Mathematical problems in mechanics/Differential geometry
A nonlinear shell model of Koiter's type
Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 227-234.

We define a new two-dimensional nonlinear shell model “of Koiter's type” that can be used for the modeling of any type of shell and boundary conditions and for which we establish an existence theorem. The model uses a specific three-dimensional stored energy function of Ogden's type that satisfies all the assumptions of John Ball's fundamental existence theorem in three-dimensional nonlinear elasticity and that is adapted here to the modeling of thin nonlinearly elastic shells by means of specific deformations that are quadratic with respect to the transverse variable.

Nous définissons un nouveau modèle bidimensionnel non linéaire de coques « de type Koiter » qui peut être utilisé pour la modélisation de tout type de coque et de conditions aux limites et pour lequel nous établissons un théorème d'existence. Ce modèle utilise une densité d'énergie de type Ogden satisfaisant toutes les hypothèses du théorème d'existence fondamental de John Ball en élasticité tridimensionnelle non linéaire et qui est adaptée ici à la modélisation des coques non linéairement élastiques minces au moyen de déformations particulières, qui sont quadratiques en la variable transverse.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.12.005
Ciarlet, Philippe G. 1; Mardare, Cristinel 2

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 Sorbonne Universités, Université Pierre-et-Marie-Curie, Laboratoire Jacques-Louis-Lions, Paris, France
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Ciarlet, Philippe G.; Mardare, Cristinel. A nonlinear shell model of Koiter's type. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 227-234. doi : 10.1016/j.crma.2017.12.005. http://www.numdam.org/articles/10.1016/j.crma.2017.12.005/

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