  A new $n-$ noded polygonal plate element is proposed for the analysis of
plate structures comprising of thin and thick members. The formulation is based
on the discrete Kirchhoff Mindlin theory. On each side of the polygonal
element, discrete shear constraints are considered to relate the kinematical
and the independent shear strains. The proposed element: (a) has proper rank;
(b) passes patch test for both thin and thick plates; (c) is free from shear
locking and (d) yields optimal convergence rates in $L^2-$norm and
$H^1-$semi-norm. The accuracy and the convergence properties are demonstrated
with a few benchmark examples.
