Problem 4: In the Figure shown, the Q8 element has equally-spaced nodes. The nodes 1, 4, 6 of the Q8 element are collaps

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Problem 4 In The Figure Shown The Q8 Element Has Equally Spaced Nodes The Nodes 1 4 6 Of The Q8 Element Are Collaps 1 (100.98 KiB) Viewed 25 times

Problem 4: In the Figure shown, the Q8 element has equally-spaced nodes. The nodes 1, 4, 6 of the Q8 element are collapsed into one node; and nodes 7 and 2 are moved towards the collapsed node at a distance equal to one fourth the length of the element sides 1-8 and 1-3 to form an F6 element, as shown below. The F6 element is used to model fracture mechanics problem with the crack tip placed at the collapsed node. 1) Derive x and y in terms of E and ŋ for the Q8 element where & and n are coordinates of the master element. n 2) Modify and derive x and y in terms of Ę and ŋ for the F6 element. 3) Determine the variation of Exx and Eyy along r. Check for singularity at the collapsed node. у у (0,2) (2,2) 7 8 8 o 6 7 05 1,4,6 r 65 2 1 3 X Х 3 (0,0) (2,0) 2 F6 Q8