Static and buckling analyses of carbon nanotubes (CNTs) are carried out with newly
developed nonlocal continuum models. Small-scale effects are explicitly derived
for bending deformation solutions for CNTs subjected to general flexural
loading first. Solutions via nonlocal continuum models are expressed by
simple terms related to scale coefficients in addition to remaining terms via
local continuum models in which the simplicity of the nonlocal continuum
models is clearly observed. Discussions on various derivations of Young’s
modulus for CNTs from existing experimental work in the literature are
provided, revealing the applicability of the nonlocal continuum models. In
addition, a simple equation for the buckling load of CNTs with various general
boundary conditions subject to axial loading via the nonlocal elastic beam
model is explicitly derived for instability analysis. The results of this research
provide benchmark solutions for the response of CNTs subject to general
static loading, with small-scale effects modeled and revealed. Thus, the work
has great potential in studying mechanical properties of CNTs of various
sizes.
