Consider the thermal stress problem in a circular ring as shown in the figure. Assuming the temperature and stress fields depend only on the radial coordinate r, the general solution is given by (12.7.4). If the surfaces r = a and r = b are to be stress free, show that the solution can be written as:

for appropriate constants A_i. Note for this type of problem the logarithmic term is retained as long as the ring is only a segment and not a full ring. For this case the displacements at each end section need not be continuous.

Equation 12.7.4

Ea or +42 (2 log +1)+24 / Tror Or a a