Accurate, Efficient, and Robust Q4-Like Membrane Elements Formulated in Cartesian Coordinates Using the Quasi-Conforming Element Technique

Table 2

List of element models for comparison study.

No.	Symbols	Formulation methods	References
1	Q4	4-node isoparametric membrane element	[5]
2	Q6	4-node isoparametric element with 2 internal parameters	[5]
3	QM6	Modified Q6 element	[5]
4	QC6	Q6-like quasi-conforming isoparametric element	[5, 21]
5	PS	Q4-like hybrid stress element	[12]
6	07β	Q4-like element with drilling dof using hybrid stress method	[10]
7	QR4b	Q4-like element with drilling dof using the quasi-conforming element technique	[7]
8	QA4	Q4-like element with drilling dof using the quasi-conforming element technique	[8]
9	I-A	Q4-like element with drilling dof based on a special functional	[9]
10	RQ4	Q4 element based on rational displacement field	[26]
11	AQCE4	Q4-like quasi-conforming element based on an assumed rational strain field	[26]
12	B-Q4E	Q4-like assumed strain element based on B-bar method	[17, 18]
13	Pimpinelli	Q4-like assumed strain element with drilling dof	[15]
14	CYSE	Q4-like element by natural strain with 7 enhancing variables for membrane strains	[6]
15	QACII6	Q6-like element based on quadrilateral area coordinates	[18]
16	AGQ6-I	Q6-like element based on quadrilateral area coordinates	[5, 17]
17	AGQ6M	Modified AGQ6-I element to pass patch test	[5, 17]
18	WDQ4	Q4-like quasi-conforming element with bilinear interpolation for element domain displacement	[28]
19	WDQ4	Q4-like quasi-conforming element with complete quadratic interpolation for element domain displ.	[28]