中文摘要：

他们的不稳定性上的杆的压缩的可能性的关键效果是经由奇特理论表明的使用新方法。可压缩的杆的批评负担总是比一 Euler 杆，和一个代用品大，这被显示出批评草耙分叉，不能为 Euler 杆发生，可以为可压缩的杆发生。可压缩的杆的一张整个分叉图如下；什么时候可压缩的杆的原来的苗条海角比率， S_0，比小(1 +upsilon/3 ) 3X3 ~(1/2 ) Xpi/2，杆不弄弯；当 S_0 暗示了由时[(1+upsilon/3 ) 3X3 ~(1/2 ) pi/2，(1+upsilon/5 ) 5X5 ~(1/2 ) Xpi/4 ] ，杆可以经历 subcriticalpitchfork 分叉，倒塌可以发生；当 S_0 暗示了由时[(1 +upsilon/5 ) 5X5 ~(1/2 ) Xpi/4， +infinity ] ，杆可以经历超级批评草耙分叉。原因有点分叉转移的杆的生气的节的变丑指向到相应于更大的苗条海角比率的。

英文摘要：

The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.