Comptes Rendus
no. 8
Mathematical Problems in Mechanics/Calculus of Variations
Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence
[Dérivation de la théorie non linéaire des coques en flexion à partir de l'élasticité non linéaire tridimensionelle par Gamma-convergence]

Présenté par : J.M. Ball

Gero Friesecke1 ; Richard D. James2 ; Maria Giovanna Mora3 ; Stefan Müller3
1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
2 Department of Aerospace Engineering and Mechanics, 107 Akerman Hall, University of Minnesota, Minneapolis, MN 55455, USA
3 Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103 Leipzig, Germany
Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 697-702.

Nous montrons que la théorie non linéaire des coques en flexion émerge comme Γ-limite de la théorie de l'élasticité tridimensionelle.

We show that the nonlinear bending theory of shells arises as a Γ-limit of three-dimensional nonlinear elasticity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00028-1
Gero Friesecke 1 ; Richard D. James 2 ; Maria Giovanna Mora 3 ; Stefan Müller 3

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
2 Department of Aerospace Engineering and Mechanics, 107 Akerman Hall, University of Minnesota, Minneapolis, MN 55455, USA
3 Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103 Leipzig, Germany 
@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] E. Acerbi; G. Buttazzo; D. Percivale A variational definition for the strain energy of an elastic string, J. Elasticity, Volume 25 (1991), pp. 137-148

[2] S.S. Antman Nonlinear Problems of Elasticity, Springer, New York, 1995

[3] P.G. Ciarlet Mathematical Elasticity, Vols. II and III, Elsevier, 1997 (2000)

[4] D.D. Fox; A. Raoult; J.C. Simo A justification of properly invariant plate theories, Arch. Rational Mech. Anal., Volume 124 (1993), pp. 157-199

[5] G. Friesecke; R.D. James; S. Müller Rigorous derivation of nonlinear plate theory and geometric rigidity, C. R. Acad. Sci. Paris, Sér. I, Volume 334 (2002), pp. 173-178

[6] G. Friesecke; R.D. James; S. Müller 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] F. John Rotation and strain, Comm. Pure Appl. Math., Volume 14 (1961), pp. 391-413

[8] G. Kirchhoff Über das Gleichgewicht und die Bewegung einer elastischen Scheibe, J. Reine Angew. Math., Volume 40 (1850), pp. 51-88

[9] H. LeDret; A. Raoult 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] H. LeDret; A. Raoult The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl., Volume 73 (1995), pp. 549-578

[11] H. LeDret; A. Raoult The membrane shell model in nonlinear elasticity: a variational asymptotic derivation, J. Nonlinear Sci., Volume 6 (1996), pp. 59-84

[12] O. Pantz 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

Ces articles pourraient vous intéresser

The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity

Gero Friesecke; Richard D. James; Stefan Müller

C. R. Math (2002)

Rigorous derivation of nonlinear plate theory and geometric rigidity

Gero Friesecke; Stefan Müller; Richard D. James

C. R. Math (2002)

Derivation of a plate theory for incompressible materials

Sergio Conti; Georg Dolzmann

C. R. Math (2007)