A Hybrid Power Series Artificial Bee Colony Algorithm to Obtain a Solution for Buckling of Multiwall Carbon Nanotube Cantilevers Near Small Layers of Graphite Sheets

A hybrid power series and artificial bee colony algorithm (PS-ABC) method is applied to solve a system of nonlinear differential equations arising from the distributed parameter model of multiwalled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. The intermolecular forces are modeled using van derWaals forces. A trial solution of the differential equation is defined as sum of two polynomial parts. The first part satisfies the boundary conditions and does contain two adjustable parameters. The second part is constructed as not to affect the boundary conditions, which involves adjustable parameters. The ABC method is applied to find adjustable parameters of trial solution (in first and second part). The obtained results are compared with numerical results as well as analytical solutions those reported in the literature. The results of the presented method represent a remarkable accuracy in comparison with numerical results. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular forces, as important parameters in pull-in instability of MWCNT actuator, are evaluated by obtained power series.