[Modèles bidimensionnels non linéaires pour les plaques hétérogènes]
On considère une étude asymptotique formelle de plaques avec des hétérogénéités variant périodiquement. L'analyse asymptotique est faite lorsque la période de variation des propriétés du matériau de la plaque sont du même ordres de grandeur. On considère une plaque faite de matériaux de Ciarlet–Geymonat (P.G. Ciarlet et G. Geymonat (1982)). En fonction de l'ordre de grandeur des charges appliquées, on obtient un modèle non linéaire membranaire et un modèle non linéaire membranaire flexion-inextensionnelle comme annoncé par E. Pruchnicki (2006). Notre approche est basée sur une suite récursive de problèmes de minimisation.
We consider a formal asymptotic study of plates with periodically rapidly varying heterogeneities. The asymptotic analysis is performed when both the period of change of the material properties and the thickness of the plate are of the same orders of magnitude. We consider a plate made of Ciarlet–Geymonat type materials (P.G. Ciarlet and G. Geymonat (1982)). Depending on the order of magnitude of the applied loads, we obtain a nonlinear membrane model and a nonlinear membrane inextensional-bending model as announced in E. Pruchnicki (2006). Our approach is based on a sequence of recursive minimization problems.
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Mot clés : Développements asymptotiques, Plaques, Élasticité non linéaire, Méthodes variationnelles, Homogénéisation
Erick Pruchnicki 1
@article{CRMECA_2009__337_5_297_0,
author = {Erick Pruchnicki},
title = {Two-dimensional nonlinear models for heterogeneous plates},
journal = {Comptes Rendus. M\'ecanique},
pages = {297--302},
publisher = {Elsevier},
volume = {337},
number = {5},
year = {2009},
doi = {10.1016/j.crme.2009.06.018},
language = {en},
}
Erick Pruchnicki. Two-dimensional nonlinear models for heterogeneous plates. Comptes Rendus. Mécanique, Volume 337 (2009) no. 5, pp. 297-302. doi : 10.1016/j.crme.2009.06.018. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.06.018/
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