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Axially compressed composite cylindrical shells can attain multiple bifurcation points in their post-buckling procedure because of the natural transverse deformation restraint provided by their geometry. In this paper, the post-buckling analysis of functionally graded (FG) multilayer graphene platelets reinforced composite (GPLRC) cylindrical shells under axial compression is carried out to investigate the stability of such shells. Rather than the critical buckling limit, the focus of the present study is to obtain convergence post-buckling response curves of axially compressed FG multilayer GPLRC cylindrical shells. By introducing a unified shell theory, the nonlinear large deflection governing equations for post-buckling of FG multilayer GPLRC cylindrical shells with wide range of thickness are established, which can be easily changed into three widely used shell theories. Load-shortening curves for both symmetric and asymmetric post-buckling modes are obtained by Galerkin's method. Numerical results illustrate that the present solutions agree well with the existing theoretical and experimental data. The effects of geometries and material properties on the post-buckling behaviours of FG multilayer GPLRC cylindrical shells are investigated. The differences in the three shell theories and their scopes are discussed also.

Post-buckling analysis of functionally graded multilayer graphene platelet reinforced composite cylindrical shells under axial compression