A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell

Philippe G. Ciarlet; Cristinel Mardare

doi:10.1016/j.crma.2016.10.011

Mathematical problems in mechanics

A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell

Presented by: Philippe G. Ciarlet

Philippe G. Ciarlet ¹; Cristinel Mardare 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

Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1241-1247.

Abstract
Résumé

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 $K_{ε}$ and mean curvature $H_{ε}$ satisfy $K_{ε} = H_{ε}^{2} + O (ε^{2})$ , 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 $K_{ε}$ et sa courbure moyenne $H_{ε}$ satisfont $K_{ε} = H_{ε}^{2} + O (ε^{2})$ , où 2ε désigne l'épaisseur de la coque.

Received: 2016-10-14
Accepted: 2016-10-14
Published online: 2016-10-31

DOI: 10.1016/j.crma.2016.10.011

Author's affiliations:

Philippe G. Ciarlet ¹; Cristinel Mardare 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

@article{CRMATH_2016__354_12_1241_0,
     author = {Philippe G. Ciarlet and Cristinel Mardare},
     title = {A mathematical model of {Koiter's} type for a nonlinearly elastic {\textquotedblleft}almost spherical{\textquotedblright} shell},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1241--1247},
     publisher = {Elsevier},
     volume = {354},
     number = {12},
     year = {2016},
     doi = {10.1016/j.crma.2016.10.011},
     language = {en},
}

TY  - JOUR
AU  - Philippe G. Ciarlet
AU  - Cristinel Mardare
TI  - A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 1241
EP  - 1247
VL  - 354
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crma.2016.10.011
LA  - en
ID  - CRMATH_2016__354_12_1241_0
ER  -

%0 Journal Article
%A Philippe G. Ciarlet
%A Cristinel Mardare
%T A mathematical model of Koiter's type for a nonlinearly elastic “almost spherical” shell
%J Comptes Rendus. Mathématique
%D 2016
%P 1241-1247
%V 354
%N 12
%I Elsevier
%R 10.1016/j.crma.2016.10.011
%G en
%F CRMATH_2016__354_12_1241_0

Philippe G. Ciarlet; Cristinel Mardare. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.011/

References
Cited by

[1] R. Bunoiu; P.G. Ciarlet; C. Mardare Existence theorem for a nonlinear elliptic shell model, J. Elliptic Parabolic Eqs., Volume 1 (2015), pp. 31-48

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

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

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

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

Cited by Sources:

Comments - Policy