Modeling the vibrations of a multi-rod structure
- Volume: 31, Issue: 7, page 891-925
- ISSN: 0764-583X
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topKerdid, N.. "Modeling the vibrations of a multi-rod structure." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 31.7 (1997): 891-925. <http://eudml.org/doc/193860>.
@article{Kerdid1997,
author = {Kerdid, N.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {convergence; eigenvalues; eigenfunctions; three-dimensional linearized elasticity},
language = {eng},
number = {7},
pages = {891-925},
publisher = {Dunod},
title = {Modeling the vibrations of a multi-rod structure},
url = {http://eudml.org/doc/193860},
volume = {31},
year = {1997},
}
TY - JOUR
AU - Kerdid, N.
TI - Modeling the vibrations of a multi-rod structure
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 7
SP - 891
EP - 925
LA - eng
KW - convergence; eigenvalues; eigenfunctions; three-dimensional linearized elasticity
UR - http://eudml.org/doc/193860
ER -
References
top- [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. Zbl0603.73056MR870989
- [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. Zbl0572.73053MR761673
- [3] M. BERNADOU, S. FAYOLLE and F. LÉNÉ, 1989, Numerical analysis of junctions between plates, Comput. Methods Appl. Pech. Engrg., 74, 307-326. Zbl0687.73068MR1020628
- [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. Zbl0699.73010MR1026860
- [5] P. G. CIARLET, 1990, Plates and Junctions in Elastic Multi-Structures. An Asymptotic Analysis RMA 14, Masson, Paris. Zbl0706.73046MR1071376
- [6] P. G. CIARLET and P. DESTUYNDER, 1979, A justification of two-dimensional linear plate model, J. Mécanique, 18,315-344. Zbl0415.73072MR533827
- [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. Zbl0489.73057MR626720
- [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. Zbl0661.73013MR1025905
- [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. Zbl0653.73010MR937626
- [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. Zbl0645.73029MR901992
- [12] I. GRUAIS, 1993, Modélisation de la jonction entre une poutre et une plaque en élasticité linéarisée, RAIRO Analyse Numérique, 27, 77-105. Zbl0767.73034MR1204630
- [13] I. GRUAIS, 1993, Modeling of the junction between a plate and a rod in nonlinear elasticity, Asymptotic Anal., 7, 179-194. Zbl0788.73040MR1226973
- [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. Zbl0773.73047MR1214429
- [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. Zbl0842.73038MR1367822
- [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. Zbl0741.73026
- [18] H. LE DRET, 1989, Folded plates revisited, Comput. Mech, 5, 345-365. Zbl0741.73025
- [19] H. LE DRET, 1989, Modelling of the junction between two rods, J. Math. Pures Appl., 68,365-397. Zbl0743.73020MR1025910
- [20] H. LE DRET, 1990, Vibration of a folded plate, Modélisation Mathématique et Analyse Numérique, 24, 501-521. Zbl0712.73044MR1070967
- [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. Zbl0801.73045MR1268905
- [22] H. LE DRET, 1991, Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications, RMA 19, Masson, Paris. Zbl0744.73027MR1130395
- [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. Zbl0866.73031
- [24] A. RAOULT, 1992, Asymptotic modeling of the elastodynamics of a multistructure, Asymptotic Anal., 6, 73-108. Zbl0777.73033MR1188078
- [25] P. A. RAVIART and J. M. THOMAS, 1983, Introduction à l'analyse numérique des équations aux dérivées partielles, Masson, Paris. Zbl0561.65069MR773854
- [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. Zbl0736.73032MR1108524
- [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. Zbl0646.73024MR902000
- [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. Zbl0637.73003MR1017507
- [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. Zbl0777.73028MR1076964
- [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. Zbl0850.73126MR1020349
- [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. Zbl0873.73041MR1422507
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