A variable ESL/LW kinematic plate formulation for free-vibration thermoelastic analysis of laminated structures

In this article, a fully-coupled thermoelastic formulation is developed to deal with the free-vibration analysis of multilayered plate composite and sandwich structure. Some advanced theories are obtained by expanding the unknown displacement variables along the thickness direction and using equivalent-single-layer (ESL) models, layer-wise (LW) models, and variable-kinematic models. The variable-kinematic models permit to reduce the computational cost of the analyses grouping some layers of the multilayered structure with ESL models and keeping the LW models in other zones of the multilayer. This model is here extended for the free-vibration analysis of fully-coupled thermomechanical problems. The used refined models are grouped in the Carrera unified formulation (CUF), and they accurately describe the displacement field and the temperature distributions along the thickness of the multilayered plate. The governing equations are derived from the principle of virtual displacement, and the finite element method (FEM) is employed to solve them. Isotropic plates, cross-ply composite plates, and sandwich structures with composite skins and simply-supported edges are analyzed. Various aspect ratios are considered. The results, obtained with different theories within CUF context, are compared with the elasticity solutions, and other higher-order analytical and FEM solutions given in the literature. From the results, it is possible to conclude that the plate element based on the CUF is very efficient in the study of thermomechanical problems of composite structures. The variable-kinematic models combining the ESL with the LW models, permit to have a reduction of the computational costs, respect with the full LW models, preserving the accuracy of the results.