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

Table 7

The normalized deflections at the free end of the MacNeal’s slender beam by using one layer of different trapezoidal membrane elements.

Element model	= 0°				= 45°
	Load 1	Load 2	Load 1	Load 2	Load 1	Load 2
Q4	0.093	0.093	—	—	0.022	0.003
Q6	1.000	0.993	—	—	0.093	0.106
QM6	1.000	0.993	—	—	0.037	0.044
AGQ6-I	1.000	0.993	—	—	1.000	0.994
AGQ6M	1.000	0.993	—	—	0.046	0.051
PS	—	—	0.117	0.133	0.046	0.052
YHP [30]	—	—	0.117	0.133	0.047	0.518
PS-E [31]	—	—	0.950	0.951	0.955	0.955
SPS ( = 50) [32]	—	—	0.415	0.494	0.394	0.476
SYHP ( = 50) [32]	—	—	0.416	0.495	0.398	0.480
SPS ( = 5000) [32]	—	—	0.983	0.978	0.983	0.978
SYHP ( = 5000) [32]	—	—	0.983	0.978	0.983	0.978
QCQ4-1	0.910	0.904	0.107	0.134	0.026	0.074
QCQ4-2	1.000	0.993	0.110	0.139	0.053	0.077