Buckling and Post-buckling Analysis of FG-CNTRC Beams: An Exact Closed Form Solution

The present work derives the exact analytical solutions for buckling and post-buckling analysis of nano-composite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on the Euler-Bernoulli beam theory and principle of virtual work. The reinforcements are considered to be aligned in the polymeric matrix either uniformly distributed (UD) or functionally graded (FG) distributed through the thickness direction of the beam. In FG beams, material properties vary gradually along the thickness direction. The effective material properties of the nano-composite beam are predicted based on the extended rule of mixture. Also, by applying von Kármán assumptions, the geometric nonlinearities are taken into consideration. The developed governing equations are solved by utilizing analytical methods and exact closed form solutions for buckling and post-buckling loads of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam with different boundary conditions are obtained. By comparing the present post-buckling load results with the ones reported in the literature, the accuracy and reliability of the current method are demonstrated. Eventually, the numerical results are provided and the effects of CNTs distribution, CNTs volume fraction, slenderness ratio, maximum deflection of the beam and boundary conditions on the post-buckling characteristics of the CNTRC beam are discussed.