A non-classical model for transversely isotropic magneto-electro-elastic circular Kirchhoff plates is established based on the extended modified couple stress theory. The Gibbs-type variational principle is used to obtain the governing equations and boundary conditions. To illustrate the newly derived model, the static bending problem of a clamped circular plate subjected to a uniformly distributed constant load is solved numerically by Fourier–Bessel series. The numerical results show that the values of transverse displacement, electric and magnetic potentials predicted by the current model are always smaller than those of the classical model, and the differences are diminishing as the plate thickness increases. In addition, it is shown that the magneto-electro-elastic coupling effect plays an important role in the transverse displacement, electric potential and magnetic potential of the magneto-electro-elastic circular Kirchhoff plates. Furthermore, several reduced specific models are provided for simpler cases.

基于扩展修正偶应力理论，建立了横向各向同性磁电弹性圆形基尔霍夫板的非经典模型。Gibbs型变分原理用于获得控制方程和边界条件。为了说明新推导出的模型，受均匀分布的恒定载荷作用的夹紧圆板的静态弯曲问题通过傅立叶-贝塞尔级数进行数值求解。数值结果表明，当前模型预测的横向位移、电势和磁势值总是小于经典模型的值，并且随着板厚的增加，差异逐渐减小。此外，还表明磁电弹性耦合效应在横向位移中起重要作用，磁电弹性圆形基尔霍夫板的电势和磁势。此外，还为更简单的情况提供了几个简化的特定模型。