Dynamics of geometrically-exact sandwich beams/1-D plates: computational aspects

Abstract

A Galerkin projection of the complete equations of motion of geometrically-exact sandwich beams applicable to 1-D plates is presented here. The beam can take any arbitrary initial position in the 2-D space. Each layer of the beam can have different material constants with no restriction on the mass distribution and layer thickness; further, each layer can take on different length, thus allowing the modeling of multilayer structures with ply drop-offs. Finite rotation and shear deformation are accommodated for in each layer. The deformed cross section of the beam is continuous, piecewise linear. The continuity of displacement across the interlayer boundaries is exactly enforced. Extensive numerical examples including sandwich beams with three identical layers, sandwich structures with ply drop-off, free flying and spin-up maneuver of sandwich beams are presented to illustrate the applicability and versatility of the proposed formulation.