An exact thermopiezoelasticity solution for a three-phase composite cylinder

An exact solution is first derived for the stress field in a three-phase piezoelectric composite cylinder induced by a uniform heat flux together with an anti-plane shear and in-plane electric field 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 and the electric displacement in the inclusion is always linearly proportional to the coordinate. The numerical results demonstrates that the continuity conditions at the interface are indeed satisfied and shows the effects of material mismatch on the stress and electric displacement fields.