Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations

In the present study, thermal buckling and post-buckling analysis of Functionally Graded Material (FGM) Timoshenko beams resting on a non-linear elastic foundation are examined. Thermal and mechanical properties of the FGM media are considered to be functions of both temperature and position. Theory of Timoshenko beam combined with von-Karman's strain–displacement relations are applied in virtual work principle to obtain the system of non-linear equilibrium equations. Different types of boundary conditions such as clamped, simply supported, and rolled edges are assumed for edge supports. Generalized Differential Quadrature Method (GDQM) is employed to discrete the equilibrium equations in space domain. Post-buckling equilibrium paths are depicted for different values of the power law index, non-linear elastic foundation parameters, boundary conditions, thermal loading type, and slenderness ratio. It is found that depending on the boundary conditions and the type of thermal loading, the response of the structure may be of the bifurcation-type or unique stable path.

► The GDQM is adopted to study the geometrically non-linear behavior of FGM beams.
► Temperature dependency has a great effect on buckling temperature, buckled shape and post-buckling equilibrium path.
► Boundary conditions and thermal loading type have great influences on equilibrium path of the beam.
► Elastic foundation has great effects on critical buckling temperature and buckled shape of the beam.