Flexoelectricity effect on the size-dependent bending of piezoelectric nanobeams resting on elastic foundation

A numerical investigation is performed to examine the static bending behavior of piezoelectric nanoscale beams subjected to electrical loading, considering flexoelectricity effects and different kinematic boundary conditions. The nanobeams are modeled by the Bernoulli-Euler beam theory, and the stress-driven integral nonlocal model is used in order to capture size influences. It is also considered that the nanobeams are embedded in an elastic medium. The Winkler and Pasternak elastic foundation models are used for simulating the substrate medium. Based upon Hamilton's principle and the electrical Gibbs free energy, the governing equations are derived which are then numerically solved via a finite difference-based method. Numerical results are presented to study the influences of nonlocal, flexoelectric and Winkler/Pasternak parameters on the bending response of piezoelectric nanobeams under various end conditions.