1
CE-5155 Finite Element Analysis of Structural Systems Final Exam, Fall 2009 Take Home Exam. Due Date: 10 March 2010 Maximum Marks: 100 Question. No. 1. (15 Marks) (-1, 1)
10
4
9
3
(1, 1)
η, v 11
16
8
15 ξ, u
(-1, -1) a) b) c)
12
13
14
1
5
6
7
2
(1, -1)
Determine the shape function for Node 4 in Natural Coordinates: N4 (ξ, η) (5 marks) Plot the value of u displacement along edge 4-10-9-3 for a set of prescribed nodal displacements: u4 = 1.0, v4 = 2.0 and all other nodes u = v = 0.0 (5 marks) Plot εx along edge 4-10-9-3 for the prescribed displacements in part b. (5 marks)
Question. No. 2. (25 Marks)
3
(0, 5)
(6.5, 7 )
η
(-1, 1)
3
4
4
(1, 1)
y, v ξ 1 (0, 0)
2 x, u Actual Element
(5, 0)
2
1 (-1, -1)
(1, -1)
Parent Element 1