压杆过屈曲分析中轴线无伸长假设的定量讨论

A Quantitative Study of the Assumption That the Axis Is Inextensible in Analysis of Postbuckling of Compressed Rods

基于轴线可伸长杆的过屈曲精确数学模型，采用打靶法对两端简支压杆过屈曲行为进行了数值分析，定量地给出了杆的轴向变形与其长细比之间的关系，并指出轴线不可伸长假设随着杆长细比的不断增大而趋于合理，当长比趋于无限大时，假设精确成立．

Based on an accurate mathematical model of the postbuckling of axially extensible rods, a numerical analysis of the postbuckling behavior of simply supported compressed rods by a shooting method is presented in this paper. The relation between the axial deformation and the slenderness of the rods is given quantitatively. From the results it can be concluded that the assumption that the axis of the rod is inextensible becomes more reasonable as the slenderness is larger, especially, and the assumption is precisely fitting when the slenderness tends to infinity.