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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
投稿时间:2019-05-05  修订日期:2019-05-30
DOI:
中文关键词:  空间曲线索  平衡方程  静不定  动不定  理想柔索  曲线梁
英文关键词:spatially curved cable  equilibrium equation  statically indeterminate  kinematically indeterminate  ideally flexible cable  curved beam
基金项目:
作者单位E-mail
张志宏 上海师范大学 zhangzh@zuaa.zju.edu.cn 
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中文摘要:
      本文主要讨论空间曲线索的平衡方程和单索的几何判定问题。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。本文围绕单根空间曲线索的基本问题展开讨论,希望能够对深入理解单索的力学本质有所帮助。
英文摘要:
      This paper mainly discusses the equilibrium equation of spatial curved cable and geometric analysis of a single curved cable. The equilibrium equation of spatially curved cable can be generated based on the assumption of ideally flexible cable or degenerated from that of spatially curved beams. This paper gives out the later way and discusses it in details. The objective is to unite all of them regarding mechanical models of spatially curved cable. If ideally flexible cable assumption is adopted, cable should remain in a plane. The equilibrium equation in natural coordinate system and that in 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 could be a little helpful for deeply understanding of single spatially curved cable in practical engineering.
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