Le problème de Signorini dans la théorie des plaques minces de Kirchhoff–Love

In the framework of the Kirchhoff–Love asymptotic theory of elastic thin plates we consider the unilateral contact problem with friction for a plate on a rigid foundation (Signorini problem with friction). First, we notice, when the thickness vanishes, that the order of the friction force must be lower than that of the contact pressure. These two measures are connected by Coulomb law. Consequently, at least formally, the friction force must be vanishing when the thickness goes to zero. We actually prove that any sequence of solution of the sequence of three-dimensional scaled Signorini problems with friction strongly converges to the unique solution of a two-dimensional Signorini plate problem without friction. To cite this article: J.-C. Paumier, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 567–570.