任意截面形状直杆扭转问题的解析解

Analytical solution of torsion problems of arbitrary shape cross section bars

用分离变量法找出扭转应力函数在极坐标下的一般解，然后将边界条件进行付里叶展开，由此条件和方程Ｍ＝２∫φｒｄｒｄθ便可得到任意截面形状直杆扭转问题的解析解．

In this paper, a general solution of torsion stress function in polar coordinates is worked out by using the separation of Variables, and then the equation of boundary condition is represented by Fourier Series. From that condition and equation M=2∫∫φrdrdθ, the analytical solution to torsion problems of arbitary shape cross bars is obtained.