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

TL;DR

This paper introduces a novel locking-free polygonal plate element based on Reissner-Mindlin theory, capable of accurately analyzing both thin and thick plates with optimal convergence and no shear locking.

Contribution

The paper presents a new n-node polygonal plate element that is shear locking-free, passes patch tests for thin and thick plates, and demonstrates optimal convergence rates.

Findings

Passes patch test for thin and thick plates

Free from shear locking

Achieves optimal convergence rates

Abstract

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.