Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems

Abstract

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-processing procedure, which was firstly prosolutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.

A new quadrilateral area coordinate method (QACM‐II) for developing quadrilateral finite element models

“…From Equation (15), it can be seen that the new area coordinates Z 1 and Z 2 will degenerate to the isoparametric coordinates and for rectangular element cases.…”

“…However, the numerical integration method would be more convenient for computer coding. Thus, by using Equation (15), Equation (76) can be expressed in terms of isoparametric coordinates as follows:…”

“…Then it was generalized to a Mindlin-Reissner plate element [14] and a laminated composite plate element [15] by Cen et al The shape functions of the deflection field of element ACGCQ, which are expressed using QACM-I, obtained further applications of Zhu et al [16], Zhu and Wu [17] and Brunet and Sabourin [18] for the explicit dynamic shell analysis and metal forming problem. Compared with those traditional models using isoparametric coordinates, these new models possess better performance and are free of various locking phenomena caused by mesh distortion [19,20].…”

A hybrid-stress element based on Hamilton principle

“…Since the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, the number of the stress variables can be reduced from 3 to 2, and thus the new hybrid-stress elements are simpler than the traditional ones. Furthermore, several enhanced post-processing schemes [27][28][29][30][31] are employed for improving the stress accuracy of the new element, and the performance of the proposed elements are finally validated by selected numerical examples.…”

Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method

“…Those element models by QACM can successfully overcome the disadvantages of isoparametric elements, and especially, prevent many kinds of locking phenomena in severely distorted meshes. So far Long and Cen's research group has proposed various QACM elements: 4-to 8-node quadrilateral membrane elements [4][5][6], 4-node quadrilateral thin plate element [7], 4-node quadrilateral Mindlin-Reissner plate element [8], 4-node quadrilateral composite plate element [9], and so on. Since the use of generalized conforming conditions (a kind of relaxed conforming requirements) [10][11][12][13] and the transformation between quadrilateral area coordinates and Cartesian coordinates is always linear, the loss of accuracy has been successfully avoided when element shapes are distorted.…”