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Nonlinear numerical computation of exact and approximate solutions of classical catenary theory[J].计算力学学报,2018,35(5):635~642

Nonlinear numerical computation of exact and approximate solutions of classical catenary theory
Nonlinear numerical computation of exact and approximate solutions of classical catenary theory

DOI：10.7511/jslx20170321001

 作者 单位 E-mail 郭小刚 湘潭大学 土木工程与力学学院, 湘潭 411105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 410012 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 410012 周涛 湘潭大学 土木工程与力学学院, 湘潭 411105 zhoutao20080602@126.com 宋晓东 湘潭大学 土木工程与力学学院, 湘潭 411105 邓旭辉 湘潭大学 土木工程与力学学院, 湘潭 411105

针对经典悬链线数学解中存在两个未知参数，即水平张力h和广义倾角α迄今尚未妥善解决的问题，进行了深入细致的分析。利用悬链线两点边值约束条件和不可拉伸假设，推导出求解隐含独立未知量水平张力的超越方程。引进互逆的量纲参数求解超越方程中的水平张力，使得水平张力形式上具有最简单的参数依赖关系。探讨了广义倾角β，αθ与几何参数的相互关系，得出广义倾角α不是独立未知参数的结论。提出了水平距离趋于0和趋于极限距离的各种近似解、在真小数全局计算范围内的近似解以及这些近似解关于精确解的误差程度，其结果在工程上具有应用价值。

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.