In the present study, critical bending buckling moment of perfect and defected single-walled carbon nanotubes (SWCNTs) have been investigated using structural mechanics approach. Nonlinear finite element analysis is designed for determination of critical bending buckling moment and postbuckling behaviour of SWCTs. For applying pure bending moment, a new displacement-control procedure based on large deformation theory is employed to the ends of the SWCNT incrementally. By doing so, moment-curvature diagram could be derived during pure bending loading. In case applying moment reaches a critical value, bending buckling onset of SWCNT is appeared and critical bending moment and critical bending curvature is determined. In the following, the postbuckling behaviour of defected and perfect SWCTs is revealed. The effects of SWCNT aspect ratio (length/diameter) and defect types (vacancies and Stone-Wales) on the critical bending moment and critical bending curvature are studied for zigzag nanotubes. For perfect SWCNTs, results have good agreement with those in the literature. Also, it is found that vacancies defect decreases the critical bending moment more than Stone-Walls defect.
In last decade, structural mechanics (SM) approach has been one of the most known and effective tools for the determination of the mechanical properties of carbon nanotubes (CNTs) such as elastic modulus, shear modulus, natural frequency, and critical axial buckling strain. Considering increasing applications of CNTs as resonators at low and high temperatures, a new temperature-dependent structural mechanics model is presented here. The proposed model can be utilized to predict the effect of temperature on the mechanical response of CNTs as functional resonators. Mechanical and geometrical properties of equivalent beam element are correlated to the CNT’s coefficient of thermal expansion (CTE). Owing to elaborate series of finite element simulations, the frequency shift of a CNTs-based mass sensor with different attached mass and aspect ratio in temperature range of 0–1600 K is calculated. Afterwards, the critical buckling temperature of CNTs-based mass sensor due to increasing the axial force by changing ambient temperature is obtained. Results show that decreasing the first natural frequency is clearly appeared by attaching a mass more than about 1 zg on the CNTs structure. In other words, CNTs can be used to detect particles with mass above 1 zg. Moreover, it is shown that the variation of CTE versus temperature is a critical parameter that influences the vibration and buckling behavior of CNTs-based mass sensors. Increasing temperature leads to decreasing natural frequency due to rising axial forces along the CNTs axis. As a result, the natural frequency approaches to zero when the temperature rises up to the critical buckling temperature. In addition, increase in temperature over the critical buckling temperature changes the mode shape of CNT vibration to the next mode shape.