中文摘要：

基于Kirchhoff动力学比拟理论讨论悬垂弹性杆的几何形态。文中以沿杆中心线的弧坐标为自变量,杆截面转角为未知变量,建立弹性细杆在重力作用下的大变形平衡方程。以抗弯刚度与重力因素之比为小参数,柔索的悬链线为零次近似,导出非线性方程的近似解析积分。实际工程问题中常将悬链线作为细长缆线或管线等悬垂工程对象几何形态的近似表达,导出的公式可用于悬链线受抗弯刚度影响的误差修正。

英文摘要：

The geometrical shape of a hanging thin elastic rod was discussed based on Kirchhoff theory of dynamical analogy.Taking the arc-coordinate along the centerline of rod as independent variable,and the rotating angle of the cross section of rod as dependent variable,the equilibrium equations of a thin elastic rod with large deformation were established under the action of gravitation force.Selecting the ratio of bending rigidity of the rod to the gravitation factor as a small parameter,and the catenary of a flexible cord as zero-th approximation,the approximate analytical solution of nonlinear equations was obtained.Since in engineering practice the catenary is used to express the curve of a thin long rope or pipe approximately,the formulas can be applied as a correction of the influence of bending rigidity to the catenary.