Mathematical problems in mechanics
A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1241-1247.

We propose a new nonlinear shell model of Koiter's type, i.e. one that combines membrane and flexural strains, which can be used in the case where the middle surface of the undeformed shell is “almost spherical”, in the sense that its Gaussian curvature Kε and mean curvature Hε satisfy Kε=Hε2+O(ε2), where 2ε denotes the thickness of the shell.

Nous proposons un nouveau modèle non linéaire de coques du type de Koiter, c'est-à-dire combinant les déformations membranaires et en flexion, qui peut être utilisé lorsque la surface moyenne de la coque non déformée est « presque sphérique », au sens que sa courbure gaussiene Kε et sa courbure moyenne Hε satisfont Kε=Hε2+O(ε2), où 2ε désigne l'épaisseur de la coque.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.011
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, 4, place Jussieu, 75005 Paris, France
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Ciarlet, Philippe G.; Mardare, Cristinel. A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1241-1247. doi : 10.1016/j.crma.2016.10.011. http://www.numdam.org/articles/10.1016/j.crma.2016.10.011/

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[2] Ciarlet, P.G. Mathematical Elasticity, Volume III: Theory of Shells, North-Holland, Amsterdam, 2000

[3] Ciarlet, P.G. An Introduction to Differential Geometry with Applications to Elasticity, Springer, Dordrecht, The Netherlands, 2005

[4] P.G. Ciarlet, C. Mardare, A well-posed nonlinear model of Koiter's type for elliptic shells, in preparation.

[5] Ciarlet, P.G.; Miara, B. Justification of the two-dimensional equations of a linearly elastic shallow shell, Commun. Pure Appl. Math., Volume 45 (1992), pp. 327-360

[6] Klingenberg, W. A Course in Differential Geometry, Springer, Berlin, 1978

[7] Koiter, W.T. On the nonlinear theory of thin elastic shells, Proc. K. Ned. Akad. Wet. B, Volume 69 (1966), pp. 1-54

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