加权残值法分析轴压圆柱薄壳后屈曲问题

Postbuckling of Axially Compressed Circular Cylindrical Thin Shells Analysed by MWR

本文首次应用了样条配点法分析了受到轴向压力的圆柱形薄壳的后屈问题,壳体的方程是L.H.Donnell的非线性正交异性圆柱形壳体方程,壳体的挠度试函数及应力函数试函数都是于轴向用了五次B样条函数基函数,周向用余弦函数。计算模型是周向为半个波长的壳块,可适应后屈曲实验变形跳跃现象。非线性代数方程组用了Newton—Rophson迭代法求解。由此所得的理论上的后屈曲曲线与国外近代实验相符。

For the first time, this paper presents the analysis of the postbuckling of axially compressed circular cylindrical thin shells by the method of spline collocation, the Donnell's equation of non-linear orthotropie circular cylindrical shell having been used. Trial functions of the deflection and the stress function consist of a cardinal function of the quintic B-spline function in the axial direction multiplied by a cosine function in the circumferential direction. The model for analysis is a panel cut from the shell with a circumferential length of half of a cosine wave, in this way the jump of deformation as well as the load capacity of the shell can easily be followed. The non-linear algebraic equations thus formed are solved by the Newton-Raphson's iterative method. The postbuckling curve of load-deformation thus obtained therectically basically agrees with that of the experiment by modern means.