Static analysis of flexoelectric nanobeams incorporating surface effects using element free Galerkin method

Abstract

The present study addresses the static bending analysis of a dielectric nanobeam subjected to external electro-mechanical loads, considering the flexoelectric coupling, surface elasticity (SE) and surface residual stresses (SRS). In the current model, surface energies corresponding to the surface elastic strains and a traction jump across surfaces, based on the generalized Youngs-Laplace model, have been included. The numerical analysis is carried out by deriving the element free Galerkin (EFG) model for the dielectric beam based on a moving least squares (MLS) interpolation of the field variables. The effect of SE and SRS over the flexoelectric behaviour of the dielectric nanobeam are thoroughly examined here. The contrary effects of SE over the converse and direct flexoelectric behaviour is noted here. The effect of the SRS is observed to be dependent on the electrical field gradients. The present study reveals the significance of the SE and SRS for analysis involving flexoelectric behaviour in nano-sensors and actuators.