Postbuckling Analysis of a Nonlocal Nanorod Under Self-Weight

Abstract

This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.