A size-dependent nonlinear finite element free vibration analysis of multilayer FG-GPLRC toroidal micropanels in thermal environment

A nonlinear finite element model based on the modified strain gradient theory (MSGT) in combination with the first-order shear deformation theory (FSDT) of shells for the free vibration of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal micropanels is developed. The nine-noded shell elements with five degrees of freedom per node are used to accurately simulate thin as well as moderately thick toroidal micropanels without shear locking phenomena. In addition to initial thermal stresses, the influences of nonlinear elastic foundation and the elastic rotational springs at the micropanel edges are considered. The formulation and corresponding computer codes are validated by performing convergence study and doing comparison studies with some existing results in the literature. Then, the impacts of amplitude ratio, geometric parameters, ratio of thickness-to-material length scale parameter (MLSP), temperature rise, coefficients of elastic foundation and rotational springs, and different GPLs distribution patterns on the nonlinear vibrational behaviors of the multilayer FG-GPLRC toroidal micropanels are investigated. The results show that the size dependence of material properties increases the impact of geometric nonlinearity on the vibrational behavior of the micropanels. In addition, it affects the nonlinear vibrational behavior more than the linear one in a widespread range of thickness-to-MLSP ratio.