Dv. Griffiths et Ggw. Mustoe, SELECTIVE REDUCED INTEGRATION OF 4-NODE PLANE ELEMENT IN CLOSED-FORM, Journal of engineering mechanics, 121(6), 1995, pp. 725-729
The exactly integrated four-node plane element is known to ''lock'' as
elastic incompressible conditions are approached. The use of uniform
reduced integration removes this problem but introduces another in the
form of a zero-energy mode, which can result in ''hourglass'' deforma
tions. A popular compromise is known as selective reduced integration
(SRI), in which the shear contribution to stiffness is exactly integra
ted and the volumetric contribution is evaluated using reduced integra
tion. This SRI approach is readily coded in a numerical algorithm but
requires the evaluation of five stiffness matrix contributions per ele
ment. This paper describes a closed-form version of the SRI stiffness
matrix that was generated with the help of computer algebra systems. I
t is shown that this ''analytical'' approach considerably reduces the
central processing unit (CPU) time consumed during element integration
.