Inhomogeneous Electric Field Induced Bending Stresses in Piezoelectric Medium with Flexoelectricity

Abstract

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. With the proper assumption of flexoelectric coefficients, the bending stresses are presented which are contributed by both flexoelectric effect and piezoelectric effect. The size effect on bending stresses is also investigated in this work and the size-dependent stress distributions are presented as demonstration.