Some remarks concerning the linear theory of heterogeneous orthotropic shells

Expressions are obtained for the equations of Gauss and the equations of Codazzi-Mainardi, the equations of in-plane equilibrium and compatibility, and the equations of out-of-plane equilibrium and compatibility for orthotropic heterogeneous shells. A systematic calculus reveals coupling, the static-kinematic analogy, and the separation of symmetric and antimetric tensors. The general variational principle of Washizu (1968) is used to derive a mixed variational principle, which shows that the normal displacement and the in-plane stress function are sufficient to solve the problem for a spherical shell.