalues and eigenfunctions equivalently characterized as leading terms in asymptotic expansion of three-dimensional solutions PDF BibTeX XML Cite \textit{P. G. Ciarlet} and \textit{S. Kesavan}, Comput. Methods Appl. Mech. Eng. 26, 145--172 (1981; Zbl 0489.73057) Full Text: DOI OpenURL References: [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 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.