A Timoshenko beam model is applied for the analysis of the flexoelectric effect for a curved nano-beam. This theory transforms the beam to a 1-d problem along the beam axis. The electric intensity vector for the open-circuit condition can be expressed by mechanical quantities, namely strains and strain gradients. The variational principle is applied to derive the system of ordinary differential equations (ODEs) for the beam deflection, cross-section rotation, and in-plane displacement. A numerical solution based on the Taylor series expansion with Cartesian coordinate along the beam is proposed for the system of ODEs. A convergence analysis with respect to the number of terms in the Taylor series expansion is performed. Numerical results for the beam deflection, rotation, in-plane displacement, and induced electric intensity vector are presented for various flexoelectric coefficients and the beam curvature.

蒂莫申科梁模型用于弯曲纳米束的柔电效应分析。该理论将光束沿光束轴转换为一维问题。开路条件下的电强度矢量可以用机械量表示，即应变和应变梯度。应用变分原理来导出光束偏转，截面旋转和面内位移的常微分方程组（ODE）。针对ODEs系统，提出了一种基于泰勒级数展开式的方法，该展开式具有沿光束的直角坐标。对泰勒级数展开中的项数进行收敛性分析。光束偏转，旋转，平面内位移的数值结果，