A size-dependent quasi-3D isogeometric model for functionally graded graphene platelet-reinforced composite microplates based on the modified couple stress theory

The paper presents a size-dependent model based on the NURBS basis functions integrated with quasi three-dimensional (quasi-3D) shear deformation theory and the modified couple stress theory (MCST) for free vibration and buckling analyses of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) microplates. The quasi-3D shear deformation theory, which only includes four unknown variables, considers the bending, shear deformations and thickness stretching effect. To consider length scale effect, a material length scale parameter (MLSP) is added into the classical continuum theory. A rule of mixture is used to compute the effective density mass and Poisson's ratio, while the Young's modulus is determined according to the Halpin-Tsai model. The uniform and functionally graded distributions of graphene platelets (GPLs) are considered. The discretize governing equations are obtained by applying the principle of virtual work. Numerical validations are performed to evaluate effects of geometrical parameters, boundary conditions, material length scale parameter and weight fraction on natural frequencies and buckling load of the microplates. As shown in numerical results, it can be concluded that a rise of natural frequency and buckling load of multilayer FG GPLRC microplates is observed by using the MCST. Besides, the classical quasi-3D model is recovered when MLSP equals to zero.