The Boundary Layer for the Reissner–Mindlin Plate Model

Abstract

The structure of the solution of the Reissner–Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. For the transverse displacement, rotation, and shear stress, asymptotic expansions in powers of the plate thickness are developed. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary layer. Rigorous error bounds are given for the errors in the expansions in Sobolev norms. As applications, new regularity results for the solutions and new estimates for the difference between the Reissner–Mindlin solution and the solution to the biharmonic equation are derived. Boundary conditions for a clamped edge are considered for most of the paper, and the very similar case of a hard simply-supported plate is discussed briefly at the end. Other boundary conditions will be treated in a forthcoming paper.