FEA3701
Assignment 03
Finite Element Analysis
Year 2025
, Question 1 [40]
For the plane strain element given in Figure 1, determine the following:
(a) Element stresses σx , σy , and τxy [25]
(b) Principal stress σ1 [5]
(c) Principal stress σ2 [5]
(d) Principal angle θp [5]
The nodal displacements are as follows:
u1 = 0.005 mm, v1 = 0.002 mm, u2 = 0 mm, v2 = 0 mm, u3 = 0.005 mm, v3 = 0 mm
Let E = 105 GP a, ν = 0.3, t = 1
All coordinates are given in millimeters.
i=1 m=3
(5, 15) (25, 15)
j = 5)
(15, 2
Figure 1
Solution
Step 1: Area of the element
1 5 15
1 1
A = det 1 15 5 = (200) = 100 mm2
2 2
1 25 15
—
1
Assignment 03
Finite Element Analysis
Year 2025
, Question 1 [40]
For the plane strain element given in Figure 1, determine the following:
(a) Element stresses σx , σy , and τxy [25]
(b) Principal stress σ1 [5]
(c) Principal stress σ2 [5]
(d) Principal angle θp [5]
The nodal displacements are as follows:
u1 = 0.005 mm, v1 = 0.002 mm, u2 = 0 mm, v2 = 0 mm, u3 = 0.005 mm, v3 = 0 mm
Let E = 105 GP a, ν = 0.3, t = 1
All coordinates are given in millimeters.
i=1 m=3
(5, 15) (25, 15)
j = 5)
(15, 2
Figure 1
Solution
Step 1: Area of the element
1 5 15
1 1
A = det 1 15 5 = (200) = 100 mm2
2 2
1 25 15
—
1
