Analysis of flexoelectric response in nanobeams using nonlocal theory of elasticity

This paper is concerned with the derivation of exact solutions for the static responses of simply supported nonlocal flexoelectric nanobeams. Considering both the direct and the converse flexoelectric effects, and employing the nonlocal theory of elasticity, the governing equations and the associated boundary conditions of the beams are derived to obtain the exact solutions for the displacements, nonlocal stresses and the electric potential in the beams. Both the direct and the converse flexoelectric effects are influenced by the nonlocal parameter. Active beams significantly counteract the applied mechanical load by virtue of the converse flexoelectric effect. The normal and the transverse shear deformations in the beams are affected by the converse flexoelectric effect resulting in the coupling of bending and stretching deformations in the beams even if the beams are homogeneous. Because of the consideration of the nonlocal theory of elasticity, the nonlocal stiffness of the beam appears to be less than the classical stiffness of the beam. The nonlocal elasticity does not influence the stresses of the passive beam while the nonlocal stresses in the active beam due to converse flexoeletric effect are less than the local or classical stresses in the active beam. The benchmark results presented here may be useful for verifying the numerical model and experimental results for nonlocal flexoelectric nanobeams. The present study suggests that the flexoelectric nanobeams may be effectively exploited for developing advanced smart nanosensors and nanoactuators. The research work carried out here also conveys that the nonlocal theory of elasticity must be employed for accurate analysis of flexoelectric solids.