空间曲线索的平衡方程及单索几何判定

Equilibrium equation of spatially curved cable and geometric analysis of a single curved cable

空间曲线索平衡方程可在理想柔索假定的基础上进行推导,也可以由空间曲线梁平衡方程退化得到。本文给出后者的连续化分析过程并进行了初步的讨论,目的在于将空间曲线索的各种力学模型统一起来。采用理想柔索假定后单索只能是平面曲线,自然坐标系和整体直角坐标系下平面曲线索的平衡方程是等价的。同时,针对以往单索连续化分析中几何判定的不足,基于空间曲线的弧长独立参数概念,指出单根理想柔索本质上为静不定和动不定体系。

This paper mainly discusses the equilibrium equation of spatially curved cables and geometric analysis of a single curved cable.The equilibrium equation of spatially curved cables can be generated based on the assumption of an ideally flexible cable or reduced from that of a spatially curved beams.This paper adopts the latter way and discusses it in details.The objective is to unite all of them regarding mechanical models of spatially curved cable.If the ideally flexible cable assumption is adopted,cable should remain in a plane.The equilibrium equation in a natural coordinate system and that in the rectangular coordinate system are equivalent.The second part of this paper focuses on the geometric analysis of a single ideally flexible cable.As a spatial curve contains only an independent parameter in mathematics,it is easy to understand why the computational degrees of freedom of a spatially curved cable is-1.This paper discusses these two basic problems inversely and mathematically.It should be helpful for deeper understanding of single spatially curved cables in practical engineering.