斜直圆筒内基于Euler-Rodrigues参数的细长杆螺旋屈曲研究  

Helix Buckling of a Slender Rod in Inclined Cylinder:Analysis with Euler-Rodrigues Parameters

作　　者：袁张贤[1] 王鑫伟[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,江苏南京210016

出　　处：《计算物理》2012年第4期549-556,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(No.10972105)资助项目

摘　　要：基于Euler-Rodrigues参数描述受约束细杆的后屈曲变形状态,建立相应的能量泛函,导出非线性平衡微分方程及接触力表达式.采用有限元法对能量泛函进行分析计算,通过与现有文献中数值、理论结果比较,验证了公式和求解过程的正确性.结合算例,揭示了正弦屈曲模态与螺旋屈曲模态之间的转化过程,证实了在受约束细长杆的后屈曲响应中存在不同屈曲模态之间的互相转变.Post-buckling configuration of a slender rod constrained in a cylinder is described with Euler-Rodrigues parameters. Corresponding energy function is obtained. Nonlinear differential equilibrium equation and contact force are established through the energy function. The problem is solved successfully with finite element method. To verify the formulations and solutions, comparisons with existing data or solutions are made. Numerical resuhs revealed conversion process from sinusoidal buckling to helix buckling. Possibility of mode changing in post-buckling process is verified.

关 键 词：Euler-Rodrigues参数 斜直圆筒 螺旋屈曲 模态转变 有限元 

分 类 号：O343.9[理学—固体力学] TB121[理学—力学]