 
Summary: SIAM J. MATH. ANAL. c 1996 Society for Industrial and Applied Mathematics
Vol. 27, No. 2, pp. 486514, March 1996 009
ASYMPTOTIC ANALYSIS OF THE BOUNDARY LAYER
FOR THE REISSNERMINDLIN PLATE MODEL
DOUGLAS N. ARNOLD and RICHARD S. FALK
Abstract. We investigate the structure of the solution of the ReissnerMindlin 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 tractionfree 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 ReissnerMindlin
solution and the solution to the corresponding biharmonic model.
Key words. Reissner, Mindlin, plate, boundary layer
AMS(MOS) subject classifications. 73K10, 73K25
1. Introduction. The ReissnerMindlin model for the bending of an isotropic
elastic plate in equilibrium determines , the transverse displacement of the midplane,
and , the rotation of fibers normal to the midplane, as the solution of the partial
