缆线在铅垂面内弯曲的大变形曲线微分方程及其数值解法  

Differential equation of large deformation curve for cables bending in vertical plane and its numerical solution method

作　　者：李立新[1] 王猛[1] 张巍[1] LI Li-xin;WANG Meng;ZHANG Wei(Institute of Mechanical Design Zhejiang University,Hangzhou 310058,China)

机构地区：[1]浙江大学机械设计研究所,杭州310058

出　　处：《计算力学学报》2024年第5期970-976,共7页Chinese Journal of Computational Mechanics

摘　　要：针对民用与工业应用中经常用到的自然弯曲的软管和柔缆,归纳出5个共同特点,作为本文研究缆线的基本假设。从这些假设出发,根据受力和应力分析,首次推导了缆线在铅垂面内弯曲的大变形曲线方程。列出了多种端部约束条件下相对应的求解大变形曲线的方程组。证明了悬链线与纯弯曲线都是本文的特例。提出了获得数值解的递进法,并针对两端夹持约束的情形给出了具体算例。说明了存在多解的原因以及比较不同解稳定性的方法。For the natural bending hoses and flexible cables often used in civil and industrial applications,5 common characteristics are summarized as the basic assumptions of the cables researched in this paper.Based on these assumptions and according to the force and stress analysis,the differential equation of the large deformation curve for cables bending in the vertical plane is derived for the first time.The corresponding equations for solving the large deformation curves under various end constraints are listed.It is proved that catenary and pure bending curves are special cases of this paper.A progressive method for obtaining numerical solutions is proposed with a specific example for the case of clamped-clamped boundary constraints.The reasons for the existence of multiple solutions are given and the method to compare the stability of different solutions is discussed.

关 键 词：缆线 大变形曲线 铅垂面内弯曲 泛函极值 数值方法 

分 类 号：TH123.1[机械工程—机械设计及理论] O176.1[理学—数学]