On the finite element approximation of the obstacle problem of a Naghdi shell

In this work we consider the finite element approximation of two equivalent formulations of an obstacle problem of a Naghdi shell. This second one is a new formulation of the continuous problem set on the unconstrained space of the displacement field and the rotation. Namely in order to enforce the tangency requirement on the rotation and the inequality constraint, two Lagrange multipliers are introduced. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive a priori error estimates. We further prove the convergence of the Uzawa algorithm associated with this variational inequality. Numerical tests that validate and illustrate our approach are given.