A MIXED FINITE-ELEMENT FOR SHELL-MODEL WITH FREE-EDGE BOUNDARY-CONDITIONS .1. THE MIXED VARIATIONAL FORMULATION

After a very brief recall on general shell theory, we construct a mixe d variational formulation based on the introduction of a new unknown: the rotation of the normal to the medium surface. In Koiter shell theo ry (for instance), this rotation can be expressed with respect to the three components of the displacement field of the medium surface and t heir derivatives. The Lagrange multiplier corresponding to this relati on (known as the Kirchhoff-Love kinematical assumption), is also intro duced as an independent unknown. There are two main difficulties: one is due to the differential geometry of surfaces and is rather technica l; the other is to define correctly the dual space for the Kirchhoff-L ove relation. The difficulty is similar to the one met in the characte rization of the dual space of the Sobolev space: H-1(omega) (omega bei ng the medium surface of the shell), for which a boundary component ap pears except for clamped shells which is a very restrictive situation.