Static Buckling Behavior of FGM Timoshenko Beam Theory Resting on Winkler Elastic Foundation

Basing on the Timoshenko beam theory, the static buckling behavior of functionally graded materials (FGM) beam exposed to axial force resting on Winkler elastic base is investigated. Using a power-law distribution, mechanical properties of the FGM beam such as shear modulus and Young’s modulus are supposed to differ in the thickness direction. Also, the Poisson ratio value can be considered constant in the thickness direction. This term, by applying the total potential principle, the governing equations are derived. According to the Navier-type solution manner the load of critical buckling is employed for simply supported beam. The effects of spring constant and power-law exponent of FGM on the critical buckling load are discussed. The results obtained by numerical methods show an excellent agreement through comparison with the results available in the previous studies. Furthermore, the critical load of buckling decreases as the slenderness ratio and the power-law index values increase.