关于细长压杆临界力的讨论

Discussion on the critical load of slender compressive rod

以两端铰支细长压杆为例,考虑轴向位移的边界条件,通过建立微弯平衡状态下的挠曲线方程确定了微弯压力.将微弯状态的挠曲线退化成直线,即压杆对应的直线平衡状态,计算推演了最小临界压力,进而讨论了最小临界力与微弯压力的区别.对压杆施加扰动,讨论了压杆非最小临界力与给予压杆扰动的稳定性关系.结果表明,微弯压力值只有在轴向位移无限趋近于零时,才会接近最小临界压力值;对细长压杆来说,在扰动下,非最小临界压力会导致挠度无限增大,因此只有最小临界力才具有实际意义.

With a slender hinged support rod as an example,determined the microbend pressure through the establishment of micro bending deflection curve equation of equilibrium using the axial displacement boundary conditions.The micro bending deflection curve state degenerate into a straight line,it corresponds the line balance of the pressure bar,in this state calculated and deduct the minimum critical pressure,and then discussed the differences between a minimum critical stress and micro bending stress.Applying the perturbation of pressure bar,discussed the stability between the pressure bar non minimum critical force and the pressure rod disturbance.The results shown that microbend pressure value will be close to the minimum critical pressure value only when the axial displacement of the infinite approaches zero.For the slender bar,non minimum critical pressure will cause the deflection increases indefinitely under disturbed,so only the minimum critical force has practical significance.