微纳米尺度下挠曲电效应相对于传统压电效应具有较高的机电耦合转换效率，其在传感、致动和俘能领域极具应用前景。然而目前多数商用有限元软件未包含挠曲电本构模型，无法对挠曲电结构进行有效的数值模拟。本研究基于Abaqus用户自定义单元（UEL）子程序进行二次开发，将挠曲电效应内化到计算模型。首先，结合配点混合有限元法（CMFEM），推导了挠曲电结构的力电耦合方程，并在Abaqus中开发了挠曲电单元，提供了挠曲电结构响应分析的数值模拟技术。与传统的混合有限元法（MFEM）相比，该方法的优点是易于建模，降低了计算自由度，提高了计算效率，节省了运算成本，并且挠度与电场强度指标都比其他方法更接近解析解。然后，通过上述数值模拟方法，建立了挠曲电结构响应分析数值模型，开展了矩形梁及弧形梁在不同边界条件下的力电耦合响应计算与分析。分析结果展示了梁的几何参数影响结构应变梯度\left|{\eta }_{\mathrm{113}}\right|的作用机制，表明在使用同一材料设计挠曲电梁时，可通过控制变形梯度来控制输出电压的大小。研究表明，改变梁的弯曲程度，可有效提高梁输出的开路电压，减小梁的挠度。相同程度弯曲下，弧形悬臂梁向下弯曲的开路电压大于弧形悬臂梁向上弯曲的开路电压。当向上弯曲弧形梁的圆心角为38°，左边缘为滑动支座，右边缘为铰链支座时，开路电压最大，可达214.07 mV，比悬臂矩形梁增加5倍。此外，相同模型若仅考虑压电效应，开路电压将下降89.3%。

At the micro-nano scale, the flexoelectric effect exhibits a higher electromechanical coupling conversion efficiency in comparison with the traditional piezoelectric effect. Therefore, it holds potential applications in the fields of sensing, actuation, and energy harvesting. However, most commercially available finite element analysis software packages lack the flexoelectric constitutive model, rendering it impossible to perform a precise numerical simulation of flexoelectric structures. Therefore, this study incorporated the flexoelectric effect into the calculation model based on the development of Abaqus user-defined element (UEL) subroutine. Additionally, we derived the electromechanical coupling equations of the flexoelectric structure and developed a flexoelectric element in Abaqus, which provides numerical simulation technology for analyzing the structural flexoelectric response. Compared with the traditional mixed finite element method (MFEM), this proposed method has the advantages of easier modeling, high efficiency and low computational cost. And its deflection and electric field strength metrics are closer to the analytical solution than either of the other methods. Then, using this numerical simulation method, this study established a flexoelectric structural response analysis numerical model, conducted force-electromechanical coupling response calculations, and analyzed straight and curved beams under different boundary conditions. The analysis results show the mechanism of the geometric parameters of the beam affects the structural strain gradient, and show that the output voltage can be controlled by controlling the deformation gradient when designing a flexoelectric beam using the same material. It is shown that changing the degree of bending of the beam is effective in increasing the open-circuit voltage of the beam output and reducing the deflection of the beam. The open-circuit voltage of a curved cantilever beam bent downward is greater than the open-circuit voltage of a curved cantilever beam bent upward for the same degree of bending. When the circular arc angle of the upward bending curved beam is 38°, the left edge is a sliding bearing, and the right edge is a hinge bearing, the open-circuit voltage is the maximum, up to 214.07 mV, which is five times more than that of the cantilevered rectangular beam. In addition, by considering the piezoelectric effect alone, the open-circuit voltage will decrease by 89.3% in the same model.