力学与实践 ›› 2020, Vol. 42 ›› Issue (2): 223-225.DOI: 10.6052/1000-0879-19-188

• 教育研究 • 上一篇    下一篇

均布扭力矩作用下圆截面圆环的稳定性分析1)

李道奎*,2), 刘军虎, 周仕明*   

  1. *国防科技大学空天科学学院,长沙 410073;
    北京航天长征飞行器研究所,北京 100076
  • 收稿日期:2019-05-13 修回日期:2019-06-18 发布日期:2020-05-11
  • 通讯作者: 2) 李道奎,教授,主要从事结构设计与分析科学研究和材料力学教学工作。 E-mail:lidaokui@nudt.edu.cn
  • 基金资助:
    1) 湖南省2019年教学改革研究项目,国防科技大学2017年本科教育教学研究重点立项课题(U2017105)资助

STABILITY OF CIRCULAR RING OF CIRCULAR CROSS-SECTION UNDER UNIFORMLY DISTRIBUTED TORSION 1)

LI Daokui*,2), LIU Junhu, ZHOU Shiming*   

  1. *National University of Defense Technology, College of Aerospace Science and Engineering, Changsha 410073, China;
    Beijing Institute of Space Long March Vehicle, Beijing 100076, China
  • Received:2019-05-13 Revised:2019-06-18 Published:2020-05-11

摘要: 圆环在均布扭力矩作用下的变形特殊且容易发生跳跃,不考虑稳定性而得到的一些结论将可能不存在。本文利用最小势能原理导出圆截面圆环在均布扭力矩作用下的平衡路径,并根据系统稳定性的能量判据,对圆环的平衡稳定性、变形与运动过程进行分析,最后得到稳定平衡状态下圆环横截面上的内力最大值。

关键词: 均布扭力矩, 圆环, 稳定性, 能量判据

Abstract: The circular ring will experience a special kind of deformation under a uniformly distributed torsion and is apt to jump. The stability is an important factor not to be overlooked. In this paper, the equilibrium path is derived for the circular ring of circular cross-section under the uniformly distributed torsion based on the principle of the minimum potential energy. With the energy criterion for the system’s stability, the stability of the equilibrium, the deformation and the moving process of the circular ring are analyzed. Finally, the maximum value of the internal force on the circular ring's cross-section is obtained in the stable equilibrium state.

Key words: uniformly distributed torsion, circular ring, stability, energy criterion

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