Thin Elastic Plates Supported over Small Areas. I: Korn's Inequalities and Boundary Layers

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 << 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) vertical bar ln h vertical bar. Ignoring this boundary layer effect reduces the precision order down to vertical bar ln h vertical bar(-1/2).