面外法向集中力作用下水平悬链线的构形与张力研究

Research on the configuration and tension of horizontal catenary under the action of out-of-plane normal concentrated force

悬链线理论在大跨度的空间柔性管线设计等领域应用日益广泛,但在应用中主要考虑面内竖向力或水平力的工况,利用悬链线理论来直接求解面外问题的研究仍不完善。针对这一问题,本研究从二维悬链线理论出发,建立了面外法向集中力作用在水平悬链线任意位置处的非线性方程组,并得到了面外法向集中力作用在悬链线中点处的解析解。采用二分法和Newton-Raphson迭代法分别对解析解和非线性方程组进行求解。利用柔索试验装置、有限元计算对本研究计算结果进行验证。结果表明,试验、有限元计算得到的构形与特征张力和理论计算的构形与特征张力吻合较好,理论研究成果可以解决柔性管线在竖向分布力和面外法向集中力共同作用下的初始构形找形与特征张力计算问题。

Catenary theory is increasingly widely used in the design of large-span space flexible pipelines.However,the application mainly considers in-plane vertical force or horizontal force,and the study of using catenary theory to directly solve out-of-plane problems is still not perfect.In response to this problem,this paper starts from the two-dimensional catenary theory,establishes a nonlinear equation system in which the out-of-plane normal concentrated force acts on the horizontal catenary at any position,and obtains the analytical solution of the out-of-plane normal concentrated force acting on the midpoint ofcatenary.The dichotomy and the Newton-Raphson iterative method are used to solve the analytical solutions and nonlinear equations respectively.The results of this paper are verified by flexible cable test device and finite element calculation.The results show that the configuration and characteristic tension obtained by experiments and finite element calculations are in good agreement with the configuration and characteristic tension calculated by theoretical calculations.The theoretical research results in this paper can solve the common problem of the vertical distributed force and the out-of-plane normal concentrated force of the flexible pipeline.The initial configuration form-finding and characteristic tension calculation problems under the action.