Published Paper
Inserted: 20 feb 2017
Last Updated: 20 feb 2017
Year: 2016
Abstract:
A thin anisotropic elastic plate clamped along its lateral side and
also supported at a small area $\theta_h$ of one base is considered; the
diameter of $\theta_h$ is of the same order as the plate relative thickness
$h\ll1$. In addition to the standard Kirchhoff model with the Sobolev point
condition, a three-dimensional boundary layer is investigated in the vicinity
of the support $\theta_h$, which with the help of the derived weighted
inequality of Korn's type, will provide an error estimate with the bound
$ch^{1/2}
\ln h
$. Ignoring this boundary layer effect reduces the precision
order down to $
\ln h
^{-1/2}$.
Keywords: Asymptotic Analysis, Kirchhoff plate, small support zones, boundary layers, weighted Korn inequality
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