朱先奎   刘光廷
    （清华大学水利水电工程系  北京 100084）

[提要]  采用阶梯刚度折算法，将任意变截面曲杆转化为阶梯截面曲杆分析。利用由等截面圆弧形曲杆的稳定微分方程和导出的弯矩方程一般表达式所得到的径向位移解析解，以折算后的阶梯截面径向位移和拱端截面弯矩为基本未知参量，建立了在静水压力作用下不同约束（两铰、无铰和弹性转动约束）支承的对称型变截面圆拱和圆环稳定分析的代数方程组，得到了可以足够精确计算临界载荷的特征方程。算例表明方法简单、有效、实用。
[关键词]  变截面  圆拱 圆环 稳定分析 解析解 阶梯折算法

Adopting the step stiffness convert method, this paper treats a curved bar with arbitrarily variable cross-sections as one with step cross-section. By using the analytic solutions of radial displacements of a
curved bar with constant cross-sections which are gotten from the differential equation of stability and the general equation  of bending moment, with the radial displacements of the converted step cross-sections and the moment of the arch end as the fundamental unknown quantities, it  is established that the  algebraic equation systems for the stability calculation of circular arches and ring with symmetric variable cross-sections and different support constrains under the hydrostatic pressure. Then the characteristic equations, which can enough exactly calculate the critical loads of stability, are obtained.
Kevwords: variable section; circular arch; circular ring; stability analysis; step convert method