悬链线竖向集中力作用下的构形分析和张力计算  

Configuration analysis and tension calculation of catenary under vertical concentrated force

作　　者：郭小刚[1,2] 王刚 宋晓东 邓旭辉 赵珂[1] GUO Xiao -gang;WANG Gang;SONG Xiao -dong;DENG Xu-hui;ZHAO Ke(School of Civil Engineering and Mechanics,Xiangtan University,Xiangtan 411105,China;State Key Laboratory of Exploitation and Utilization of Deep-sea Mineral Resources,Changsha Research Institute of Mining & Metallurgy,Changsha 410012,China;CMCU Engineering LTD,Chongqing 400000,China)

机构地区：[1]湘潭大学土木工程与力学学院,湘潭411105 [2]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 [3]中机中联工程有限公司,重庆400000

出　　处：《计算力学学报》2020年第4期431-438,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金重点项目(51434002);大洋协会重大专项基金(DY125-14-T-03)资助项目。

摘　　要：目前,悬链线在竖向集中力和均布荷载共同作用下的构形分析和受力计算的理论仍不完善。针对这一问题,通过引入悬链线的几何约束方程、力平衡方程和超越方程,建立了竖向集中力与均布荷载共同作用下的非线性方程组。采用牛顿迭代法求解方程组,得到了悬链线的构形和受力情况。为了验证理论计算的正确性,进行了算例和试验验证。结果表明,算例的计算结果与文献结论保持一致,试验测得的构形和水平张力大小与理论计算的构形和水平张力大小吻合较好。本文的理论计算可以更加简单精确地计算出悬链线在竖向集中力和均布荷载共同作用下的构形和受力情况,为实际工程提供重要的理论指导。At present,the theory of structural analysis and stress calculation of catenary under vertical concentrated force and uniform load is not perfect.For this problem,by introducing the geometric constraint equation,force balance equation and transcendental equation of catenary,the nonlinear equations of a catenary under a vertical concentrated force and uniform load are established.Newton’s iterative method is used to solve the equations,and the configuration and stress of the catenary are obtained.In order to verify the theoretical calculation,theoretical and experimental validations are carried out.The results show that the calculated results of the example are consistent with the conclusions of the literature.The measured configuration and horizontal tension are in good agreement with the theoretical calculation.The theoretical calculation in this paper can easily and accurately to calculate the configuration and stress of a catenary under the joint action of a vertical concentrated force and uniform load and provide important theoretical guidance for practical engineering.

关 键 词：竖向集中力 水平张力 构形 悬链线 同步求解 非线性方程组 

分 类 号：O316[理学—一般力学与力学基础]