An existence and uniqueness theorem for the dynamics of flexural shells

In this paper, we define, a priori, a natural two-dimensional model for a time-dependent flexural shell. As expected, this model takes the form of a set of hyperbolic variational equations posed over the space of admissible linearized inextensional displacements, and a set of initial conditions. Using a classical argument, we prove that the model under consideration admits a unique strong solution. However, the latter strategy makes use of function spaces, which are not amenable for numerically approximating the solution. We thus provide an alternate formulation of the studied problem using a suitable penalty scheme, which is more suitable in the context of numerical approximations. For the sake of completeness, in the final part of the paper, we also provide an existence and uniqueness theorem for the case where the linearly elastic shell under consideration is an elliptic membrane shell.