扇形截面杆扭转的应力分析

柱体扭转的基本方程为非齐次偏微分方程,在极坐标系下,利用分离变量法及傅立叶级数展开法,求出了扭转应力函数,进一步即可计算出扇形截面杆在外力偶作用下,扭转角和横截面上剪应力的精确解答。这种方法为精确解法,在各种机械及其他工程设备中,对受扭转作用的扇形截面杆设计,有一定实用价值。

Stress analysis for torsion on prismatic bars with sectorial cross-section

The torsion equation of prismatic bars is nonhomo-geneous partial differential equation.In polar coordinate system,the torsion stress function was derived by means of the method of separation of variables and the method of expansion of Fourier series.Then,torsion angle and shear stresses on cross section of bars bearing external couples were calculated.This method is an approach of precise solution and has some applicational value in design of prismatic bars with sectorial cross-section in engineering.