Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

ABSTRACTBuckling and post-buckling thermomechanical deformations of a functionally graded material (FGM) Timoshenko beam resting on a two-parameter non-linear elastic foundation and subjected to only a temperature rise have been numerically investigated with the shooting method. The material properties are assumed to vary only in the thickness direction according to a power law function. Through-the-thickness temperature distribution is determined by numerically solving the one-dimensional heat conduction equation. Geometric non-linearities in the strain-displacement relations and the non-linear traction-displacement relations at the interface between the beam and the foundation are considered. For clamped-clamped and immovable simply supported beams, critical values of the ratio of temperatures of the top and the bottom surfaces of the beam for transitions in buckling modes to occur are determined. Post-buckled equilibrium paths and configurations of the heated FGM beam are illustrated for different valu...