Some approximate buckling solutions of triple-walled carbon nanotube

The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using the Euler─Bernoulli model. The present study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clamped-simply supported carbon nanotube. Using Bubnov─Galerkin and Petrov─Galerkin methods, the continuum model estimates the critical buckling load. The main advantage of these two approximate methods is to obtain a quick and valid result. The first and second Euler critical buckling loads decrease with the increase of length to outer diameter ratio for boundary conditions like simply-simply, clamped-clamped, and clamped-simply supported. Interestingly, the increase in the length to outer diameter ratio results in the rise in third Euler critical buckling for all three different boundary conditions. These two approximate methods provide reliable buckling load estimation using suitable polynomials.