The buckling of multiwalled carbon nanotubes under torsional load coupling with temperature change is researched. The effects of torsional load, temperature change, surrounding elastic medium, and van der Waals forces between the inner and outer nanotubes are taken into account at the same time. Using continuum mechanics, an elastic multishell model with thermal effect is presented for buckling of a multiwalled carbon nanotube embedded in an elastic matrix under thermal environment and torsional load. Based on the model, numerical results for the general case are obtained for the thermal effect on buckling of a multiwalled carbon nanotube under torsional load. It is shown that the buckling torque of a multiwalled carbon nanotube under a certain value of temperature change is dependent on the wave number of torsional buckling modes, and a conclusion is drawn that at room or lower temperature the critical torsional load for infinitesimal buckling of a multiwalled carbon nanotube increases as the value of temperature change increases, while at temperature higher than room temperature the critical torsional load for infinitesimal buckling of a multiwalled carbon nanotube decreases as the value of temperature change increases.
Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory
