An isogeometric formulation for free vibration and buckling analyses of FG graphene platelets-reinforced porous beams based on a two-variable shear deformation theory

The paper presents an isogeometric study for free vibration and buckling behaviors of functionally graded (FG) porous nanocomposite beams reinforced by graphene platelets (GPLs) based on a two-variable shear deformation theory. It is assumed that porosities are dispersed by symmetric and asymmetric models. Besides, GPLs are distributed along the beam thickness both uniformly and nonuniformly. Based on the closed-cell Gaussian random field model and the Halpin-Tsai micromechanical scheme, the mechanical properties of the porous nanocomposite beams are evaluated. In the presented theory, a nonlinear variation for the transverse shear stress across the beam thickness is considered which satisfies shear stress free surface condition. The governing equations are derived using the Hamilton's principle and then discretized employing the isogeometric analysis (IGA) as an effective numerical method. It is shown that the proposed theory is very simple and efficient to analyze free vibration and buckling of the graphene platelet-reinforced porous composite (GPLRPC) beams.