Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection

Graphene reinforced composites have attracted a great deal of attention in recent years due to their outstanding mechanical properties. The present work focuses on the size-dependent postbuckling characteristics of functionally graded (FG) graphene platelets reinforced composite (GPLRC) multilayer microtubes containing initial geometrical imperfection. It is assumed that the distribution of GPL reinforcements in microtubes is uniform or layer-wise change across the radial direction, and five typical distribution patterns (i.e., UD, FG-X, FG-O, FG-V and FG-A) are considered. Based on the modified couple stress theory and a refined higher-order beam theory, the non-classical governing equations with the account of von K?rm?n geometrical non ?linearity for postbuckling analysis are derived by employing the principle of minimum potential energy and solved by using an analytical method. After validating the analytical solutions by comparing with results reported in the literature, the influences of various important parameters on the postbuckling of FG-GPLRC multilayer microtubes are investigated. It is found that the microstructure effect on the postbuckling behavior is significant when the outer radius of the microtube is comparable to the material length scale parameter. Moreover, the initial geometrical imperfection decreases the postbuckling load-carrying capacity at small deflection, but increases it at large deflection. Additionally, our results indicate that the FG-V distribution pattern produces the highest postbuckling load-carrying capacity for FG-GPLRC multilayer tubes, which differs from the cases for FG-GPLRC multilayer beams, plates and thin shells where the FG-X distribution pattern always has the best reinforcing effect. The present work could provide theoretical guidelines for the optimal design and safety assessment of graphene reinforced composite tubular structures, and may find potential application in microscale engineering devices and systems.