General multilayer geometrically-exact beams/1-D plates with deformable layer thickness: Equations of motion

We formulate a theory of geometrically-exact multilayer beams and one-dimen sional plates that account Sor the through-the-thickness deformation in eac h layer. in addition to shear deformation. The complete set of nonlinear eq uations of motion together with the appropriate boundary conditions are der ived. and a linear constitutive law is postulated for the model. The number of layers is arbitrary and unlimited, with a reference layer arbitrarily c hosen among the layers. The length and the thickness of each layer are also variable, making the modeling of multilayer structures with ply drop-offs possible. The present theory reduces exactly to the case of multilayer stru ctures without through-the-thickness deformation; and to the case of single -layer structures. The formulation allows the description of large deformat ion and large overall motion ill multilayer structures.