Mechanical properties of group IV single-walled nanotubes: a finite element approach based on the density functional theory.In this article, the density functional theory is applied to characterize the mechanical properties of single-walled nanotubes of group IV of the periodic table.  These materials include carbon nanotube, silicon nanotube, germanium nanotube, and stanene nanotube.  (10,10) armchair nanotube is selected for the investigation.  By establishing a link between potential energy expressions in molecular and structural mechanics, a finite element approach is proposed for modeling nanotubes.  In the proposed model, the nanotubes are considered as an assemblage of beam elements.  Young's modulus of the nanotubes is computed by the proposed finite element model.  Young's modulus of carbon, silicon, germanium, and tin nanotubes are obtained as 1029, 159.82, 83.23, and 83.15 GPa, respectively, using the density functional theory.  Also, the finite element approach gives the values as 1090, 154.67, 85.2, and 82.6 GPa, respectively.  It is shown that the finite element model can predict the results of the density functional theory with good accuracy.
C