悬索桥空间缆成桥找形分析的线形变化刚度矩阵法

STIFFNESS MATRIX METHOD FOR FORM-FINDING ANALYSES OF SPATIAL CABLE SYSTEMS IN SUSPENSION BRIDGES

  • 摘要: 悬索桥空间主缆成桥线形计算中,如何建立控制点位移与初始力的精确对应关系是关键难题,本文提出了线形变化刚度矩阵法,可针对关键控制点一次性建立位移误差与初始力修正量的对应关系。建立了空间主缆-吊索协同分析模型,主缆和吊索简化为柔性索并形成空间协同作用关系。基于该模型,将索段无应力长度作为变量,建立完整Jacobi矩阵并严格消去该变量,推导出主缆Jacobi矩阵和吊索逆Jacobi矩阵;引入力传递矩阵和累积传递矩阵,构建全局方程,直接提取针对关键控制点的刚度矩阵,建立控制点位移误差与初始力修正量的线性关系。采用C++实现本文算法并以西安灞河元朔大桥验证,迭代23次、耗时1s~2s达到收敛。与BNLAS软件对比,计算结果高度吻合,且具有较好的初值鲁棒性,验证了方法的正确性。

     

    Abstract: In the spatial main cable configuration calculation of suspension bridges, establishing an accurate correspondence between control point displacements and initial forces is a critical challenge. This paper proposes a configuration stiffness matrix method that directly establishes the correspondence between displacement errors and initial force corrections for key control points in a single step. A spatial main cable-hanger collaborative analysis model is established, where both the main cable and hangers are simplified as flexible cables to form a spatial interaction relationship. Based on this model, the unstressed cable length is treated as a variable to establish a complete Jacobi matrix, which is then rigorously eliminated through partial differentiation, yielding the main cable Jacobi matrix and the hanger inverse Jacobi matrix. Force transfer matrices and cumulative transfer matrices are introduced to construct a global equation system, from which the stiffness matrix for three key control points is directly extracted, establishing a linear relationship between control point displacement errors and initial force corrections. The algorithm is implemented in C++ and validated using the Xi'an Bahe Yuanshuo Bridge. The convergence is achieved in 23 iterations with a computation time of 1~2 seconds. The computational results show an excellent agreement with those of BNLAS software and demonstrate strong robustness with respect to the initial value selection, verifying the correctness and engineering applicability of the method proposed.

     

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