具有初曲率和初挠率弹性直杆的平衡稳定性

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Greenhil判据也适用于带初挠率直杆的更普遍情形，非圆截面直杆的不稳定区随非对称性的增加而扩大。

Stability of Equilibrium of a Straight Elastic Rod with Intrinsic Curvature and Twisting

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.