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     朱先奎   劉光廷
    （清華大學(xué)水利水電工程系  北京 100084）

[提要]  采用階梯剛度折算法，將任意變截面曲桿轉(zhuǎn)化為階梯截面曲桿分析。利用由等截面圓弧形曲桿的穩(wěn)定微分方程和導(dǎo)出的彎矩方程一般表達(dá)式所得到的徑向位移解析解，以折算后的階梯截面徑向位移和拱端截面彎矩為基本未知參量，建立了在靜水壓力作用下不同約束（兩鉸、無(wú)鉸和彈性轉(zhuǎn)動(dòng)約束）支承的對(duì)稱(chēng)型變截面圓拱和圓環(huán)穩(wěn)定分析的代數(shù)方程組，得到了可以足夠精確計(jì)算臨界載荷的特征方程。算例表明方法簡(jiǎn)單、有效、實(shí)用。
[關(guān)鍵詞]  變截面  圓拱 圓環(huán) 穩(wěn)定分析 解析解 階梯折算法

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