Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models

Nonlocal elastic beam and shell models are developed and applied to investigate the small scale effect on buckling analysis of carbon nanotubes (CNTs) under compression. General and explicit solutions are derived and expressed in terms of the solutions via local or classical elastic models, in which the scale effect is not accounted, to reveal the small scale effect on CNTs buckling results. The dependence of the scale effect with respect to the length, radius, and buckling modes of CNTs is clearly established and observed from the universal solutions derived in the manuscript. It is clearly seen from the results that the buckling solutions for CNTs via local continuum mechanics are overestimated and hence the scale effect is indispensable in providing more accurate results for mechanical behaviors of CNTs via continuum mechanics.