The most accessible problems for the mechanics of deformable solid bodies
are those for thin bodies, namely, rods and shells, because their
equations respectively have but one and two independent spatial variables.
There is a voluminous literature devoted to the derivations of various models for such bodies
undergoing small deformations. On the other hand, geometrically exact theories
are derived directly from fundamental principles. They readily accommodate
general nonlinear material response. This lecture describes solutions of