 
Summary: SIAM J. MATH. ANAL. c 1990 Society for Industrial and Applied Mathematics
Vol. 21, No. 2, pp. 281312, March 1990 001
THE BOUNDARY LAYER FOR THE
REISSNERMINDLIN PLATE MODEL*
DOUGLAS N. ARNOLD and RICHARD S. FALK
Abstract. The structure of the solution of the ReissnerMindlin 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 ReissnerMindlin 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
simplysupported plate is discussed briefly at the end. Other boundary conditions will be treated in
a forthcoming paper.
Key words. Reissner, Mindlin, plate, boundary layer
AMS(MOS) subject classifications. 73K10, 35B25
1. Introduction. The ReissnerMindlin model describes the deformation of a
plate subject to a transverse loading in terms of the transverse displacement of the
midplane and the rotation of fibers normal to the midplane [9], [10]. This linear
