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 , 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 GPa, 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
Solutions
Step 1: Geometry, Area and B-matrix Coefficients
The area is
1 5 15
1
A= det 1 15 5 = 100 mm2 .
2
1 25 15
Coefficients:
b1 = −10, b2 = 0, b3 = 10, c1 = 10, c2 = −20, c3 = 10.
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 , 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 GPa, 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
Solutions
Step 1: Geometry, Area and B-matrix Coefficients
The area is
1 5 15
1
A= det 1 15 5 = 100 mm2 .
2
1 25 15
Coefficients:
b1 = −10, b2 = 0, b3 = 10, c1 = 10, c2 = −20, c3 = 10.
1
