Problem 1:
The figure shows part of a 2D plane stress domain discretized into constant stress triangles. Body forces are ignored and all surface tractions are zero. The modulus of elasticity of the material is E=1 and the thickness t=1. Details of the geometry and the obtained solutions are shown in the tables. All variables are expressed in consistent units. Consider the shaded triangle
Element Information
|
Node
|
1
|
2
|
3
|
|
Elem
|
|
|
|
|
26
|
...
|
...
|
...
|
|
27
|
...
|
...
|
...
|
|
28
|
10
|
25
|
103
|
|
29
|
...
|
...
|
...
|
Nodal Information
|
Node
|
x
|
y
|
|
10
|
5
|
5
|
|
...
|
|
|
|
25
|
15
|
7
|
|
...
|
|
|
|
103
|
10
|
15
|
Solution
|
Node
|
qx
|
qy
|
|
10
|
1
|
1
|
|
...
|
|
|
|
25
|
3
|
2
|
|
...
|
|
|
|
103
|
2
|
3
|
For the shaded triangular element 28, calculate the strain and the stress for Poisson ratio v=0.25
Problem 2:
Consider the axial member, shown in the figure, for which A=1 ft2 and E=1000(lb/ft2) The structure is subjected to surface traction that varies linearly, as shown in the figure, and the body forces are ignored. A single linear displacement Finite Element is used for the Finite Element solution. The shape functions of this element are given in terms of the Cartesian coordinates as shown in the figure.
Compute:
a) The nodal equivalent force vector that corresponds to the particular variation of the tractions.
b) A FEM solution is obtained and the displacement at the free end is computed as q2=1ft. Compute the strain energy in the structure.
Problem 3:
Use the Rayleigh Ritz method to find the displacement of the midpoint of the rod shown in the Figure. Assume A=E=1 and body force per unit volume g=1. Discuss the solution.
