中文摘要：

平面曲梁的纯弯曲过程是固体力学领域中的一个重要分支,但是由于曲梁初始曲率的存在,导致对其精确解析的复杂性。相对而言,直梁的平面弯曲及弹复过程却相对容易实现定量预测。为简化平面曲梁纯弯曲的理论分析模型,针对小曲率平面曲梁的小弯曲变形特点,通过引入曲梁截面弯曲应变的线性分布假设导出曲梁纯弯等价定理。基于板材的四点弯曲特点,同时依托于高精度的三坐标测量仪器,采用不同的板坯试样在不同的弯曲工艺条件下的试验验证该等价定理的可行性。最终试验结果表明,采用直梁弯曲的曲率叠加曲梁初始曲率的方式来代替曲梁弯曲后曲率值,最终结果的绝对误差小于5×10–5,相对误差不大于4.5%,完全满足工程精度的需求。

英文摘要：

The pure bending process of the plane curved beam is one of the most important parts in the field of solid mechanics.However,because of exist of the initial curvature,it is difficult to give the accurately analysis result.Relatively,the bending process of the straight beam can be easily predicted.To simplify the analytical model of plane curved beam bending,according to the feature of small deformation in small curved beam bending process,the equivalence relation of curved beam pure bending is given by introducing the linear distribution assumption of the bending strain.Based on the feature of four-point bending process,and relying on the measuring equipment with high precision,the experimental results prove the feasibility of equivalence relation by the ways of different plank stuff and different technological parameter.The final results suggest the absolute error is less than 5×10–5,the relative error is less than 4.5%,when using the addition curvature instead the bending result of the curved beam.