J.-M.SAC-ÉPÉE * & J.SAINT JEAN PAULIN ** Université de Metz, Département de Mathématiques, Ile du Saulcy, 57045 Metz, France.

* [email protected],univ-metz.fr ** [email protected]

ABSTRACT We consider a thin plate, periodically perforated by cylindrical holes, the axes of which are perpendicular to the plane of the domain. On a horizontal cross section, we denote by ε the size of the period, and by e the thickness of the plate. On this domain, we consider an elasticity problem with Fourier boundary conditions. First, we pass to the limit in ε, then in e. Next, we pass to the limit in the reverse order. In each of these asymptotic processes, we consider two cases depending on the value of the data on the lateral boundary of the holes.