[Une théorie de gauchissement non uniforme]
Cette Note propose une théorie de gauchissement non uniforme prenant en compte les effets de la torsion et des efforts tranchants. Basée sur un modéle cinématique utilisant trois paramètres de gauchissement associés aux trois fonctions de gauchissement de torsion et d'efforts tranchants de St Venant, cette théorie, qui s'affranchit naturellement des hypothèses classiques sur les gauchissements ou les cisaillements, est valable pour toute section homogène élastique et isotrope. La comparaison aux résultats de St Venant permet aussitôt de dégager les effets induits par la non-uniformité du gauchissement. En particulier, cette théorie permet de préciser la contribution de chacun des efforts intérieurs ainsi que l'effet de la non-symétrie de la section sur le comportement global de la poutre.
This Note proposes a non-uniform warping beam theory including the effects of torsion and shear forces. Based on a displacement model using three warping parameters associated to three St Venant warping functions corresponding to torsion and shear forces, this theory is free from the classical assumptions on the warpings or on the shears, and is valid for any kind of homogeneous elastic and isotropic cross-section. The result on the structural behavior of the beam specifies the effect of the non-symmetry of the cross-section, and the closed form results obtained for the stresses show the contribution of each internal force. Comparison with St Venant beam theory highlights the additional effects due to the non-uniformity of the warping.
Accepté le :
Publié le :
Mot clés : Mécanique des solides numérique, Gauchissement, Torsion, Effort tranchant, St Venant, Couplage, Contrainte axiale, Cisaillement
@article{CRMECA_2007__335_8_467_0,
author = {Rached El Fatmi},
title = {A non-uniform warping theory for beams},
journal = {Comptes Rendus. M\'ecanique},
pages = {467--474},
publisher = {Elsevier},
volume = {335},
number = {8},
year = {2007},
doi = {10.1016/j.crme.2007.05.025},
language = {en},
}
Rached El Fatmi. A non-uniform warping theory for beams. Comptes Rendus. Mécanique, Volume 335 (2007) no. 8, pp. 467-474. doi : 10.1016/j.crme.2007.05.025. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.025/
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Commentaires - Politique
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