2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18715The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333 (1992)\rbrack and shows to be content with the classic shell theory by which the Young's modulus, the Poisson ratio and the effective wall thickness of SWNTs are obtained as $Y=4.70$TPa, $ν=0.34$, $h=0.75{\rm Å}$, respectively. The elasticity of a multi-walled carbon nanotube (MWNT) is investigated as the combination of the above SWNTs of layer distance $d=3.4 {\rm Å}$ and the Young's modulus of the MWNT is found to be an apparent function of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$.4 pages, 1 figureMaterials ScienceMesoscale and Nanoscale Physicstext