Analytical Model for the Nonlinear Buckling Responses of the Confined Polyhedral FGP-GPLs Lining Subjected to Crown Point Loading

This paper focuses on the nonlinear buckling responses of the confined functionally graded porous (FGP) lining with polyhedral shapes reinforced by graphene platelets (GPLs). The FGP-GPLs polyhedral lining is surrounded tightly and rigidly by a medium. It is assumed that the interface is smooth between the lining and pipeline. The deformation of the lining may be represented by an admissible displacement expression when a point load is applied at the crown position. Afterward, the nonlinear governing equilibrium equations are obtained explicitly by combining the thin-walled shell theory and the principle of minimum potential energy. Solving the nonlinear governing equilibrium equations yields the critical buckling load. A comparison study is strictly completed with the other closed-form solutions when the polyhedral lining reduces to a circular one. In addition, an improvement factor is quantified to understand the effect of polyhedral shapes on the bending stiffness. Finally, the effects of polyhedral shapes, porosity coefficient, weight fraction, and geometric parameters of the GPLs are explored in terms of buckling load, hoop force, and bending moment.