A strain-and-displacement-based variational method applied to geometrically non-linear shells

A geometrically non-linear hybrid nine-node finite 2D-shell element is presented. The theoretical formulation is based on a Reissner functional in strains and displacements. The increments of which are interpolated with respect to different spatially fixed triads: both the displacement and rotation increments in the material frame (global rectangular Cartesian) and the Green-Lagrange-strain increments in a suitably chosen local rectangular Cartesian in the centroid of the considered element in the reference configuration. Corresponding transformations then deliver the components on the shell mid-surface. Although a single element possesses one spurious zero-energy mode, an assemblage performs excellently (also in comparison with a full-rank element).