Benchmark solutions for the material length scale effect in flexoelectric nanobeam using a couple stress theory

This paper is concerned with the derivation of the exact solutions for investigating the effect of material length scale on the static responses of the simply supported flexoelectric nanobeams considering a couple stress theory. The material length scale parameter estimates the coefficient linearly relating the rotational strain gradient to the couple stress in terms of the shear modulus of the beam material. Exact solutions for the displacements, stresses, electric displacements and the electric potential are derived while the beam is under closed circuit and open circuit conditions. Optimum value of the length parameter below which the response of the beam becomes independent of the couple stress effect has been determined while the beam acts as an actuator. The effect of this length parameter on the performance of the beam as an energy harvester has also been investigated for finding the optimum value of this length parameter. The benchmark results presented here may be useful for verifying further research and suggests that the flexoelectric nanobeams may be effectively exploited for developing advanced smart nanosensors and nanoactuators. (c) 2022 Elsevier Inc. All rights reserved.