Asymptotic behavior of a plate with a non-planar top surface

Abstract

In this paper, we study the asymptotic behaviors of a plate with non-planar top surface in the framework of linear elasticity. For this plate, we give a decomposition of the displacements. We show that every displacement of the plate is the sum of a Kirchhoff-Love displacement and a residual displacement that takes into account the deformations of the fibers of the plate and shear. We also prove Korn's type inequalities.