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| Differential equation of large deformation curve for cables bending in vertical plane and its numerical solution method |
| Received:March 10, 2023 Revised:June 15, 2023 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20230301002 |
| KeyWord:cable large deformation curve bending in the vertical plane functional extremum numerical solutions method |
| Author | Institution |
| 李立新 |
浙江大学 机械设计研究所, 杭州 |
| 王猛 |
浙江大学 机械设计研究所, 杭州 |
| 张巍 |
浙江大学 机械设计研究所, 杭州 |
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| Abstract: |
| 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. |