Thermal buckling and postbuckling of porous FGM beams with elastically restrained ends resting on nonlinear elastic foundations

The combined influences of porosity, elasticity of tangential end constraints, nonlinear elastic foundations and initial geometrical imperfection on the buckling and postbuckling of functionally graded material (FGM) beams under uniform temperature rise are investigated in this paper. The pores are distributed into FGM according to the even and uneven types. The properties of constituent materials are assumed to be temperature-dependent and effective properties of porous FGM are determined using a modified rule of mixture. Two ends of beams are assumed to be simply supported or clamped and under tangentially elastic constraints. Equilibrium equations are derived based on Timoshenko beam theory taking into account the von Kármán nonlinearity, initial geometrical imperfection and interactive pressure from nonlinear elastic foundation. Analytical solutions are assumed and Galerkin method is used to obtain the expressions of buckling loads and nonlinear load–deflection relation. An iteration process is adopted to determine the critical buckling temperatures and postbuckling temperature–deflection curves. Parametric studies are carried out to analyze the effects of porosity, degree of in-plane constraints of ends, out-of-plane boundary conditions, imperfection, slenderness ratio and elastic foundations on the thermal buckling and postbuckling behaviors of porous FGM beams.