Analytical analysis of buckling and post-buckling of fluid conveying multi-walled carbon nanotubes

In this work, buckling and post-buckling analysis of fluid conveying multi-walled carbon nanotubes are investigated analytically. The nonlinear governing equations of motion and boundary conditions are derived based on Eringen nonlocal elasticity theory. The nanotube is modeled based on Euler-Bernoulli and Timoshenko beam theories. The Von Karman strain-displacement equation is used to model the structural nonlinearities. Furthermore, the Van der Waals interaction between adjacent layers is taken into account. An analytical approach is employed to determine the critical (buckling) fluid flow velocities and post-buckling deflection. The effects of the small-scale parameter, Van der Waals force, ends support, shear deformation and aspect ratio are carefully examined on the critical fluid velocities and post-buckling behavior.