Perturbation Method for Thermal Post-buckling Analysis of Shear Deformable FG-CNTRC Beams with Different Boundary Conditions

This research aims to analyze the thermal buckling and post-buckling of carbon nanotube (CNT) reinforced composite beams. It is assumed that the beam is rested on a nonlinear elastic foundation which contains the Winkler spring, shear layer, and nonlinear spring. Distribution of CNTs across the thickness may be non-uniform which results in a functionally graded media. The elastic properties of the beam are evaluated using the refined rule of mixtures which contains efficiency parameters. Temperature dependency of the constituents is also taken into account. Using three different beam models, namely, first-order, third-order, and sinusoidal theories, the governing equations for the composite beam are established. Three different types of edge supports are considered which are pinned–pinned, clamped–clamped, and clamped–roller. With the aid of the two-step perturbation technique, closed-form expressions are extracted to obtain the elevated temperature as a function of the post-buckling deflection in the beam. Results of this study are compared with the available data in the literature. After that, new results are given to discuss the effects of important factors such as foundation parameters, geometrical characteristics, boundary conditions, the CNT volume fraction, and CNT pattern. It is shown that the critical buckling temperature of pinned–pinned and clamped–roller beams is the same while their post-buckling responses are totally different.