A Linear Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Existence and Uniqueness

In this paper we derive the linear elastic Cosserat shell model incorporating in variational problem effects up to order $O(h^{5})$ thickness $h$ as a particular case of recently introduced geometrically nonlinear model. The existence and uniqueness solution is proven suitable admissible sets. To end, inequalities Korn-type for shells are established which allow show coercivity Lax-Milgram theorem. We also showing an result truncated $O(h^{3})$ Main issue treatment curved reference configuration shell. Some connections classical Koiter membrane-bending highlighted.