Buckling analysis of multi-span non-uniform beams with functionally graded graphene-reinforced foams

This paper conducts the buckling analysis of multi-span functionally graded (FG) beams reinforced by three-dimensional graphene foams (3D-GFs) restrained by elastic supports. The graphene foams are considered as graded variation in the thickness direction according to four different porosity distributions. The width and height of the non-uniform beams vary in the longitudinal direction in accordance with the power-law principle, and the multi-span beams consist of two types of optional beams. The governing equations of buckling behavior are derived based on the Timoshenko beam theory and the principle of virtual displacements, and solved by the discrete singular convolution (DSC) method. The purpose of this paper is to obtain the critical buckling load of FG 3D-GFs reinforced beams under the consideration of variable cross-section and multi-span beams with 2–4 spans. The effect of porosity coefficients, slenderness ratio, and spring constants on the buckling characteristic also are studied. The results suggest that the taper ratio of beams and the configuration of multi-span beams lead to remarkable changes in the critical buckling load of beams.