[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/
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- Nonlinearly elastic membrane model for heterogeneous shells by using a new double scale variational formulation: A formal asymptotic approach, Journal of Elasticity, Volume 84 (2006) no. 3, pp. 245-280 | DOI:10.1007/s10659-006-9066-0 | Zbl:1100.74043
- Nonlinear partial differential equations of fourth order under mixed boundary conditions, Mathematische Zeitschrift, Volume 254 (2006) no. 1, pp. 33-54 | DOI:10.1007/s00209-005-0917-3 | Zbl:1220.35071
- A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models, Multiscale Modeling Simulation, Volume 5 (2006) no. 2, p. 664 | DOI:10.1137/050646251
- Some remarks on the asymptotic invertibility of the linearized operator of nonlinear elasticity in the context of the displacement approach, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, Volume 86 (2006) no. 5, pp. 400-409 | DOI:10.1002/zamm.200510249 | Zbl:1097.35011
- Nonlinearly elastic thin plate models for a class of Ogden materials. II: The bending model, Analysis and Applications (Singapore), Volume 3 (2005) no. 3, pp. 271-283 | DOI:10.1142/s0219530505000571 | Zbl:1236.74022
- Geometric rigidity of conformal matrices, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, Volume 4 (2005) no. 4, pp. 557-585 | Zbl:1170.30308
- An introduction to differential geometry with applications to elasticity, Journal of Elasticity, Volume 78-79 (2005) no. 1-3, pp. 3-201 | DOI:10.1007/s10659-005-4738-8 | Zbl:1086.74001
- Second-order analysis for thin structures, Nonlinear Analysis: Theory, Methods Applications, Volume 56 (2004) no. 5, p. 679 | DOI:10.1016/j.na.2003.10.007
- The continuity of a surface as a function of its two fundamental forms., Journal de Mathématiques Pures et Appliquées. Neuvième Série, Volume 82 (2003) no. 3, pp. 253-274 | DOI:10.1016/s0021-7824(03)00017-5 | Zbl:1042.53003
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Communications on Pure and Applied Mathematics, Volume 55 (2002) no. 11, pp. 1461-1506 | DOI:10.1002/cpa.10048 | Zbl:1021.74024
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