Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model

We investigate the structure of the solution of the Reissner-Mindlin plate equations in its dependence on the plate thickness in the cases of soft and hard clamped, soft and hard simply supported, and traction free boundary conditions. For the transverse displacement, rotation, and shear stress, we develop asymptotic expansions in powers of the plate thickness. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary layer, which is stronger for the soft simply supported and traction-free plate and weaker for the soft clamped plate than for the hard clamped and hard simply supported plate. We give rigorous error bounds for the errors in the expansions in Sobolev norms. As an application, we derive new regularity results for the solutions and new estimates for the difference between the Reissner-Mindlin solution and the solution to the corresponding biharmonic model.