Reinforcement of a thin plate by a thin layer

We study the bending of a thin plate, stiffened with a thin elastic layer, of thickness (delta). We describe the complete construction of an asymptotic expansion with respect to (delta)of the solution of the Kirchhoff-Love model and give optimal estimates for the remainder. We identify approximate boundary conditions, which take into account the effect of the stiffener at various orders. Thanks to the tools of multi-scale analysis, we give optimal estimates for the error between the approximate problems and the original one. We deal with a layer of constant stiffness, as well as with a stiffness in(delta) -1.