计算弯曲变形的几何法

Geometric method of calculating bending deformation

弯曲变形问题本质上是几何问题,即杆轴线上任意点的位移都可以视为由起点处横截面的转角和杆的弯曲导致的。基于此来找出位移与微段杆弯曲、起点处横截面的转角的关系式,引入弯曲变形与内力的关系式,从而将杆的位移表示成杆的弯曲和旋转。该方法可以拓展到任意形状杆件的平面弯曲变形的计算,且对比传统方法更具一般性;而且在增加初参数的情况下,该方法可以分析超静定杆件的弯曲变形问题。通过两个求解杆弯曲位移方程的算例,验证了该方法的正确性。

Substantially, the bending deformation is a geometric problem, that is, the displacement of a specified point in the bar is produced by the rotation of the cross-section at a starting point and the bending of bar. On this basis, we find out the rotation and bending in relation to displacement. And the relation equation between the moment-curvature and internal force is used. The displacement is expressed by the function of the bending and rotation of the bar. This method of computing the bending displacement can be easily expanded to fix the plane bending of various shapes of bars. Comparing with the conventional method of analyzing bending bars, this method is more general and can be used to analyze the statically indeterminate bars by introduction of initial parameters. Moreover, two examples are given to demonstrate the method.