Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM

Nonlocal elasticity theory is a popular growing technique for the mechanical analyses of MEMS and NEMS structures. The nonlocal parameter accounts for the small-size effects when dealing with nano-size structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to investigate the stability response of SWCNT embedded in an elastic medium. For the first time, both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the (SWCNT) with the surrounding elastic medium. A differential quadrature approach is utilized and numerical solutions for the critical buckling loads are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter and aspect ratio of the SWCNT on the critical buckling loads are analyzed and discussed. The present study illustrates that the critical buckling loads of SWCNT are strongly dependent on the nonlocal small-scale coefficients and on the stiffness of the surrounding medium.