On considère le modèle de coque non linéairement élastique « peu profonde » proposé par L.H. Donnell, V.Z. Vlasov, K.M. Mushtari & K.Z. Galimov et W.T. Koiter. On montre que les champs de tenseurs, linéarisés de changement de courbure et non linéaire des déformations, apparaissant dans l'énergie de ce modèle peuvent être pris comme les seules inconnues du problème, au lieu du champ des déplacements comme à l'accoutumée. Afin de justifier cette « approche intrinsèque » de ce modèle non linéaire de coques, on identifie des conditions de compatibilité non linéaires que ces nouvelles inconnues doivent satisfaire. Ces conditions sont du type de Donati, au sens qu'elles se présentent sous la forme de relations intégrales d'orthogonalité à des champs de tenseurs à divergence nulle.
We consider the model of a nonlinearly elastic “shallow” shell proposed by L.H. Donnell, V.Z. Vlasov, K.M. Mushtari & K.Z. Galimov, and W.T. Koiter. We show that the linearized change of curvature and nonlinear strain tensor fields appearing in the energy of this model can be taken as the sole unknowns of the problem, instead of the displacement field as is customary. In order to justify this “intrinsic approach” to this nonlinear model, we identify nonlinear compatibility conditions that these new unknowns must satisfy. These conditions are of Donati type, in the sense that they take the form of integral orthogonality relations against divergence-free tensor fields.
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Philippe G. Ciarlet 1 ; Oana Iosifescu 2
@article{CRMATH_2017__355_2_232_0,
author = {Philippe G. Ciarlet and Oana Iosifescu},
title = {Une approche intrins\`eque d'un mod\`ele non lin\'eaire de la th\'eorie des coques},
journal = {Comptes Rendus. Math\'ematique},
pages = {232--242},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2017.01.001},
language = {fr},
}
TY - JOUR AU - Philippe G. Ciarlet AU - Oana Iosifescu TI - Une approche intrinsèque d'un modèle non linéaire de la théorie des coques JO - Comptes Rendus. Mathématique PY - 2017 SP - 232 EP - 242 VL - 355 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2017.01.001 LA - fr ID - CRMATH_2017__355_2_232_0 ER -
Philippe G. Ciarlet; Oana Iosifescu. Une approche intrinsèque d'un modèle non linéaire de la théorie des coques. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 232-242. doi : 10.1016/j.crma.2017.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.001/
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