应用突变理论分析Euler压杆的稳定性

Stability Analysis of the Euler Pole by the Catastrophe Theory

建立了Euler压杆问题的能量表达式。对此模型 ,应用突变理论进行稳定分析 ,得出了系统全部的分叉集与突变流形。突变流形为一族层层嵌套、互不交叉的抛物线。分析的结论要比有限差分法、有限单元法、大范围非线形分析等数值计算的结果简洁、明了 ,有助于压杆后屈曲问题的研究。

The energy model of the Euler pole is established in the paper. All of the bifurcation sets and the catastrophe manifolds are obtained by the catastrophe theory. The catastrophe manifolds are composed of a cluster of parabolas that successively sheathe and are non intersect. The conclusion of stability analysis is more simple and definite than numerical analysis method, for example: method of finite difference, finite element method, non linear analysis method in large. And it is applicable to the analysis of post buckling of pole.