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

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.