buckling of functionally graded beams with rectangular and annular sections subjected to axial compression

the current study presents a new analytical method for buckling analysis of rectangular and annular beams made up of functionally graded materials with constant thickness and poisson’s ratio. the boundary conditions of the beam are assumed to be simply supported and clamped. the stability equations were obtained by using conservation of energy. the critical buckling load and first mode shape were obtained using variational calculus method. increasing in buckling capacity and improvement in the behavior of functionally graded beams in comparison to homogenous beams have been investigated. after simplifying results, duffing differential equation for homogeneous beam without oscillations was obtained and validity of this new work was proved.