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| Nonlinear numerical computation of exact and approximate solutions of classical catenary theory |
| Received:March 21, 2017 Revised:July 25, 2017 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20170321001 |
| KeyWord:classical catenary horizontal tension exact solution approximate solution error estimation |
| Author | Institution |
| 郭小刚 |
湘潭大学 土木工程与力学学院, 湘潭 ;长沙矿冶研究院、深海矿产资源开发利用技术国家重点实验室, 长沙 |
| 金星 |
长沙矿冶研究院、深海矿产资源开发利用技术国家重点实验室, 长沙 |
| 周涛 |
湘潭大学 土木工程与力学学院, 湘潭 |
| 宋晓东 |
湘潭大学 土木工程与力学学院, 湘潭 |
| 邓旭辉 |
湘潭大学 土木工程与力学学院, 湘潭 |
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| Abstract: |
| There are two unknown parameters in the mathematic solution of classical catenary,namely horizontal tension h and generalized angle α.They are analysed in detail.By using the constraint condition of the two-point boundary value problem and the assumption of non-extension,a transcendental equation to solve the implicit and independent unknown horizontal tension is deduced.A group of reciprocal dimensionless parameters are adopted,which leads to the simplest expression the horizontal tension as a function of relevant parameters.The interrelation of the generalized angle β and α as well as θ with the geometric parameters is discussed, and it is concluded that generalized α is not an independent unknown parameter.The authors put forward a number of approximate solutions which can simulate the situations when horizontal distances tend to zero,or to the limit distance or vary within the scope of the global calculation of true decimal,also have discussed the degree of accuracy of approximate solutions in relation to the exact solution.These mathematic solutions of classical catenary are of great significance in engineering. |
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