Buckling analysis of functionally graded Grover beams

The compact solution of buckling for a beam made of functionally graded material under axial loading is introduced. In this study, simply supported boundary conditions and Grover shear deformation theory are considered. The governing equations are derived using the principle of stationary potential energy, and these equations are solved by closed-form method. Finally, critical buckling load is investigated based on newest beam theory (Grover beam theory). The obtained results are compared with Timoshenko and Reddy beam theories. The effects of material compositions and slenderness ratios that lead to the considerable changes in buckling behaviors are investigated. Results of thisanalysis illustrate that first-order theory underestimates the amplitude of buckling, while Grover and Reddy shear deformation theories show very close results in the course of the critical buckling load.