Nonlinear Bending Analysis of Nanocomposite Beams Reinforced by Graphene Platelets using Harmonic Differential Quadrature Method

The nonlinear bending analysis of a composite beam reinforced by graphene platelets (GPL) nanofillers having nonuniform distribution through the thickness, is presented. Governing nonlinear differential equations are derived based on the first order shear deformation theory with the aid of minimum potential energy principle. The nonlinear differential equations are solved using harmonic differential quadrature method (HDQM). The modified Halpin-Tsai model is implemented to determine the effective Young’s modulus of graphene platelet reinforced composite (GPLRC) beams. Moreover, the rule of mixture is used for definition of the effective Poisson’s ratio. At first, conventional nanocomposite beams are studied for evaluation of the applicability of the proposed method for nonlinear bending analyses. Then for the beams reinforced by graphene platelets, the effects of some parameters including boundary conditions, number of layers, weight fraction and distribution pattern of graphene platelet on the nonlinear bending characteristics of the GPLRC beams, are investigated. This study shows the capability of the proposed method to solve the nonlinear problems and to get the beams behavior under bending loading. In addition, by increasing the weight fraction of graphene platelets in the beam, the bending strength of the beam improves and the beam deflection decreases. Moreover, increasing the number of layers for GPLRC tends to smoother variation of stress through the beam thickness.