Asymptotic modeling of a reinforced plate with a thin layer of variable thickness

In this paper, mathematical modeling of a reinforced Kirchhoff–Love plate with a thin layer of variable thickness is investigated. From a numerical point of view, the treatment of structures involving thin layers is difficult. Thus, asymptotic expansion method is used to justify an approximate model in which the thin layer is eliminated geometrically but whose effect is taken into account through new approximate boundary conditions. More precisely, an extension of the results obtained in a previous work, where the case of a layer with constant thickness was studied, is given. More general approximate boundary conditions are derived, valid for a larger class of layers, having a thickness variation as a function of geometry coordinates. Optimal Error estimates between the exact and the approximate solutions of the reinforced problem are proved.