受非线性弹簧约束受压柱稳定问题讨论

zsq-w

描述：
如图1所示的细长柱， 高度为L，截面bXh（h>b）. 柱子底部固支、顶部受压F.

                                   
                                                  图1 问题描述


在柱中部的弱轴方向有一个非线性弹簧（弹簧刚度K1和K2，K1>K2，如下图所示）. 假设弹簧刚度并不是非常大，以至于受压时柱子仍然首先沿着弱轴方向失稳.                  
                                 
                                                      图2 弹簧刚度

问题：
    分析这个有弹簧约束的失稳求解临界力的时候，可以把非线性弹簧视为刚度为K1的线性弹簧来分析么？

     欢迎大家讨论。

tonnyw

I was thinking that if you use K1 you might get the upper limit of the critical buckling load while K2 lets you have the lower limit. Is that right?

zsq-w

tonnyw 发表于 2013-7-13 18:20
I was thinking that if you use K1 you might get the upper limit of the critical buckling load while  ...

Initially，I had the same concept with you. After think it over, I suppose that buckling happens with a transverse deflection being much less than width of the section, b. In this regard, deduction with K1 should give better critical force during buckling.

I am not sure if I confused myself or not on this problem.

tonnyw

Is it possible that analytical solution can be obtained for this problem?

zsq-w

tonnyw 发表于 2013-7-13 18:48
Is it possible that analytical solution can be obtained for this problem?

I am presently seeking for the analytical solution. I think it is achievable.

Dr. W, do u wanna try?

tonnyw

zsq-w 发表于 2013-7-13 19:33
I am presently seeking for the analytical solution. I think it is achievable.

Dr. W, do u wanna t ...

Analytical solution is definitely doable. Here we have boundary conditions at the top and bottom ends. We have continuity condition at the support place. Then we have two governing equations for two parts. The derivation is going to be nasty. Having said that, it can be done.