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

Abstract

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 der Waals 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.

Study of the Flow and Heat Transfer of a Viscoelastic Fluid Using Hybrid Neural Network-Particle Swarm Optimization (Hnnpso)

“…In recent years, some new artificial methods have been introduced to solve differential equations arising from engineering problems [28][29][30][31][32][33][34]. Noghrehabadi et al [30] studied the buckling shape of a multi-wall carbon nanotube cantilever. The buckling of the nanotube follows a fourth-order non-linear boundary value differential equation.…”

“…Afterward, Artificial Bee Colony (ABC) algorithm was employed to adjust the power series variables to satisfy the governing differential equation in the domain of the solution. Using the power series as a trial function and ABC as the training method, Noghrehabadi et al [30] have successfully reported a semianalytic solution in the form of a power series for the buckling shape of the nanotube.…”

“…The approaches utilized in [28][29][30][31][32][33][34] can be considered as hybrid methods. An advantage of the hybrid method is that it can provide an analytical approximation to a wide class of nonlinear equations without the computational difficulties of HAM.…”

“…The hybrid method is simple and powerful to solve different differential equations, while the results have excellent agreement with numerical methods. In the previous studies [28][29][30][31][32][33][34], the hybrid method was applied for a single high order differential equation. Although there are various practical systems of differential equations, there has been no attempt to develop the hybrid method to the case of the system of high order differential equations.…”

Numerical solution to nonlinear biochemical reaction model using hybrid polynomial basis differential evolution technique

“…In recent years many authors have used nature and biologically inspired based computation techniques as an alternative for solving nonlinear ODEs arising in diverse fields of engineering and science [6][7][8][9][10][11][12][13][14][15][16]. Very recently Malik et al [6,7] employed heuristic technique based on hybrid genetic algorithm for numerically solving the nonlinear singular boundary value problems in physiology and the Bratu problem.…”