Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects

This paper uses the finite element method to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, in which the flexoelectric effect is taken into consideration. The finite element formulations are established by employing a new type of shear deformation theory, which does not need any shear correction factors, but still accurately describes the stress field of the plate. The numerical results show clearly that the flexoelectric effect has a strong influence on the mechanical responses of the nanoplates. In particular, the normal stress distribution in the thickness direction is no longer linear when the flexoelectric coefficient is large enough, and this phenomenon differs completely from that of conventional plates. In addition, the distribution of the electric field and the polarization also depend on boundary conditions, which were not investigated in the published works.