| This work has two parts: (1) On the geometrically-exact sandwich beams/1-d plates and (2) On the geometrically-exact sandwich shells.; Most recent formulations in regard to sandwich structures have incorporated the geometric nonlinearity as high-order deformation, and are not suitable for problems that include the large overall motion. On the other hand, formulations proposed for analyzing large overall motion of sandwich structures in general bypass the kinematic description of the deformation in different layers to use the classical single-layer Euler-Bernoulli beam theory, which cannot describe a relative thick sandwich structure exactly.; In the first part of this work, a Galerkin projection of the equations of motion 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-offs. Extensive numerical examples are presented which underline the salient features of the formulation. Saint-Venant principle is demonstrated for very short sandwich beams. Numerical examples also including sandwich structures with ply drop-offs, free flying and spin-up maneuver of sandwich beams are presented to illustrate the applicability and versatility of the proposed formulation.; Classical treatments of shells are all cast in terms of the complex differential geometric object such as the covariant derivatives, the Riemann connections or the Christoffel symbols. In dealing with sandwich shell the situation gets even more complex due to the complexity of the sandwich shells itself. To avoid these complexities, efforts have been made on a numerical scheme called degenerated solid approach. In the degenerated solid approach, numerical integrations are made through out the thickness of the shell which have reduced the fully 3-dimensional equations of motion to 2-dimensional equations of motion. While this scheme avoids the complexity of the classical theory of sandwich shells, it suffers more expense due to numerical integrations through the thickness of the shell. Furthermore, there is no mathematical analysis to the degenerated solid approach in its numerical integrations through the thickness.; The geometrically-exact theory provides a simpler way in dealing with the dynamics of fully nonlinear structures. Thus in the second part, following the similar procedures as the works on geometrically-exact sandwich beams and one-dimensional plates, we present a geometrically-exact sandwich shell theory, entirely in terms of stress resultants which accommodates finite deformations in membrane, bending, and transverse shear. The motion of the shell are referred directly to the inertial frame; the transverse fiber of the sandwich shell has a motion identical to that of a chain of three rigid links connected by revolute joints. An important approximated theory is developed from the general nonlinear equations, the classical linear theory is recovered by the consistent linearization.; The weak form of the fully-nonlinear resultant equations of motions are derived. The weak form is then linearized exactly. The linearized weak form of the equations of motions are used in the Newton-Raphson iterative solution procedure, which leads to quadratic convergence rate in the solution procedure. The traditional finite element projection is used in both the static and dynamic cases. To avoid shear locking, selective reduced integration is used. |
