Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation

Abstract In this study, a NURBS formulation based on the four-variable refined plate theory (RPT) for free vibration , buckling and static bending analyses of multilayer functionally graded graphene platelets reinforced composite (FG GPLRC) plates, for the first time, is proposed. The distributions of graphene platelets (GPLs) in the polymer matrix either uniformly or non-uniformly including different patterns are considered. The Young’s modulus of the nanocomposites is predicted by the modified Halpin–Tsai model, while the Poisson’s ratio and density mass are implemented by the rule of mixtures. Governing equations are derived and the NURBS formulation is employed to obtain natural frequencies, critical buckling loads and deflections of multilayer FG GPLRC plates. Thanks to continuous higher-order derivatives of NURBS basis functions in isogeometric analysis (IGA), the present approximation is easy to satisfy the C1-continuty requirement of the RPT model. In addition, a rotation-free technique is applied to eliminate the bending and shear slopes in the case of clamped boundaries. Effects played by GPLs weight fraction, GPLs distribution patterns, number of layers, thickness-to-length ratio are investigated. Numerical results indicate that the inclusion of GPLs can significantly improve the stiffness of plates.