An exact solution for thermal stresses in a three-phase composite cylinder under uniform heat flow

An exact solution is given for the stress field in a three-phase composite cylinder induced by a uniform heat flow applied at infinity. Based on the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stress functions are derived explicitly in each medium of a three-phase composite cylinder. It is discovered that the stress in the inclusion is always linearly proportional to the coordinate z. Comparison is made with the special case of a two-phase composite cylinder, which shows that our results presented here are exact and general.