  The paper is concerned with the geometrically non-linear theory of
6-parametric elastic shells with drilling degrees of freedom. This theory
establishes a general model for shells, which is characterized by two
independent kinematic fields: the translation vector and the rotation tensor.
Thus, the kinematical structure of 6-parameter shells is identical to that of
Cosserat shells. We show the existence of global minimizers for the
geometrically non-linear 2D equations of elastic shells. The proof of the
existence theorem is based on the direct methods of the calculus of variations
using essentially the convexity of the energy in the strain and curvature
measures. Since our result is valid for general anisotropic shells, we analyze
separately the particular cases of isotropic shells, orthotropic shells, and
composite shells.
