# Thin elastic plates supported over small areas I. Korn's inequalities and boundary layers

created by buttazzo on 20 Feb 2017

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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 $\ln h ^{-1/2}$.