扇形截面杆扭转的数值分析

在机械设计与应用中，为了计算扇形截面杆在外力偶作用下，杆的扭转角和横截面上的剪应力，提出了一种数值计算方法．柱体扭转的基本方程为非齐次偏微分方程，在极坐标系下，利用分离变量法及特解法，求出扭转应力函数，再由边界配置法计算出满足扭转问题边界条件的待定常数，得到了扭转应力函数的近似数值解，进一步即可计算横截面上的剪应力．给出了几种不同顶角的扇形截面杆的剪应力与扭转刚度，计算结果表明，这种方法具有足够的精确度，有一定实用价值．分离变量法与边界配置法的结合，简化了计算过程，适宜于工程设计应用．

Numerical Analysis for Torsion of Prismatic Bars with Sectorial Cross-section

In mechanical design and application, in order to calculate torsion angle and shear stresses of prismatic bars with seetorial cross-section undergoing extemal couples, the numerical method is presented. The torsion equation is nonhomogeneous partial differential equation. First, using the method of separation of variables, torsion stress function is acquired in polar coordinate. Then, the method of boundary collocation is improved to calculate the undetermined parameters. Finally,approximate numerical solutions of stress function and shear stresses in cross-section are obtained. It is given the several calculation results of shear stresses of prismatic bars with different vertex angles. These results show that the method has some precision and application feasibility in engineering design. The method of separation of variables is combinied with the method of boundary collocation simplified calculation process.