[Extension aux sections composites orthotropes de la théorie du gauchissement non uniforme des poutres]
Cette Note propose une extension aux sections composites de la théorie gérérale du gauchissement non uniforme récemment établie pour une poutre homogène isotrope et de section quelconque par El Fatmi (C. R. Mecanique 335 (2007) 467–474). Cette extension se restreint, dans la présente Note, aux sections symétriques à phases orthotropes, mais introduit aussi la prise en compte des effets Poisson dans la déformation des sections. Les résultats théoriques concernent le comportement généralisé de la poutre et l'expression 3D des contraintes ; celles-ci, comparées à celles de Saint Venant, montrent explicitement la contribution de chacun des nouveaux efforts intérieurs induits par la non uniformité des gauchissements et des effets Poisson. Comme première application, quelques résultats numériques obtenus pour la torsion et la flexion simple d'une poutre console de section sandwhich sont présentés.
This Note proposes an extension to composite section of the non-uniform (out-of-plane) warping beam theory recently established for homogeneous and isotropic beam by R. El Fatmi (C. R. Mecanique 335 (2007) 467–474). For the present work, which constitutes a first step of this extension, the cross-section is assumed to be symmetric and made by orthotropic materials; however, Poisson's effects (called here in-plane warping) are also taken into account. Closed form results are given for the structural behavior of the composite beam and for the expressions of the 3D stresses; these ones, easy to compare with 3D Saint Venant stresses, make clear the additional contribution of the new internal forces induced by the non-uniformity of the (in and out) warpings. As first numerical applications, results on torsion and shear-bending of a cantilever sandwich beam are presented.
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Mot clés : Solides et structures, Gauchissement, Effet de Poisson, Torsion, Effort tranchant, Saint Venant, Contrainte, Cisaillement
Nejib Ghazouani 1 ; Rached El Fatmi 1
@article{CRMECA_2010__338_12_704_0,
author = {Nejib Ghazouani and Rached El Fatmi},
title = {Extension of the non-uniform warping theory to an orthotropic composite beam},
journal = {Comptes Rendus. M\'ecanique},
pages = {704--711},
publisher = {Elsevier},
volume = {338},
number = {12},
year = {2010},
doi = {10.1016/j.crme.2010.09.002},
language = {en},
}
Nejib Ghazouani; Rached El Fatmi. Extension of the non-uniform warping theory to an orthotropic composite beam. Comptes Rendus. Mécanique, Volume 338 (2010) no. 12, pp. 704-711. doi : 10.1016/j.crme.2010.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.09.002/
[1] Interlaminar shear stresses in solid composite beams using a complete out of plane shear deformation model, Computers and Structures, Volume 66 (1998) no. 6, pp. 713-723
[2] A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams, International Journal of Solids and Structures, Volume 41 (2004), pp. 2521-2537
[3] Assessment of beam modeling methods for rotor blade applications, Mathematical and Computer Modelling, Volume 33 (2001), pp. 1099-1112
[4] On the structural behavior and the Saint Venant solution in the exact beam theory. Application to laminated composite beams, Computers and Structures, Volume 80 (2002), pp. 1441-1456
[5] Non-uniform warping theory for beams, C. R. Mecanique, Volume 335 (2007), pp. 467-474
[6] Non-uniform warping including the effects of torsion and shear forces. Part-II: Analytical and numerical applications, International Journal of Solids and Structures, Volume 44 (2007), pp. 5930-5952
[7] New concepts for linear beam theory with arbitrary geometry and loading, European Journal of Mechanics, Volume 17 (1998) no. 3, pp. 377-402
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