Consider an aluminium bar 2014-T6 AB as shown in Figure 1. An axial load P = 100 kN is applied in the middle. The temperature is then rased to 150 K. The length of the bar is 300 mm. The diameter at A is 20 mm and diameter B is 10 mm.

Figure 1

a) Model the problem with one-dimensional finite element.

b) Write down expressions for the element stiffness matrices and element force vectors.

c) Assemble the global stiffness matrix K and global force vector F.

d) Using suitable approach, solve the nodal displacement.

e) Evaluate the stresses in each element.

f) Evaluate the stresses at each node.

g) Compare with the von-Mises stress.

h) What if there is no wall at the end of B.