On the geometrically nonlinear analysis of sandwich shells with viscoelastic core: A layerwise dynamic finite element formulation

The objective of this work is to present a finite element formulation for dynamic analysis of sandwich shells with viscoelastic core under large deformation. The present study is based on an incremental updated Lagrangian approach together with the Newmark integration scheme. The viscoelastic constitutive model which is used to define the behavior of the core, comes from the Riesz theorem and the corresponding creep functions are estimated using Dirichlet-Prony series. Also, the viscoelastic deferred strain is derived in an appropriate incremental form using the state variables. The employed layerwise shell element which is based on zig-zag theory has eight nodes on its mid layer. What's more, in addition to three translational and two rotational degrees of freedom per node, the upper and lower layers are allowed to rotate independently relative to their neighbor layers. Thus, the damping effect of the viscoelastic core could be well described within the shear deformable displacement field. The presented nonlinear formulation is then implemented to a nonlinear finite element program to be appraised by solving different kinds of problems. The obtained numerical results correlate well with those available in the literature.