An improved four‐node hybrid‐mixed element based upon Mindlin's plate theory

Abstract

SUMMARYBased on the mixed shear projected (MiSP) approach (Reference [54]: Int. J. Numer. Meth. Engng 1998; 42:1149-1179, an enhanced bending approximation for homogeneous isotropic plates is presented. Some hard benchmark tests, such as the skew plate (30 • ) problem, have often shown poor convergence when low-order elements (3-or 4-node element) are developed using linear approximations for kinematic variables. To put right this weakness, we propose a high-order interpolation for rotational dofs which results in more rich bending curvatures. The mid-side rotational nodes are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypotheses. The derived 4-node quadrilateral element, called MiSP4+, is free of shear locking and passes all patch tests for thick and thin plates in an arbitrary mesh.

Application of the quadrilateral area co‐ordinate method: a new element for Mindlin–Reissner plate

“…The radius, Young's modulus and Poisson's ratio of the plate were assumed to be 5, 10.92 and 0.3, respectively. The detailed expressions of analytical solution can be found in References [42,43]. Results obtained from the analyses are presented in Tables X and XI.…”

“…References [42,43] show that many displacement-based elements cannot present satisfactory results for the distribution of shear force T r along a radius, especially for the thin-plate case. This problem may be solved by the proposed hybrid post-processing procedure.…”

“…The bending moment field {M} and the shear force field {T} are only required to satisfy C −1 continuity between two elements [42,43]. Thus, {M} can be assumed as follows: From the equilibrium Equation (12) of a plate, the shear force field {T} can be expressed as…”

A triangular hybrid equilibrium plate element of general degree

“…However the modelling of plate bending problems continues to drive developments of new elements with improved abilities to model the more extreme cases such as plates which are very thin and may lead to locking, or thick and/or composite plates. Many papers are still being published with the objectives of formulating plate elements which have a good performance but without numerical problems [2][3][4]. Displacement elements may conform with each other to produce compatible models, hybrid and mixed elements do not always achieve complete conformity, and in general equilibrium is only satisfied in a weak sense.…”

Analysis of some low order quadrilateral Reissner-Mindlin plate elements

“…We only consider these four elements for the sake of exposition, while it is believed that our methodology can be applied equally to analyze other quadrilateral Reissner-Mindlin plate elements that have appeared in the literature [8,9,38].…”