Bending and buckling behavior analysis of the carbon nanotubes reinforced composites Timoshenko beams

Bending and buckling behavior of the macro CNTRCs (carbon nanotubes reinforced composites) beam was studied considering the scale effect of CNTs (carbon nanotubes). Based on the EMT (Eshelby-Mori-Tanaka) method and using nonlocal theory to characterize the scale effect of CNTs, the nonlocal EMT constitutive model was established. According to the Timoshenko beam theory, the static differential equations and boundary conditions of CNTRCs beams were derived through Hamilton principle. Bending response and ultimate buckling load of CNTRCs beams at S-S (simply supported) edges were obtained and compared with the literature to verify the correctness of the proposed model and solution method. Influences of the scale effect parameters and volume fraction of CNTs and the slenderness ratio of composite beams on the bending response and ultimate buckling load of S-S CNTRCs beams were analyzed. Results show that the equivalent stiffness of the CNTRCs beam is weakened by considering the scale effect of CNTs, and the volume fraction of CNTs and the scale effect parameter both have a great impact on the bending response and ultimate buckling load of the CNTRCs beam with a large slenderness ratio.