Postbuckling characteristics of nanobeams based on the surface elasticity theory

Abstract

In the present paper, an attempt is made to numerically investigate the postbuckling response of nanobeams with the consideration of the surface stress effect. To accomplish this, the Gurtin–Murdoch elasticity theory is exploited to incorporate surface stress effect into the classical Euler–Bernoulli beam theory. The size-dependent governing differential equations are derived and discretized along with various end supports by employing the principle of virtual work and the generalized differential quadrature (GDQ) method. Newton’s method is applied to solve the discretized nonlinear equations with the aid of an auxiliary normalizing equation. After solving the governing equations linearly, to obtain each eigenpair in the nonlinear model, the linear response is used as the initial value in Newton’s method. Selected numerical results are given to show the surface stress effect on the postbuckling characteristics of nanobeams. It is found that by increasing the thickness of nanobeams, the postbuckling equilibrium path obtained by the developed non-classical beam model tends to the one predicted by the classical beam theory and this anticipation is the same for all selected boundary conditions.