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| Equilibrium equation of spatially curved cable and geometric analysis of a single curved cable |
| Received:May 05, 2019 Revised:May 30, 2019 |
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| DOI：10.7511/jslx20190505001 |
| KeyWord:spatially curved cable equilibrium equation statically indeterminate kinematically indeterminate ideally flexible cable curved beam |
| Author | Institution |
| 张志宏 |
上海师范大学 土木系, 上海 |
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| Abstract: |
| 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. |