[Décomposition des déformations des coques – Comportement asymptotique du tenseur des déformations de Green–St Venant]
Dans cette Note nous présentons une nouvelle méthode, basée sur une décomposition des déformations, pour l'étude des coques minces. En particulier, nous donnons le comportement asymptotique du tenseur de Green–St Venant.
This Note deals with a new method, based on a decomposition of the deformations, to study thin shells. In particular, we give the asymptotic behavior of the Green–St Venant's strain tensor.
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@article{CRMATH_2009__347_17-18_1099_0,
author = {Dominique Blanchard and Georges Griso},
title = {Decomposition of shell deformations {\textendash} {Asymptotic} behavior of the {Green{\textendash}St} {Venant} strain tensor},
journal = {Comptes Rendus. Math\'ematique},
pages = {1099--1103},
publisher = {Elsevier},
volume = {347},
number = {17-18},
year = {2009},
doi = {10.1016/j.crma.2009.06.018},
language = {en},
}
TY - JOUR AU - Dominique Blanchard AU - Georges Griso TI - Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor JO - Comptes Rendus. Mathématique PY - 2009 SP - 1099 EP - 1103 VL - 347 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2009.06.018 LA - en ID - CRMATH_2009__347_17-18_1099_0 ER -
%0 Journal Article %A Dominique Blanchard %A Georges Griso %T Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor %J Comptes Rendus. Mathématique %D 2009 %P 1099-1103 %V 347 %N 17-18 %I Elsevier %R 10.1016/j.crma.2009.06.018 %G en %F CRMATH_2009__347_17-18_1099_0
Dominique Blanchard; Georges Griso. Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1099-1103. doi : 10.1016/j.crma.2009.06.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.018/
[1] Decomposition of deformations of thin rods. Application to nonlinear elasticity, Anal. Appl., Volume 7 (2009) no. 1, pp. 21-71
[2] Mathematical Elasticity, Theory of Shells, vol. III, North-Holland, Amsterdam, 2000
[3] A nonlinear Korn inequality on a surface, J. Math. Pures Appl., Volume 85 (2006), pp. 2-16
[4] An introduction to shell theory (P.G. Ciarlet; T.T. Li, eds.), Differential Geometry: Theory and Applications, World Scientific, Singapore, 2008, pp. 94-184
[5] A theorem on geometric rigidity and the derivation of nonlinear plate theory from the three-dimensional elasticity, Comm. Pure Appl. Math., Volume LV (2002), pp. 1461-1506
[6] A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, Arch. Rational Mech. Anal., Volume 130 (2006), pp. 183-236
[7] Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma convergence, C. R. Acad. Sci. Paris, Ser. I, Volume 336 (2003), pp. 697-702
[8] Decomposition of displacements of thin structures, J. Math. Pures Appl., Volume 89 (2008), pp. 199-233
[9] Asymptotic behavior of structures made of plates, Anal. Appl., Volume 3 (2005) no. 4, pp. 325-356
[10] On the justification of the nonlinear inextensional plate model, Arch. Rational Mech. Anal., Volume 167 (2003) no. 3, pp. 179-209
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