Semi-analytical postbuckling analysis of polymer nanocomposite cylindrical shells reinforced with functionally graded graphene platelets

In this study, the postbuckling analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical shells is presented. The continuous uniform and functionally graded distribution of GPLs is considered through the thickness direction of the shell. In order to present the effective mechanical properties of GPL-reinforced composites the modified Halpin-Tsai micromechanical model is taken into account. On the basis of first-order shear deformation shell theory and von-Karman geometrically nonlinear relations, the nonlinear governing equations are present in the context of the variational formulation. Employing the Fourier series and variational differential quadrature (VDQ) numerical approach, the semi-analytical solution methodology is further presented. The pseud arc-length continuation method in conjunction with a load disturbance approach was utilized to solve the nonlinear governing equations and trace the postbuckling path. Note that based on the proposed formulation, the mode changes and secondary buckling can be considered through the postbuckling path. The results indicate that in addition to geometrical parameters, distribution patterns and weight fractions of GPLs have significant effects on the buckling and postbuckling characteristics of FG-GPLRC cylindrical shells.