Abstract: A practicable analytic solution is obtained for any sector by means of Fourier series with singular items. It is proved that the method is equal to Williams' method of separation of variables. The non-linear characteristic equation is transformed into the polynomial equation.

Key words: series method, method of separation of variables, sector, characteristic equation

摘要： 从位移场带奇性分离的Fourier级数表达式着手，得到扇形问题可实际操作的解析解，可以证明此级数解法与Williams分离变量法等价。对于任意尺度的扇形，只要内外弧边界上应力边界条件能被展开成Fourier级数，便可求解。Williams分离变量法中的非线性的特征方程转化成了多项式方程。

关键词: 级数解法, 分离变量法, 扇形, 特征方程