@article{M2AN_1997__31_7_891_0,
author = {Kerdid, N.},
title = {Modeling the vibrations of a multi-rod structure},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {31},
year = {1997},
pages = {891-925},
mrnumber = {1489177},
zbl = {0895.73037},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1997__31_7_891_0}
}
Kerdid, N. Modeling the vibrations of a multi-rod structure. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 891-925. http://gdmltest.u-ga.fr/item/M2AN_1997__31_7_891_0/
[1] and , 1986, A justification of the one-dimensional linear model of elastic beam, Math. Meth. Appl. Sri., 8, p. 1-14. | MR 870989 | Zbl 0603.73056
[2] and , 1984, Une justification des équations de la thermoélasticité des poutres à section variable par des méthodes asymptotiques, RAIRO, Analyse Numérique, 18,347-376. | Numdam | MR 761673 | Zbl 0572.73053
[3] , and , 1989, Numerical analysis of junctions between plates, Comput. Methods Appl. Pech. Engrg., 74, 307-326. | MR 1020628 | Zbl 0687.73068
[4] and , 1989, Modeling and justification of eigenvalue problems for junctions between elastic structures, J. Funct. Anal., 87,392-427. | MR 1026860 | Zbl 0699.73010
[5] , 1990, Plates and Junctions in Elastic Multi-Structures. An Asymptotic Analysis RMA 14, Masson, Paris. | MR 1071376 | Zbl 0706.73046
[6] and , 1979, A justification of two-dimensional linear plate model, J. Mécanique, 18,315-344. | MR 533827 | Zbl 0415.73072
[7] and , 1981, Two-dimensional approximation of three-dimensional eigenvalue problems in plate theory, Comp, Meth. Appl. Mech. Eng., 26, 145-172. | MR 626720 | Zbl 0489.73057
[8] , and , 1989, Junctions between three-dimensional and two-dimensional linearly elastic structures, J. Math. Pures Appl., 68, 261-295. | MR 1025905 | Zbl 0661.73013
[9] , , and , 1988, Asymptotic theory and analysis for displacement and stress distributions in nonlinear elastic straight slender rods, J. Elasticity, 19, 111-161. | MR 937626 | Zbl 0653.73010
[10] , 1987, Sur l'analyse numérique de raccords de poutres et de plaques, Thèse de 3e cycle, Université Pierre et Marie Curie, 1987.
[11] , and , 1987, Stress distribution in anisotropic elastic composite beams, in: P.G. Ciarlet and E. Sanchez-Palencia, eds. Applications of Multiple Scalings in Mechanics, RMA 4, Masson, Paris, pp. 118-133. | MR 901992 | Zbl 0645.73029
[12] , 1993, Modélisation de la jonction entre une poutre et une plaque en élasticité linéarisée, RAIRO Analyse Numérique, 27, 77-105. | Numdam | MR 1204630 | Zbl 0767.73034
[13] , 1993, Modeling of the junction between a plate and a rod in nonlinear elasticity, Asymptotic Anal., 7, 179-194. | MR 1226973 | Zbl 0788.73040
[14] , 1993, Comportement asymptotique quand l'épaisseur tend vers zéro du problème de valeurs propres pour une poutre mince encastrée, en élasticité linéaire, C. R. Acad. Sci. Paris, t. 316, Série I, 755-758. | MR 1214429 | Zbl 0773.73047
[15] , 1995, Modélisation des vibrations d'une multi-structure forme de deux poutres, C. R. Acad. Sci. Paris, t. 321, Série I, 1641-1646. | MR 1367822 | Zbl 0842.73038
[16] , 1995, Étude de problèmes de jonctions de poutres en élasticité linéaire, Thèse de Doctorat, Université Pierre et Marie Curie.
[17] , 1990, Modeling of folded plate, Comput. Mech,, 5, 401-416. | Zbl 0741.73026
[18] , 1989, Folded plates revisited, Comput. Mech, 5, 345-365. | Zbl 0741.73025
[19] , 1989, Modelling of the junction between two rods, J. Math. Pures Appl., 68,365-397. | MR 1025910 | Zbl 0743.73020
[20] , 1990, Vibration of a folded plate, Modélisation Mathématique et Analyse Numérique, 24, 501-521. | Numdam | MR 1070967 | Zbl 0712.73044
[21] , 1994, Elastodynamics for multiplate structures, in: H. Brezis and J. L. Lions eds, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. XI, pp. 151-180. | MR 1268905 | Zbl 0801.73045
[22] , 1991, Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications, RMA 19, Masson, Paris. | MR 1130395 | Zbl 0744.73027
[23] , Modeling and junction of an eigenvalue problem for a plate inserted in a three-dimensional support, Modélisation Mathématique et Analyse Numérique, to appear. | Numdam | Zbl 0866.73031
[24] , 1992, Asymptotic modeling of the elastodynamics of a multistructure, Asymptotic Anal., 6, 73-108. | MR 1188078 | Zbl 0777.73033
[25] and , 1983, Introduction à l'analyse numérique des équations aux dérivées partielles, Masson, Paris. | MR 773854 | Zbl 0561.65069
[26] and , 1991, Couplage flexion-torsion-traction dans les poutres anisotropes à section hétérogène, C. R. Acad. Sci. Paris, t. 312, Série, 337-344. | MR 1108524 | Zbl 0736.73032
[27] and , 1987, Derivation of generalized models for linear elastic beams by asymptotic expansion methods, in: P. G. Ciarlet and E. Sanchez-Palencia, eds. Applications of multiple Scalings in Mechanics, RMA 4, Masson, Paris, pp. 302-315. | MR 902000 | Zbl 0646.73024
[28] and , 1988, A derivation of generalized Saint Venant's torsion theory from three dimensional elasticity by asymptotic expansion methods, Applicable Analysis, 31, 129-148. | MR 1017507 | Zbl 0637.73003
[29] and , 1990, A new approach of Timoshenko's beam theory by the asymptotic expansion method, Mathematical Modelling and Numerical Analysis, 24, 651-680. | Numdam | MR 1076964 | Zbl 0777.73028
[30] and , 1989, Existence and characterisation of higher order terms in an asymptotic expansion method for linearized elastic beams, Asymptotic Anal., 2, 223-255. | MR 1020349 | Zbl 0850.73126
[31] and , 1995, Mathematical Modeling of Rods, in: P. G. Ciarlet and J. L. Lions, eds, Handbook of Numerical Analysis, Vol. IV, North-Holland, Amsterdam, pp. 487-969. | MR 1422507 | Zbl 0873.73041