A stabilized one‐point integrated quadrilateral Reissner–Mindlin plate element

Abstract

A new quadrilateral Reissner–Mindlin plate element with 12 element degrees of freedom is presented. For linear isotropic elasticity a Hellinger–Reissner functional with independent displacements, rotations and stress resultants is used. Within the mixed formulation the stress resultants are interpolated using five parameters for the bending moments and four parameters for the shear forces. The hybrid element stiffness matrix resulting from the stationary condition can be integrated analytically. This leads to a part obtained by one‐point integration and a stabilization matrix. The element possesses a correct rank, does not show shear locking and is applicable for the evaluation of displacements and stress resultants within the whole range of thin and thick plates. The bending patch test is fulfilled and the computed numerical examples show that the convergence behaviour is better than comparable quadrilateral assumed strain elements. Copyright © 2004 John Wiley & Sons, Ltd.

Structural analysis of composite laminates using a mixed hybrid shell element

“…[13], but not with the bilinear displacement interpolation inserted in the transverse shear strains (3) 3 , see Ref. [18] in case of a linear plate. Thus the finite element approximation of the Green-Lagrangean strains reads…”

A linear quadrilateral shell element with fast stiffness computation

“…The fulfillment of the bending patch test is discussed in [28], where for a plate it is shown, that with the transverse shear strains (4) 3 the patch test can not be fulfilled within the present mixed formulation. The non constant part of the shear strains according to (4) 3 leads for a constant stress state to a contribution of the shear energy on the element level.…”

“…In this context we also refer to the expressions for a plate in [28]. Due to the introduced constantsξ andη one obtains a matrix H only with diagonal entries ) .…”

Application of the curvature smoothing technique for four-node quadrilateral Reissner-Mindlin plate element

“…The geometry and material parameters are given as length L = 10, thickness t = 0.1 , Young's modulus E = 1092000, Poisson's ratio v = 0.3 and p = 1. The series solution considered as analytical solution of Kirchhoff theory is given in [11]. Although a shear correction factor now is chosen to be a large value k = 1000 that the finite element solutions often converge against the Kirchhoff solution, the convergence behaviour of the MISCk elements in this case is very good for the deflection and the bending moment, see in Fig.…”