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

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.

Shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

“…The normalized results of the deflections at the central point c of the plate are presented in Tables 6 and 7. The results obtained by other polygonal elements, including DKMT‐ngon 20 and PRMn‐PL, 4 are also given in Table 7 for comparison. And their meshes are denoted by C1–C4 (for DKMT‐ngon), and D1–D4 (for PRMn‐PL), respectively.…”

“…And the element method was developed for static and dynamic analyses of plates and shells by a new arbitrary polytope formulation named polytopal composite finite element 19 . Videla et al 20 proposed another locking‐free polygonal plate element based on Mindlin–Reissner plate theory and assumed shear strain fields. Katili et al 21 also constructed a polygonal thin/thick plate element by smoothed finite element method.…”

First-order VEM for Reissner–Mindlin plates

“…The scientific attention on the developments of discretization methods for Reissner-Mindlin plates is still very animated [2][3][4], with a recent focus on polygonal elements [5][6][7][8]. Indeed, polygonal meshes may be particularly appealing for a number of applications, e.g.…”

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

“…However, the shear-locking phenomenon of Reissner-Mindlin plate elements emerges when the thickness reaches the thin limit, and this is due to spurious transverse shear strains/stresses in bending. A development residing on node-based kinematics that aims at alleviation of the shear-locking effect and local improvement of stress recovery has been recently presented by Valvano et al [1] Besides, many researchers proposed large amounts of effective elements to address this difficulty, such as the assumed natural discrete shear gap (DSG) method [2][3][4][5], strain (ANS) methods [6,7], and also the methods in [8][9][10][11][12][13][14][15][16]. All the methods show excellent performance in reducing the shear-locking deficiency and increasing the solution accuracy.…”