Accurate, efficient, and robust Q4-like membrane elements formulated in Cartesian coordinates using the quasi-conforming element technique
type: Item
instance of: scholarly article
title: Accurate, efficient, and robust Q4-like membrane elements formulated in Cartesian coordinates using the quasi-conforming element technique
zbMATH Open document ID: 1394.74095
DOI: 10.1155/2015/198390
author: Y. Liu
author: X. Wang
author: Guangyu Shi
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: By using the quasi-conforming element technique, two four-node quadrilateral membrane elements with 2 degrees of freedom at each node (Q4-like membrane element) are formulated in rectangular Cartesian coordinates. One of the four-node quadrilateral membrane elements is based on the assumed strain field with only five independent strain parameters and accounting for the Poisson effect explicitly. There are no independent internal parameters and numerical integration involved in the evaluation of the strain parameters in these four-node quadrilateral membrane elements, and their element stiffness matrices are computed explicitly in Cartesian coordinates. Consequently, the formulation of these four-node quadrilateral membrane elements is extremely simple, and the resulting elements are very computationally efficient. These two quasi-conforming quadrilateral membrane elements pass the patch test and are free from shear locking and insensitive to the element distortion in the range of practical application. The numerical result comparison with other four-node quadrilateral membrane elements, including Q4-like plane elements with drilling degrees of freedom and the Q6-type isoparametric elements with very complicated nonconforming modes, shows that the present quasi-conforming quadrilateral membrane elements are not only reliable and robust, but also very accurate in both displacement and stress evaluations in the analysis of practical plane elasticity problems.
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 6925743
Wikidata QID: Q59117578
describes a project that uses: LS-DYNA
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/198390
OpenAlex ID: W1537123233
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description: scientific article; zbMATH DE number 6925743