水平悬链线中点集中力作用下的非线性分析及计算

首先，对均布力作用下悬链线理论进行了深入分析研究，推导出求解水平张力单参数和双参数形式的隐含超越方程，在算法上验证了两种方程的等价性。对于悬链线固有的广义倾角、曲率半径、约束反力和水平张力的嵌入关系等给出了具有新意的表达公式。然后，建立了水平悬链线在对称集中力作用下的平衡方程，对于不同垂向集中力作用下水平张力的变化情况和最大垂直距离差所在水平位置随集中力的变化等进行了非线性计算。本文在理论构建和分析方面具有创新性，在理论探索和工程应用上具有重要意义。

Nonlinear analysis and computation on horizontal catenary midpoint under concentrating force

At first this article carries out thorough research on the catenary theory,derives the implicit transcendental equations with a single parameter and with double parameters for the horizontal tension, and proves the equivalence of two transcendental equations by algorithm.New mathematical formulas for the intrinsic generalized angle,radius of curvature,constraint forces of the catenary as well as the embedded relation of relative horizontal tension are presented.Besides,the equilibrium equation of horizontal catenary under the symmetric concentrating force is established,and the unknown vertical distance is determined.The paper calculates the nonlinear variation of horizontal tension and maximum of vertical distance with concentrated force location.The theory-and analysis presented are novel,which is of great significance in the engineering and in theoretical exploration.