The small-scale effect on critical buckling load has been investigated for single wall carbon nanotubes (SWCNT) with shear deformation theory using differential transformation method (DTM). The present buckling analysis considers the nonlocal continuum elasticity and Timoshenko beam
theory. The present semi-analytical method in evaluating the nonlocal critical buckling loads is faster and convenient as compared to its peers. Convergence study is carried out to determine the number of terms to be employed in the DTM computation. The present computed critical buckling loads
are in excellent agreement with the exact solutions reported in the literature. Further, effect of (i) nonlocal parameter (ii) various boundary condition (iii) size of the carbon nanotube and (iv) Timoshenko beam theory on the critical buckling load are studied. It is observed that nonlocal
parameters and nonlocal Timoshenko beam theory have significant influence on the critical buckling loads of nano size SWCNTs.
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