Geometrically-exact sandwich shells: The static case

The present formulation offers a general method for analyzing the static re sponse of geometrically-exact sandwich shells undergoing large deformation. The layer directors at a point in the reference surface are connected to e ach other by universal joints, and form a chain of rigid links. Finite rota tions of the directors in every layer are allowed, with shear deformation i ndependently accounted for in each layer. The thickness and the length of e ach layer can be arbitrary, thus allowing the modeling of an important clas s of multilayer structures having ply drop-offs. The present formulation is thus suitable to model shell structures with patches of constrained viscoe lastic materials or of piezoelectric materials. The nonlinear weak form of the governing equations of equilibrium is constructed here, and then the li nearization of the weak form and the associated inextensible directors upda te are derived, leading to a symmetric tangent stiffness matrix. A Galerkin finite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations, in which the interpolation ac counts for the finite rotations of the directors. We present extensive nume rical examples, including sandwich shells with three identical layers and p ly drop-offs, to illustrate the applicability and versatility of the propos ed formulation. (C) 2000 Elsevier Science S.A. All rights reserved.