Mathematical Problems in Mechanics
Nonlinear thin plate models for a family of Ogden materials
[Modèles non linéaires de plaques minces pour une famille de matériaux de type Ogden]
Comptes Rendus. Mathématique, Tome 337 (2003) no. 12, pp. 819-824.

Des modèles non linéaires bidimensionnels de plaques minces sont dérivés via une procédure asymptotique formelle mise au point par Pantz, pour une famille de matériaux de type Ogden proposée par Ciarlet et Geymonat (C. R. Acad. Sci. Paris, Ser. II 295 (4) (1982) 423–426). Ces matériaux sont plus réalistes que le Saint Venant–Kirchhoff. En conséquence, les modèles dérivés généralisent ceux obtenus pour ce matériau.

Nonlinear two-dimensional thin plate models are derived via a formal asymptotic procedure due to Pantz, for a family of Ogden materials proposed by Ciarlet and Geymonat (C. R. Acad. Sci. Paris, Ser. II 295 (4) (1982) 423–426). These materials are more realistic than the Saint Venant–Kirchhoff material. As a consequence, the derived models generalize those obtained for this material.

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DOI : 10.1016/j.crma.2003.10.029
Trabelsi, Karim 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France
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Trabelsi, Karim. Nonlinear thin plate models for a family of Ogden materials. Comptes Rendus. Mathématique, Tome 337 (2003) no. 12, pp. 819-824. doi : 10.1016/j.crma.2003.10.029. http://www.numdam.org/articles/10.1016/j.crma.2003.10.029/

[1] Ball, J.M. Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., Volume 63 (1976) no. 4, pp. 337-403

[2] Ben Belgacem, H. Relaxation of singular functionals defined on Sobolev spaces, ESAIM Control Optim. Calc. Var., Volume 5 (2000), pp. 71-85

[3] Ciarlet, P.G. Mathematical Elasticity, Vol. I. Three-Dimensional Elasticity, Stud. Math. Appl., 20, North-Holland, Amsterdam, 1988

[4] Ciarlet, P.G. Mathematical Elasticity, Vol. III. Theory of Shells, Stud. Math. Appl., 29, North-Holland, Amsterdam, 2000

[5] Ciarlet, P.; Coutand, D. An existence theorem for nonlinearly elastic “flexural” shells, J. Elasticity, Volume 50 (1998) no. 3, pp. 261-277

[6] Ciarlet, P.G.; Geymonat, G. Sur les lois de comportement en élasticité non linéaire compressible, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, Volume 295 (1982) no. 4, pp. 423-426

[7] Coutand, D. Existence d'un minimiseur pour le modèle proprement invariant de plaque en flexion non linéairement élastique, C. R. Acad. Sci. Paris, Sér. I, Volume 324 (1997) no. 2, pp. 245-248

[8] Fox, D.D.; Raoult, A.; Simo, J.C. A justification of nonlinear properly invariant plate theories, Arch. Rational Mech. Anal., Volume 124 (1993) no. 2, pp. 157-199

[9] Le Dret, H.; Raoult, A. The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl. (9), Volume 74 (1995) no. 6, pp. 549-578

[10] O. Pantz, Quelques problèmes de modélisation en élasticité non linéaire, Doctoral Dissertation, Université Pierre et Marie Curie, 2001, Paris

[11] K. Trabelsi, Nonlinear thin plate models for a family of Ogden materials, preprint

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