端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳.直杆撞击刚性平面或拉断卸载后将形成压缩波,因承载压缩载荷的长度增加可以引起失稳.冲击速度转换的压应力沿着杆件切线方向,该处弯矩和剪力为零;而众多文献设定的失稳段固支边界条件并不准确.基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件,得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5倍.对于钢丝绳拉断形成的冲击失稳,载荷恒定而长度增加,可以产生高阶屈曲即在侧向出现多次曲折,并基于尼龙-橡胶带的模拟试验给出了定性说明.

Analyses on the Instability of a Pole Loaded by Tangential Force at One End and Its Application

A slender pole or rod will show lateral buckling under axial compression. Both a bar impacting the rigid plane and a pole unloaded due to tensile failure will generate compression wave, which causes instability as the length bearing the compressive load increases. The compressive stress transformed from the impact velocity is along the tangential direction of the bar or pole, where the moment and shear force are zero. Therefore, the boundary condition for instability analyse is not the clamping at the ends of the instability length, which was used in many literatures. The critical buckling condition is obtained from the exact curvature equation of a pole subject to the compressive force pointed at a fixed point. At the critical state with the tangential load at the pole end, the critical length for the proposed solution is 1.5 times of that for the simply-supported pole. The impact instability of the steel wire rope after tension breakage is a problem with an increasing length and a constant load. The pole will exhibit high-order buckling, or multiple lateral bends. The impact instability of the extra-long pole is explained qualitatively based on the simulation test of a nylon-rubber belt.