The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory A Benzair, A Tounsi, A Besseghier et al. Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams

A nonlocal anisotropic elastic shell model of a microtubule (MT) has been established in this paper. The proposed model exactly expresses the persistence length, the growth rate for buckling and the buckling load which include the small scale effects in a closed form. The predicted results of our model indicate that the length-dependence of the persistence length is sensitive to the small scale effects when the length of the MT is short. The curves for the growth rate of a MT with the consideration of the small scale effects show that the larger the small scale parameter is, the larger the growth rate is. The buckling behavior of a MT with the consideration of the small scale effects and the filaments network surrounded the MT have been investigated, which presents the filaments network plays an important role in buckling behaviors of MTs.