[Dérivation de la théorie non linéaire des coques en flexion à partir de l'élasticité non linéaire tridimensionelle par Gamma-convergence]
We show that the nonlinear bending theory of shells arises as a Γ-limit of three-dimensional nonlinear elasticity.
Nous montrons que la théorie non linéaire des coques en flexion émerge comme Γ-limite de la théorie de l'élasticité tridimensionelle.
Accepté le :
Publié le :
Gero Friesecke 1 ; Richard D. James 2 ; Maria Giovanna Mora 3 ; Stefan Müller 3
@article{CRMATH_2003__336_8_697_0,
author = {Gero Friesecke and Richard D. James and Maria Giovanna Mora and Stefan M\"uller},
title = {Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by {Gamma-convergence}},
journal = {Comptes Rendus. Math\'ematique},
pages = {697--702},
publisher = {Elsevier},
volume = {336},
number = {8},
year = {2003},
doi = {10.1016/S1631-073X(03)00028-1},
language = {en},
}
TY - JOUR AU - Gero Friesecke AU - Richard D. James AU - Maria Giovanna Mora AU - Stefan Müller TI - Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence JO - Comptes Rendus. Mathématique PY - 2003 SP - 697 EP - 702 VL - 336 IS - 8 PB - Elsevier DO - 10.1016/S1631-073X(03)00028-1 LA - en ID - CRMATH_2003__336_8_697_0 ER -
%0 Journal Article %A Gero Friesecke %A Richard D. James %A Maria Giovanna Mora %A Stefan Müller %T Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence %J Comptes Rendus. Mathématique %D 2003 %P 697-702 %V 336 %N 8 %I Elsevier %R 10.1016/S1631-073X(03)00028-1 %G en %F CRMATH_2003__336_8_697_0
Gero Friesecke; Richard D. James; Maria Giovanna Mora; Stefan Müller. Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 697-702. doi : 10.1016/S1631-073X(03)00028-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00028-1/
[1] A variational definition for the strain energy of an elastic string, J. Elasticity, Volume 25 (1991), pp. 137-148
[2] Nonlinear Problems of Elasticity, Springer, New York, 1995
[3] Mathematical Elasticity, Vols. II and III, Elsevier, 1997 (2000)
[4] A justification of properly invariant plate theories, Arch. Rational Mech. Anal., Volume 124 (1993), pp. 157-199
[5] Rigorous derivation of nonlinear plate theory and geometric rigidity, C. R. Acad. Sci. Paris, Sér. I, Volume 334 (2002), pp. 173-178
[6] 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
[7] Rotation and strain, Comm. Pure Appl. Math., Volume 14 (1961), pp. 391-413
[8] Über das Gleichgewicht und die Bewegung einer elastischen Scheibe, J. Reine Angew. Math., Volume 40 (1850), pp. 51-88
[9] Le modèle de membrane non linéaire comme limite variationelle de l'élasticité non linéaire tridimensionelle, C. R. Acad. Sci. Paris Sér. I, Volume 317 (1993), pp. 221-226
[10] The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl., Volume 73 (1995), pp. 549-578
[11] The membrane shell model in nonlinear elasticity: a variational asymptotic derivation, J. Nonlinear Sci., Volume 6 (1996), pp. 59-84
[12] Une justification partielle du modèle de plaque en flexion par Γ-convergence, C. R. Acad. Sci. Paris, Sér. I, Volume 332 (2001), pp. 587-592
Cité par Sources :
Commentaires - Politique