Spiral Buckling of Torque and Axial Force-Prestressed Nanotubes

The 3D problem became the basis for modeling the critical states and shapes of bifurcation buckling of longitudinal force and torque-stressed nanotubes. The homogeneous system of ordinary differential equations built on the theory of rectilinear elastic rods was formulated. Its nontrivial solutions result in critical torque or longitudinal force levels at preset values of one of those entities. The closed-form solutions under chosen boundary conditions indicate that only spatial curves as variable diameter spirals with the left or right orientation consistent with that of the torque can be stability loss modes. The spiral is single-wound without longitudinal force, regardless of the tube length. If the tube is also prestressed with axial compression or tension, the bifurcation spiral is multi-wound; its number is determined by the eigenvalue of the equations, which increases with growing forces and tube length.