Galerkin Projection for Geometrically Exact Sandwich Beams Allowing for Ply Drop-off

Abstract

A Galerkin projection of the equations of equilibrium for a recent theory of geometrically exact sandwich beams that allow finite rotations and shear deformation in each layer is presented. The continuity of the displacement across the layers is exactly satisfied. The resulting finite element formulation can accommodate large deformation. The number of layers is variable, with layer lengths and thicknesses not required to be the same, thus allowing the modeling of sandwich structures with ply drop-off. Numerical examples are presented which underline the salient features of the formulation. Saint-Venant principle is demonstrated for very short sandwich beams.