两端弹性支承夹紧杆的后屈曲分析

POSTBUCKLING ANALYSES OF ELASTIGALLY SUPPORTED STRUT WITH TWO CLAMPED ENDS

本文主要讨论两端弹性支承夹紧杆的后屈曲行为与支承刚度的依赖关系.研究表明:存在一个由杆的长度以及抗弯刚度决定的支承刚度的阈值,当支承刚度不超过该阈值时,屈曲荷载是简单的,随着支承刚度的增加而增加,且除了从零开始的一个很小的基础刚度范围外,所有分岔点以及由此产生的后屈曲平衡路径皆是不稳定的;而当支承刚度超过该阈值时,杆的屈曲荷载与两端刚性支承夹紧杆的相同,相应的分岔点及由此产生的后屈曲平衡路径皆是稳定的.于是,在支承刚度阈值以下的太范围内,杆的屈曲荷载对缺陷将是敏感的.

In this paper, dependence of postbuckling behaviour of an elastically supported strut with two clamped ends on the support stiffness is discussed.It is revealed that, there is a threshold value of support stiffness, so that: (1) if the support stiffness is less than or equal to the threshold value,the buckling load of the strut will increase with the increase of support stiffness,and the bifurcation points and the corresponding postbuckling equilibrium paths are unstable for all but one small region starting from zero; (2) if the support stiffness is greater than the threshold value, the buckling load is equal to that of a strut with hinged ends supported by inflexible bracings,the bifurcation points and the corresponding postbuckling equilibrium paths are stable. Therefore, the buckling load of the strut will be sensitive to the magnitude of imperfection in a large region of support stiffness provided the support stiffness is less than or equal to the threshold value.