The theory of layerwise beam, which considers both microstructure and flexoelectric effects, is used in the curvature-based flexoelectricity theory. The displacement field function of the layerwise beam model is given. The governing equations and boundary conditions are obtained using a variational formulation based on Hamilton's principle. Analytical solutions for static bending and free vibration of a simply supported layerwise beam are derived. Isogeometric analysis (IGA) with higher-order continuity considering the flexoelectric effect is presented to numerically solve the static bending and free vibration problems. The results obtained from the analytical and IGA approaches are compared through several examples in which the microstructure and flexoelectric effects on the mechanical responses of layerwise nanobeams are analyzed.

基于曲率的挠曲电理论采用了同时考虑微观结构和挠曲电效应的层状梁理论。给出了分层梁模型的位移场函数。控制方程和边界条件是使用基于哈密顿原理的变分公式获得的。推导了简支层状梁的静态弯曲和自由振动的解析解。提出了考虑挠电效应的具有高阶连续性的等几何分析（IGA），以数值求解静态弯曲和自由振动问题。通过几个示例对分析方法和 IGA 方法获得的结果进行了比较，其中分析了层状纳米梁机械响应的微观结构和挠曲电效应。