Journal of Convex Analysis 23 (2016), No. 2, 347--386
Copyright Heldermann Verlag 2016
Thin Elastic Plates Supported over Small Areas. I: Korn's Inequalities and Boundary Layers
Giuseppe Buttazzo
Dept. of Mathematics, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
buttazzo@dm.unipi.it
Giuseppe Cardone
Dept. of Engineering, Università del Sannio, Corso Garibaldi 107, 82100 Benevento, Italy
giuseppe.cardone@unisannio.it
Sergey A. Nazarov
Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetsky pr. 28, Stary Peterhof 198504, Russia
srgnazarov@yahoo.co.uk
[Abstract-pdf]
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 $h\ll 1$. 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: Kirchhoff plate, small support zones, asymptotic analysis, boundary layers, weighted Korn inequality.
MSC: 74K20, 74B05
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