On étudie la Γ-limite de la théorie de l'élasticité non linéaire pour une coque mince à épaisseur variable autour d'une surface arbitraire de dimension 2.
We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.
Accepté le :
Publié le :
@article{CRMATH_2009__347_3-4_211_0, author = {Lewicka, Marta and Mora, Maria Giovanna and Pakzad, Mohammad Reza}, title = {A nonlinear theory for shells with slowly varying thickness}, journal = {Comptes Rendus. Math\'ematique}, pages = {211--216}, publisher = {Elsevier}, volume = {347}, number = {3-4}, year = {2009}, doi = {10.1016/j.crma.2008.12.017}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2008.12.017/} }
TY - JOUR AU - Lewicka, Marta AU - Mora, Maria Giovanna AU - Pakzad, Mohammad Reza TI - A nonlinear theory for shells with slowly varying thickness JO - Comptes Rendus. Mathématique PY - 2009 SP - 211 EP - 216 VL - 347 IS - 3-4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2008.12.017/ DO - 10.1016/j.crma.2008.12.017 LA - en ID - CRMATH_2009__347_3-4_211_0 ER -
%0 Journal Article %A Lewicka, Marta %A Mora, Maria Giovanna %A Pakzad, Mohammad Reza %T A nonlinear theory for shells with slowly varying thickness %J Comptes Rendus. Mathématique %D 2009 %P 211-216 %V 347 %N 3-4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2008.12.017/ %R 10.1016/j.crma.2008.12.017 %G en %F CRMATH_2009__347_3-4_211_0
Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza. A nonlinear theory for shells with slowly varying thickness. Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 211-216. doi : 10.1016/j.crma.2008.12.017. http://archive.numdam.org/articles/10.1016/j.crma.2008.12.017/
[1] Mathematical Elasticity, North-Holland, Amsterdam, 2000
[2] Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Γ-convergence, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 336 (2003) no. 8, pp. 697-702
[3] A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity, Comm. Pure Appl. Math., Volume 55 (2002), pp. 1461-1506
[4] A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, Arch. Ration. Mech. Anal., Volume 180 (2006) no. 2, pp. 183-236
[5] The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl., Volume 73 (1995), pp. 549-578
[6] The membrane shell model in nonlinear elasticity: a variational asymptotic derivation, J. Nonlinear Sci., Volume 6 (1996), pp. 59-84
[7] M. Lewicka, M.G. Mora, M.R. Pakzad, Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity, submitted for publication (2008), available at | arXiv
Cité par Sources :