Modeling the vibrations of a multi-rod structure
Kerdid, N.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997), p. 891-925 / Harvested from Numdam
Publié le : 1997-01-01
@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] I. Aganovič and Z. Tutek, 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] A. Bermudez and J. M. Viaño, 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] M. Bernadou, S. Fayolle and F. Léné, 1989, Numerical analysis of junctions between plates, Comput. Methods Appl. Pech. Engrg., 74, 307-326. | MR 1020628 | Zbl 0687.73068

[4] F. Bourquin and P. G. Ciarelt, 1989, Modeling and justification of eigenvalue problems for junctions between elastic structures, J. Funct. Anal., 87,392-427. | MR 1026860 | Zbl 0699.73010

[5] P. G. Ciarlet, 1990, Plates and Junctions in Elastic Multi-Structures. An Asymptotic Analysis RMA 14, Masson, Paris. | MR 1071376 | Zbl 0706.73046

[6] P. G. Ciarlet and P. Destuynder, 1979, A justification of two-dimensional linear plate model, J. Mécanique, 18,315-344. | MR 533827 | Zbl 0415.73072

[7] P. G. Ciarlet and S. Kesavan, 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] P. G. Ciarlet, H. L E Dret and R. Nzengwa, 1989, Junctions between three-dimensional and two-dimensional linearly elastic structures, J. Math. Pures Appl., 68, 261-295. | MR 1025905 | Zbl 0661.73013

[9] A. Cimetière, G. Geymonat H. Le Dret, A. Raoult and Z. Tutek, 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] S. Fayolle, 1987, Sur l'analyse numérique de raccords de poutres et de plaques, Thèse de 3e cycle, Université Pierre et Marie Curie, 1987.

[11] G. Geymonat, F. Krasucki and J. J. Marigo, 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] I. Gruais, 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] I. Gruais, 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] N. Kerdid, 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] N. Kerdid, 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] N. Kerdid, 1995, Étude de problèmes de jonctions de poutres en élasticité linéaire, Thèse de Doctorat, Université Pierre et Marie Curie.

[17] H. Le Dret, 1990, Modeling of folded plate, Comput. Mech,, 5, 401-416. | Zbl 0741.73026

[18] H. Le Dret, 1989, Folded plates revisited, Comput. Mech, 5, 345-365. | Zbl 0741.73025

[19] H. Le Dret, 1989, Modelling of the junction between two rods, J. Math. Pures Appl., 68,365-397. | MR 1025910 | Zbl 0743.73020

[20] H. Le Dret, 1990, Vibration of a folded plate, Modélisation Mathématique et Analyse Numérique, 24, 501-521. | Numdam | MR 1070967 | Zbl 0712.73044

[21] H. Le Dret, 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] H. Le Dret, 1991, Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications, RMA 19, Masson, Paris. | MR 1130395 | Zbl 0744.73027

[23] V. Lods, 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] A. Raoult, 1992, Asymptotic modeling of the elastodynamics of a multistructure, Asymptotic Anal., 6, 73-108. | MR 1188078 | Zbl 0777.73033

[25] P. A. Raviart and J. M. Thomas, 1983, Introduction à l'analyse numérique des équations aux dérivées partielles, Masson, Paris. | MR 773854 | Zbl 0561.65069

[26] J. Sanchez-Hubert and E. Sanchez-Palencia, 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] L. Trabucho and J. M. Viaño, 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] L. Trabucho and J. M. Viano, 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] L. Trabucho and J. M. Viano, 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] L. Trabucho and J. M. Viano, 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] L. Trabucho and J. M. Viaño, 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