On the justification of the frictionless time-dependent Koiter's model for thermoelastic shells

Our first objective is to identify two-dimensional equations that model the displacement of a linearly elastic flexural shell subjected to the action of an external heat source. To this end, we embed the shell into a family of linearly elastic flexural shells, all sharing the same middle surface θ ( ω ‾ ) , where ω is a domain in R 2 and θ : ω ‾ → E 3 is a smooth enough immersion and whose thickness 2 e > 0 is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as e approaches zero, the corresponding “limit” two-dimensional variational problem. Our second objective is to identify and justify a set of two-dimensional equations that are meant to approximate the original three-dimensional model in the case where the shell under consideration is either an elliptic membrane shell or a flexural shell.