Static, dynamic and buckling responses of random functionally graded beams reinforced by graphene platelets

This work proposes a multiscale numerical method that can be used to study the static, dynamic and buckling behavior of functionally graded (FG) beams reinforced with graphene platelets (GPLs), whose random gradation is achieved through tailoring the internal porosity and GPLs reinforcement, either along the transverse or the longitudinal direction. The multiscale numerical method consists of microscale homogenization and structural analysis: micromechanics homogenization methods are introduced to predict the elastic moduli of nano-composite layers with finite thickness along the transverse direction; Explicitly-expressed composite finite ele-ments are then developed through the proposed variational principle and Hamilton principle. In the meantime, the corresponding governing equations are derived for FG beams with Timoshenko theory. On this basis, the static bending deflection, fundamental frequency and critical buckling load of the FG beams are obtained through the proposed FG finite elements. The effectiveness and accuracy of the proposed method are verified against the numerical results in the existing literature and experimental results in 3D printing with good agreement. Based on the credence of the present method, the effects of boundary conditions, gradient distri-butions of GPLs and pores, microscopic parameters of GPLs and structural geometric dimension on the static and dynamic performance of the FG beams are systematically analyzed, where the bi-directional gradient distribution pattern corresponding to the GPLs along the thickness direction and the pore along the axial direction demon-strates the best improvement of both bending and dynamic performance.