[Modélisation des structures-poutres en élasticité non linéaire]
Cette Note traite de la modélisation d'une structure formée de poutres droites élastiques. Nous montrons, après une normalisation convenable, que l'infimum de l'énergie élastique totale tend vers le minimum d'une fonctionnelle qui dépend de champs définis sur les axes des poutres.
This Note deals with the modeling of a structure made of straight elastic rods whose thickness tends to 0. We show that, upon an adequate scaling, the infimum of the total elastic energy tends to the minimum of a functional which depends on fields defined on the centerlines of the rods.
Accepté le :
Publié le :
Dominique Blanchard 1 ; Georges Griso 2
@article{CRMATH_2010__348_19-20_1137_0, author = {Dominique Blanchard and Georges Griso}, title = {Modeling of rod-structures in nonlinear elasticity}, journal = {Comptes Rendus. Math\'ematique}, pages = {1137--1141}, publisher = {Elsevier}, volume = {348}, number = {19-20}, year = {2010}, doi = {10.1016/j.crma.2010.09.008}, language = {en}, }
Dominique Blanchard; Georges Griso. Modeling of rod-structures in nonlinear elasticity. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1137-1141. doi : 10.1016/j.crma.2010.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.008/
[1] Decomposition of deformations of thin rods. Application to nonlinear elasticity, Anal. Appl., Volume 7 (2009) no. 1, pp. 21-71
[2] Mathematical Elasticity, vol. I, North-Holland, Amsterdam, 1988
[3] Continuity of a deformation in as a function of its Cauchy–Green tensor in , J. Nonlinear Sci., Volume 14 (2004), pp. 415-427
[4] Asymptotic behavior of rods by the unfolding method, Math. Meth. Appl. Sci., Volume 27 (2004), pp. 2081-2110
[5] Decomposition of displacements of thin structures, J. Math. Pures Appl., Volume 89 (2008), pp. 199-233
[6] Asymptotic behavior of structures made of curved rods, Anal. Appl., Volume 6 (2008) no. 1, pp. 11-22
[7] Modeling of the junction between two rods, J. Math. Pures Appl., Volume 68 (1989), pp. 365-397
[8] A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 21 (2004) no. 3, pp. 271-293
Cité par Sources :
Commentaires - Politique