A rectangular solid under plane stress conditions is modeled using four finite elements as shown in the figure. It has been proved that the finite elements pass the patch test.

(a) When a constant displacement \(u=0.01 \mathrm{~m}\) is applied to nodes 3,6 , and 9, calculate the displacement \(\{u, v\}\) at node 5 whose initial coordinates are (0.4, 0.4).

(b) Explain how passing the patch test is important for the element's performance.

Transcribed Image Text:

y E=100 Pa, v=0.25 (0,1) (.5,1) (1,1) 7) 8 (.4,.4) 9) (1,.5) 6 (0,.4) 4) 5 u = 0.01 m 1 2 3 X (0,0) (.5,0) (1,0)