finite-element-analysis-of-structural-systems_final-term-exam_fall-2009

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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


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