摘要
研究端部受力和力矩作用 ,且存在初曲率和初挠率的非圆截面弹性直杆的平衡和稳定性问题 .描述弹性细杆平衡状态的 Kirchhoff方程存在与杆的直线平衡状态相对应的特解 .导出判断杆的直线平衡状态稳定性的解析判据 .对于圆截面杆的特殊情形 ,应用一次近似方法和 Lyapunov直接方法证明了判断无初挠率直杆稳定性的 Greenhill判据也适用于带初挠率直杆的更普遍情形 .
The problem on stability of equilibrium of a thin straight elastic rod with noncircular cross section and intrinsic curvature and twisting, subjected to forces and torques on both ends was discussed. The Kirchhoff equation in statics of an elastic thin rod has a special solution, corresponding to the straight equilibrium. The stability conditions of the straight equilibrium were obtained in an analytical form. It was proved by use of the method of first approximation and Lyapunov direct method that the Greenhill formula for the stability of a straight rod without intrinsic twisting is effective for more general case when the rod has intrinsic twisting. The unstable region of a straight rod with noncircular cross section extends with the increasing of the asymmetry of the cross section.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
2002年第11期1587-1590,共4页
Journal of Shanghai Jiaotong University
关键词
初曲率
初挠率
弹性直杆
弹性稳定性
elastic stability
Kirchhoff theory
Greenhill formula
Lyapunov direct method
