自重作用下长管柱稳定性分析

ANALYSIS OF BUCKLING FOR LONG PIPE STRING UNDER GRAVITY

详细分析和研究了自重作用下竖直长管柱的屈曲问题。首次用无穷级数法求解了其临界屈曲时的挠曲线微分方程 ,并同时用能量法给出了其临界屈曲载荷计算公式。认为能量法求解这种情况下的屈曲载荷比较困难和复杂。这主要是由于管柱长度的影响 ,使得其屈曲形态相当复杂 ,不容易找到相近的挠曲线函数 ,如果用含多个待定系数的近似函数去逼近 ,其计算变得相当繁锁。给出的级数解和能量法结果同时证明了现有文献中所发表的结果偏高。

Research and analysis have been made for buckling of long pipe string under gravity. The deflection differential equation of string has been first solved by using infinite series method, and the formula of the buckling critical loads has been obtained with energy method. It is very difficult and complicated to solve critical load with energy method, and the main reason is that the deflection line shape is complicated and it is difficult to choose a function to represent the deflection line. If a function with multi coefficient remained to be determined is chosen, the calculation is very complicated. The results obtained both by using infinite series method and energy method prove that the buckling critical loads having been published are a bit too large.