Study On Spatial Catenary Theory And Its Application In Flexible Cable Calculation

Catenary theory in large span space is increasingly widely used in such fields as flexible pipeline design,such as Yang ore hose in deep-sea mining,large span suspension bridge main cable,high voltage transmission lines,etc.,but the main consideration in the application of the operation condition of the surface in the vertical or horizontal forces,outside catenary theory is used to directly solve the surface problem did not see the relevant theoretical research.In order to solve this problem,based on two-dimensional catenary theory,this paper studies the surface under the action of concentrated force outside the space problem of catenary,further by considering the tensile stiffness,studies the spatial catenary theory when calculating the space flexible pipeline configuration and tension of the applicability of the problems,to find form for flexible pipeline engineering of space analysis provides a theoretical basis.The main research contents and conclusions of this paper are as follows:(1)This paper introduces relative depth k,the spatial catenary theory with only one unknown parameter is deduced and established,and the spatial horizontal catenary equilibrium equation under the action of a single outside normal normal concentrated force is established.At the same time,the spatial catenary equilibrium equation under the action of any concentrated force is obtained by further study.(2)For the special working condition of spatial horizontal catenary under the action of normal concentrated force outside a single plane,the solving process of analytical method and iterative method is derived in detail,and the computational efficiency of the two methods in solving the specific working condition is compared.For other working conditions,the iterative method is adopted to solve.In the process of solving the problem,the self-programmed software is used for calculation.(3)According to the working condition of spatial horizontal catenary under the action of a single outside normal concentrated force,the influence of different position and magnitude of concentrated force on catenary configuration and characteristic tension is studied,and the existence condition of minimum characteristic tension and the probability distribution law of maximum external offset of catenary are found.The model test and finite element method were used to compare the theoretical calculation results in this paper,and the error interval of the results met the accuracy requirements.(4)The influence of tensile stiffness on the configuration of space flexible pipeline was studied,the line length variation formula of space flexible pipeline was deduced,the equilibrium equations of space flexible pipeline under the action of concentrated force were established,and the self-programmed calculation was carried out.The finite element simulation is used to verify the theoretical calculation results in this paper,and the results show that the theoretical calculation is correct.