Title: The boundary layer for the Reissner-Mindlin plate model
Authors: Douglas N. Arnold and Richard S. Falk
Source: SIAM J. Math. Anal., 21 1990), pp. 281-312
Status: Published
Abstract: The structure of the solution of the Reissner-Mindlin
model of a clamped plate is investigated, emphasizing its dependence on
the plate thickness. Asymptotic expansions in powers of the plate
thickness are developed for the main physical quantities and the
boundary layer is studied. 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.
Keywords: Reissner, Mindlin, plate, boundary layer
Subj. class.: 73K10, 73K25
URL: http://www.math.rutgers.edu/~falk/papers/bdlayer.pdf