The coupled thermoelasticity of shells of revolution, based on second-order
shell theory, is considered, and the governing equations including normal
stress and strain as well as the transverse shear and rotary inertia are co
nsidered. The coupled energy equation based on the assumption of Lord and S
hulman (Lord, H. W., and Shulman, Y., "A Generalized Dynamical Theory of Th
ermoelasticity,'' Journal of Mechanics and Physics of Solids, Vol. 15, No.
5, 1967, pp. 299-309) is further considered, and the total system of equati
ons is served by means of Galerkin finite element method. it is concluded t
hat the inclusion of normal stress in the coupled equation is significant a
nd for thin shells can result in a noticeable difference in shelf response
compared to unassumed conditions.