轴压杆件刚性约束屈曲变形的连续过渡

Continuous Transition of Deformations of an Axially Compressive Strut Constrained by a Rigid Wall

从杆件整体变形连续的角度,研究了轴压杆件与刚性约束构件之间一阶模态点接触、一阶模态线接触、线接触屈曲的连续过渡。在小挠度变形假设下,推导了轴压杆件一阶模态线接触、线接触屈曲变形二阶平衡微分方程的解答。根据变形的连续性,经过理论分析得出,当杆件一阶模态点接触变形的中点曲率为零时,杆件由一阶模态点接触连续过渡到一阶模态线接触;当杆件一阶模态线接触变形的线接触区域发生一阶屈曲模态时,杆件由一阶模态线接触连续过渡到线接触屈曲。

The continuous transition of the deformations of an axially compressive strut is studied when the strut and the rigid wall successively present a single point contact and a line contact,two points contact with a buckled segment between them.Under the small deflection assumption,the second order differential equilibrium equations of the strut during line contact and two points contact are formulated and solved.The analysis of continuous deformations indicates the strut continuously transits from a point contact to a line contact when the curvature of the strut midpoint equals zero during a point contact,continuously transits from a line contact to two points contact when the line contact zone of the strut buckles to first order mode during a line contact.