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

Abstract

SUMMARYThe quadrilateral area co-ordinate method is used to formulate a new quadrilateral element for Mindlin-Reissner plate bending problem. Firstly, an independent shear field is assumed based on the locking-free Timoshenko's beam formulae; secondly, a fourth-order deflection field is assumed by introducing some generalized conforming conditions; thirdly, the rotation field is determined by the strain-displacement relations. Furthermore, a hybrid post-processing procedure is suggested to improve the stress/internal force solutions. Following this procedure, a new 4-node, 12-dof quadrilateral element, named AC-MQ4, is successfully constructed. Since all formulations are expressed by the area coordinates, element AC-MQ4 presents some different, but beneficial characters when compared with other usual models. Numerical examples show the new element is free of shear locking, insensitive to mesh distortion, and possesses excellent accuracy in the analysis of both thick and thin plates. It has also been demonstrated that the area co-ordinate 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 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.…”

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

“…It is apparent that this patch test is more rigorous than the patch test using numerical computation of pure bending and pure torsion of a smallscale plate. Then, elements such as RDKQM [15], RDKTM [16], AC-MQ4 [17], and QC-P4 [18] that can pass the above patch test functions were proposed, indicating that the shearlocking problem is solved. All these elements can be used to solve the extremely thin plate problem (the thickness/span ratio of the plate can reach to 10 −30 ).…”

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

“…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].…”