Investigation of buckling behavior of carbon nanotube reinforced nanobeams according to nonlocal elasticity and elastic foundation effects

In this study, the buckling behavior of carbon nanotube (CNT) reinforced nanobeams on an elastic foundation is investigated using the nonlocal elasticity theory and nonlocal finite element method within the framework of Euler-Bernoulli beam theory. The effects of CNT volume fraction, nonlocal parameter, elastic foundation parameter and length-to-thickness ratio on the critical buckling load are analyzed. CNT reinforced nanobeam is modeled considering short and long CNT reinforcements, and mechanical properties are determined by the rule of mixtures. To determine the critical buckling loads of CNT reinforced nanobeams, stiffness matrices and force vectors, including nonlocal effects, are derived based on the Euler-Bernoulli beam theory and analyses are carried out accordingly. The results show that increasing the CNT volume fraction significantly increases the critical buckling load, suggesting that CNTs play an essential role in strengthening the nanobeams. On the other hand, the nonlocal parameter negatively affects the critical buckling load and decreases the buckling strength of the nanobeam. However, the effect of the nonlocal parameter on the buckling strength is negligible. The elastic foundation parameter positively affects the critical buckling load and increases the buckling resistance. This finding indicates that the elastic foundation plays an important role in improving the structural stability of the nanobeams. The length-to-thickness ratio is another important parameter, indicating that long and thin nanobeams are more prone to buckling and the critical buckling load decreases with increasing this ratio. Since the effects of the above-mentioned four parameters on the buckling strength were determined using the finite element method, the results obtained will guide the subsequent numerical modeling studies of nano-sized beams.