Classical continuum models are unable to describe the size effect in nano/micro structures, even though this effect is observed experimentally. Therefore, modified continuum models are frequently applied for the investigation of nanomechanics due to their computational efficiency and capability of providing accurate results which are comparable to the atomistic models. In this paper, the Mindlin plate is extended to the piezoelectric nanoplate with nonlocal and gradient theories for size effect. The governing equations for bending moments, normal and shear stresses are derived via the Hamilton's principle. Differences between the two theories are described.
Sladek, J., Sladek, V., Kasala, J., & Pan, E. (2017). Nonlocal and Gradient Theories of Piezoelectric Nanoplates. In Procedia Engineering (Vol. 190, pp. 178–185). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2017.05.324