In this paper, using modified couple stress theory, a new cylindrical shell
element is introduced. Here, using modified couple stress theory in place of classical
continuum theory, and using shell model in place of beam model which has been
used in previous research, vibrational behavior and buckling behavior of nanotubes
is investigated via the finite element method. In addition, the new cylindrical shell
element is defined, the mass-stiffness matrix is developed, and the use of the super
element and size-dependent finite element formulation together with shell element
is extended to more precisely account for nanotube vibration and buckling. The new
cylindrical shell element has been developed based on super element’s shape function.
In special cases, in order to investigate the application of the equations developed, the
cylindrical nano-shell bending displacement is studied using modified couple stress
cylindrical shell element and the results are validated using the analytical method. In
addition, the effects of parameters such as length scale parameter, length, and thickness
on cylindrical shell displacement are investigated. The results have indicated using
the super element considerably reduces the amount of computations and analysis
time in comparison with the use of molecular dynamic simulation.