  We present a new way to discretize a geometrically nonlinear elastic planar
Cosserat shell. The kinematical model is similar to the general 6-parameter
resultant shell model with drilling rotations. The discretization uses geodesic
finite elements, which leads to an objective discrete model which naturally
allows arbitrarily large rotations. Finite elements of any approximation order
can be constructed. The resulting algebraic problem is a minimization problem
posed on a nonlinear finite-dimensional Riemannian manifold. We solve this
problem using a Riemannian trust-region method, which is a generalization of
Newton's method that converges globally without intermediate loading steps. We
present the continuous model and the discretization, discuss the properties of
the discrete model, and show several numerical examples, including wrinkles of
thin elastic sheets in shear.
