Junction of a periodic family of elastic rods with a thin plate. Part II

AbstractIn this second paper, we consider again a set of elastic rods periodically distributed over an elastic plate whose thickness tends here to 0. This work is then devoted to describe the homogenization process for the junction of the rods and a thin plate. We use a technique based on two decompositions of the displacement field in each rod and in the plate. We obtain a priori estimates on each term of the two decompositions which permit to exhibit a few critical cases that distinguish the different possible limit behaviors. Then, we completely investigate one of these critical case which leads to a coupled bending–bending model for the rods and the 2d plate