  Carbon nanotubes (CNTs) are principal constituents of nanocomposites and
nano-systems. CNT size-dependent response assessment is therefore a topic of
current interest in Mechanics of Advanced Materials and Structures. CNTs are
modeled here by a variationally consistent nonlocal strain gradient approach
for Timoshenko nano-beams, extending the treatment in [Int. J. Eng. Science 143
(2019) 73-91] confined to slender structures. Scale effects are described by
integral convolutions, conveniently replaced with differential and boundary
nonlocal laws. The theoretical predictions, exploited to analytically estimate
the reduced Young elastic modulus of CNTs, are validated by molecular dynamics
simulations.
