限制失稳杆的后屈曲分析

Study on PostBuckling of Constrained Bar

摘要:

按照不同的接触状态对杆的后屈曲性能分阶段分析.将任意两相邻接触点之间的杆分别作为研究对象.基于小变形假设，采用点接触、线接触模型，建立了通用的力学分析模型，导出了杆在不同后屈曲模态、不同接触状态下的平衡方程.通过求解平衡方程，建立了不同屈曲模态下，轴向载荷和杆、限制失稳构件之间接触状态的关系，得到了接触状态和后屈曲模态发生过渡的临界载荷条件.结果表明，当不同分段的长度相等时，将会发生后屈曲模态的过渡.与不受约束的欧拉失稳相比，杆的限制失稳过程具有丰富的分叉点.

Abstract:

The behavior of constrained bar between rigid walls can be divided into different states,such as point contact and line contact phases. The parts of the bar between arbitrary two neighboring contact points are regarded as objects to be analyzed.The buckling equilibrium equations of bilateral constrained bar in different phases are derived based on the assumption of small deformation, point contact and line contact model. The relationship between axial load and different phases can also be established on the basis of the equations. The critical load of phases transition is computed.Analytical results show that the mode transition occurs when the lengths of different segments of the bar equal. In contrast to unconstrained Euler buckling, there are rich bifurcation points in the process of constrained buckling.