Coupled Nonlinear Thermoelastic Problems

In this chapter, we formulate fundamental assumptions and relations similar to those presented in Chap. 2 for coupled linear thermoelasticity problems of shallow shells. A Timoshenko-type model including the inertial effect of rotation of shell elements is used. Both the generalized heat transfer equation and the equations governing vibration of a shell are formulated in Sect. 5.2, and then some special cases of these equations are analysed. In the next section, boundary and initial conditions are attached to the differential equations. In Sect. 5.4, the existence and uniqueness of a solution as well as the convergence of the Bubnov–Galerkin method, are rigorously discussed.