Size-dependent buckling analysis of piezoelectric nanobeams resting on elastic foundation considering flexoelectricity effect using the stress-driven nonlocal model

Presented herein is a size-dependent Bernoulli–Euler beam model for the buckling analysis of piezoelectric nanobeams under electrical loading with the consideration of flexoelectricity influence. In order to capture size effects, the stress-driven model of nonlocal theory is utilized. Moreover, it is considered that the nanobeams are embedded in an elastic medium. According to a variational approach, the governing equations including nonlocal and flexoelectricity effects are obtained. Also, using the generalized differential quadrature technique, a numerical solution approach is proposed for calculating buckling loads of piezoelectric nanobeams with different boundary conditions. The effects of flexoelectricity, nanoscale and elastic foundation on the buckling behavior of nanobeams are studied through presenting some numerical examples.