Dynamic Formulation for Geometrically Exact Sandwich Beams and One-Dimensional Plates

Abstract

A new theory of sandwich beams/one-dimensional plates is presented with finite rotations and shear allowed in each layer. The layers, variable in number from one to three, need not have the same thickness and the same length, thus allowing for ply drop-off. Restricting to planar deformation, the cross section has a motion identical to that of a multibody system that consists of rigid links connected by hinges. Large deformation and large overall motion are accommodated, with the beam dynamics referred directly to an inertial frame. An important approximated theory is developed from the general nonlinear equations. The classical linear theory is recovered by consistent linearization.