Thermal buckling analysis of a saturated porous thick nanobeam with arbitrary boundary conditions

Abstract This manuscript aims to research the thermal buckling of saturated thick (Timoshenko) nanobeams under different boundary conditions using Fourier sine and cosine series for the first time. The equation of motion and related boundary conditions are derived by using the kinematic relations of shear deformation (Timoshenko beam) theory to contain the shear effect. Consequently, the rotary inertia and transverse shear strain are considered through the mathematical analysis. Fourier sine and cosine series are used to compute the critical buckling temperature of the thick saturated nanobeam with deformable boundaries. To check the validity of the presented method, the developed Fourier series method with Stokes’ transformation is applied to validate the thermal buckling of rigidly supported thick nanobeam by giving the proper values to spring parameters. In particular, the presented analytical procedure can also be degenerated to the thin Euler-Bernoulli nanobeam by assigning proper value to shear correction factor. Influence of the deformable boundary conditions, small scale parameter and the saturated parameter (porosity coefficient) on the thermal buckling temperature are discussed in detail. The theoretical models and eigen-value formulation presented herein should also be served to solve the thermal stability response of different micro sized-structures with various temperature effects and supporting conditions.