Bending stress analysis of a piezoelectric nanoplate with flexoelectricity under inhomogeneous electric fields

Flexoelectricity has been found as an unneglectable electro-mechanical coupling effect in micro/nanoscale dielectric materials. We present a stress function based bending stress analysis method for piezoelectric nanoplate under inhomogeneous electric fields considering both piezoelectric effect and flexoelectric effect in this work. A Ritz type solution procedure is developed by means of the quasi-three dimensional stress functions with the initial assumption of out-of-plane stress functions. A standard eigenvalue problem is constructed to obtain the general solutions of governing equations which are obtained by the principle of complementary virtual work. For the numerical analysis, we investigate the bending stresses in laminated piezoelectric nanoplate with or without flexoelectricity and the size-dependent effect on the bending stress distributions. Two kinds of inhomogeneous electric fields are considered for discussion. The present work is expected to help understanding the influence of flexoelectric effect on the bending stress distributions for the future design and application of piezoelectric nanostructures.