Calculus of Variations and Geometric Measure Theory

G. Buttazzo - G. Cardone - S. Nazarov

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

created by buttazzo on 20 Feb 2017


Published Paper

Inserted: 20 feb 2017
Last Updated: 20 feb 2017

Year: 2016


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

Keywords: Asymptotic Analysis, Kirchhoff plate, small support zones, boundary layers, weighted Korn inequality