Post-buckling behavior of lattice core sandwich cylindrical shell with functionally graded graphene platelets reinforced face layer resting on elastic foundation

This paper presents the buckling and post-buckling behavior of a sandwich shell with a lattice polymer core and nanocomposite face layer reinforced with graphene platelets. The rule of mixtures is used to determine the effective mechanical properties of graphene platelet-reinforced surfaces at different distributions along the thickness. The governing deflection equations are derived using high-order shear deformation theory and consider the effects of large deformations with nonlinear von Karman strain-displacement relationships. The elastic foundation is modeled using a two-parameter model developed by Winkler-Pasternak. A closed-form solution method utilizing the Ritz energy approach and Airy stress function is employed for solving nonlinear equations and identifying post-buckling paths under external mechanical forces, including radial compression and axial force. Method validation involves comparison with prior studies' results. The analytical solution explores various parameters, including graphene platelet volume fraction, distribution, lattice core geometric characteristics, and elastic substrate properties, on the buckling and post-buckling behavior of the cylindrical shell. Results indicate that, under axial compression, a moderately long cylindrical shell shows a snap-through equilibrium path after buckling.