Nonlinear static and dynamic finite element analysis of multilayer shell structures

Firstly, the geometrically-exact sandwich shell formulation is developed to analyze sandwich shells undergoing large deformation. Finite rotation of the director in each layer is allowed, with shear deformation independently accounted for in each layer. The thickness and the length of each layer can be arbitrary, thus allowing the modeling of multilayer structures having ply drop-offs. The weak form of governing equations is constructed, and the linearization and inextensible directors update are derived. Numerical examples on elastic sandwich plates are presented to illustrate salient features of the formulation.; Furthermore, we present a low-order solid-shell element formulation—having only displacement degrees of freedom (dofs) (i.e., without rotational dofs)—that has an optimal number of parameters to pass the plate patch tests (both membrane and out-of-plane bending), thus allowing for efficient and accurate analyses of large deformable multilayer shell structures. The formulation is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing assumed strain (EAS) tensor, with improved in-plane and out-of-plane bending behaviors (Poisson thickness locking). Shear locking and curvature thickness locking are treated using the Assumed Natural Strain (ANS) method. We provide an optimal combination of the ANS method and the minimal number of EAS parameters to pass the out-of-plane bending patch test and treat the locking associated with (nearly) incompressible materials. The energy-momentum (EM) conserving algorithm for the current element is presented. Two nonlinear 3-D material models are applied directly without requiring the enforcement of the plane-stress assumption. Moreover, we present a low-order accurate piezoelectric solid-shell element formulation for piezoelectric sensors and actuators used in active shell structures. Numerical examples involving static analyses and implicit/explicit dynamic analyses of multilayer shell structures having a large range of element aspect ratios for both material and geometric nonlinearities are presented. Numerical examples involving static analyses and active vibration control of piezoelectric shell structures are also presented. The developed element formulations are accurate and efficient in modeling and analyzing general nonlinear multilayer composite shell structures.