弹性基础上的杆在轴压下的二次屈曲

本文研究弹性基础上受轴向加载的两端铰支杆当其最低两屈曲荷载很近时的后屈曲行为。首先,使用Liapunov-Schmidt约化并借助稳定性分析,揭示了杆的二次屈曲现象;基于分叉方程给出了原始后屈曲分支及二次分支的渐近展开。其次,我们使用作者建立的二次分叉的计算方法对杆的二次屈曲做了数值计算,数值结果与渐近展开符合得很好

SECONDARY BUCKLING OF A STRUT ON AN ELASTIC FOUNDATION UNDER AXIAL COMPRESSION

In this paper, the post- buckling behavior of an elastic pinended strut on an elastic foundation is studied.Attention is focused on those values of foundation stiffness at which,under axial load, the two lowest buckling loads of the strut are near.At first,we reveal the secondary buckling of the strut by means of Liapunov-Schmidt reduction and analyses of stability;furthermore,give the asymptotical unfolding of the primary post-buckling branches and secondary branches based on bifurcation equation.Secondly,numerical conputations of the secondary buckling of the strut is made by the method which have been developed by the author of this paper.The numerical results are in agreement with the asymptotical expression very well.