Nonlinear Buckling Analysis of nonlocal Boron Nitride Timoshenko nano beam based on Modified couple stress theory using DQM

In this article, nonlinear buckling analysis of nonlocal boron nitride Timoshenko nano beam on elastic foundation based on Modified couple stress theory, nonlocal elasticity Eringen’s model, and Von karman nonlinear geometry theory are investigated. The governing equation of motion and boundary conditions based on Hamilton’s principle are obtained. To solve the governing equation of motion, the differential quadrature method (DQM) is used to obtain the critical buckling load for two edges simply supported
(S-S) and simply supported-clamped (S-C) boundary conditions. The results of this research are compared with the obtained results by Murmu et al. that there is a good agreement between them. Finally, the effects of various parameters such as nonlocal Eringen’s parameter, slenderness ratio of nano beam, elastic foundation constants, electric field, temperature changes and material length scale parameter on the nonlocal critical buckling load of Timoshenko nano beam are illustrated. The results show that with increasing nonlocal parameter, slenderness ratio, electric field, and temperature changes, the critical buckling load decreases, while this results vice versa for elastic foundation constants and material length scale parameter. The critical buckling load for S-S boundary condition is lower than that of for S-C boundary condition.