论非均匀壁厚圆管的临界外压计算

长期以来,不均匀壁厚圆管的临界外压计算问题一直争议很大。这是由于非均匀壁厚圆管受外压变形,相当于一个端部铰支且具有变抗弯刚度的压杆,所建方程是一个二阶变系数微分方程,难以求解。以前的研究者们借助于能量法和变分法求得临界外压的表达式,避开直解该微分方程。但采用这些方法时,必须假设变形的屈曲形状函数。问题的焦点就在于,采用的是均匀对称变形时的屈曲形状函数和均匀变形时的边界条件,不能真正代表实际变形形状。因此,导出的非均匀壁厚圆管临界外压计算公式的计算结果误差很大,得出的结论与实际不符。分析了以前学者们在解决此问题时存在的问题,利用力学模型中的几个端点值,转变系数微分方程为常系数微分方程,然后采用几何平均处理方法求得该变系数微分方程的近似解,导出了非均匀壁厚圆管临界外压近似公式,并进行了实例计算分析,认为该导出式符合现场实际结果。

THE CRITICAL PRESSURE CALCULATION OF NON-UNIFORM WALL CASING

It has been a dispute for a long time how to calculate the critical outer pressure on non -uniform wall casing,since it is difficult to get out the solution from the binomial differential equation established when casing is deformed. The previous researchers derivated the formula of the critical outer pressure by metheds of energy and variation rather than from the equation. Ihey were used with supposing the deformation function of the bending of uniform casing wall,and resulted in error. The paper analyzes the existing problems and derivates the approximate formula of critical outer pressure of non - uniform wall casing, converting differential equation with variabl coefficient to normal one,through some point values in the model of mechanics' The poper says that the new formula is in keeping with the actual field result,based on case calculation.