We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter ε tends to zero. The cylinder is assumed to be fixed (homogeneous Dirichlet boundary condition) on the whole of one of its extremities, but only on a small part (of size εrε) of the second one; the Neumann boundary condition is imposed on the remainder of the boundary. We show that the result depends on rε, and that there are 3 critical sizes, namely , and rε=ε1/3, and in total 7 different regimes. We also prove a corrector result for each behavior of rε.
Nous étudions le comportement asymptotique de la solution d'un problème d'élasticité linéaire anisotrope et hétérogène dans un cylindre dont le diamètre ε tend vers zéro. Le cylindre est fixé (condition de Dirichlet homogène) sur la totalité de l'une de ses extrémités, mais seulement sur une petite partie (de taille εrε) de l'autre base ; sur le reste de la frontière on a la condition de Neumann. Nous montrons que le résultat depend de rε, et qu'il existe 3 tailles critiques, à savoir et rε=ε1/3, et au total 7 comportements différents. Nous donnons un résultat de correcteur pour tous les comportements de rε.
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Juan Casado-Díaz 1; Manuel Luna-Laynez 1; François Murat 2
@article{CRMATH_2004__338_12_975_0, author = {Juan Casado-D{\'\i}az and Manuel Luna-Laynez and Fran\c{c}ois Murat}, title = {Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities}, journal = {Comptes Rendus. Math\'ematique}, pages = {975--980}, publisher = {Elsevier}, volume = {338}, number = {12}, year = {2004}, doi = {10.1016/j.crma.2004.02.020}, language = {en}, }
TY - JOUR AU - Juan Casado-Díaz AU - Manuel Luna-Laynez AU - François Murat TI - Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities JO - Comptes Rendus. Mathématique PY - 2004 SP - 975 EP - 980 VL - 338 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2004.02.020 LA - en ID - CRMATH_2004__338_12_975_0 ER -
%0 Journal Article %A Juan Casado-Díaz %A Manuel Luna-Laynez %A François Murat %T Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities %J Comptes Rendus. Mathématique %D 2004 %P 975-980 %V 338 %N 12 %I Elsevier %R 10.1016/j.crma.2004.02.020 %G en %F CRMATH_2004__338_12_975_0
Juan Casado-Díaz; Manuel Luna-Laynez; François Murat. Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 975-980. doi : 10.1016/j.crma.2004.02.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.02.020/
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