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A new $n-$ noded polygonal plate element is proposed for the analysis ofplate structures comprising of thin and thick members. The formulation is basedon the discrete Kirchhoff Mindlin theory. On each side of the polygonalelement, discrete shear constraints are considered to relate the kinematicaland 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 shearlocking and (d) yields optimal convergence rates in $L^2-$norm and$H^1-$semi-norm. The accuracy and the convergence properties are demonstratedwith a few benchmark examples.

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields