We study the bending of a thin plate, stiffened with a thin elastic layer, of thickness δ. We describe the complete construction of an asymptotic expansion with respect to δ 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 too...

This paper is concerned with an investigation into the localized instability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and under different boundary conditions of clamped, hinged, sliding contact and free on the other edge, is studied. A mathematical model is used and a general solution is presented. The conditions unde...

This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy leads to the Von-Kármán’s equations (or the linear model for smaller forces) in the plate and to a one dimensional rod-model at the limit. The junction condition...