Microscopic effects in the homogenization of the junction of rods and a thin plate

Article type: Research Article

Authors: Blanchard, Dominique^{; ;} | Griso, Georges

Affiliations: Université de Rouen, UMR 6085, F-76821 Mont Saint Aignan Cédex, France. E-mail: blanchard@ann.jussieu.fr | Laboratoire d'Analyse Numérique, Université P. et M. Curie, Case Courrier 187, 75252 Paris Cédex 05, France. E-mail: georges.griso@wanadoo.fr

Note: [] Corresponding author.

Abstract: This paper is devoted to investigate a few microscopic effects in the homogenization process of the junction of a periodic family of rods with a thin plate in elasticity. We focus on the case where the thickness of the plate tends to zero faster than the periodicity. As a consequence of the studied microscopic effects, the elastic coefficients of the membrane and bending limit problems for the plate are modified. Moreover, we observe a torsion in the homogenized “continuum” of rods which depends on the curl of the membrane displacement of the plate.

Keywords: linear elasticity, rods, plates, rough boundary, homogenization

Journal: Asymptotic Analysis, vol. 56, no. 1, pp. 1-36, 2008