索网结构中的空间两节点悬链线索单元

摘要

为了分析索结构在荷载作用下的线性和非线性反应，根据索结构的受力特点，提出了一种可以充分考虑索结构非线性效应的空间两节点悬链线索单元。基于弹性悬链线的解析解，推导了索单元的切线刚度矩阵，通过迭代法求解了索结构的刚度矩阵和内力向量，利用该新型的索单元模型分析了静、动力荷载作用下结构的非线性行为，对于非线性静力分析，结构平衡方程采用牛顿迭代法求解；对于非线性动力时程分析，采用Newmark直接积分法和牛顿迭代法相结合的增量迭代法求解。数值分析结果验证了空间两节点悬链线索单元模拟索结构的精确性和可靠性。%To analyze the linear and nonlinear behaviors of cable⁃net structures based on their mechanical character⁃istics, this paper presents a spatial two⁃node catenary cable element model ( STCCE) , which can be used to ana⁃lyze the nonlinear effect cable structures under static and dynamic loads. The tangent stiffness matrix was derived based on the analytical solutions of elastic catenary;the stiffness matrix and internal force vector were calculated u⁃sing an iterative algorithm;the nonlinear behavior was analyzed using the new model STCCE under static and dy⁃namic loading. The Newton⁃Raphson method was applied to sove the structural balance equation for the nonlinear static analysis. An incremental iterative method, based on the Newmark direct integration and Newton⁃Raphson methods, was used for nonlinear dynamic time⁃history analysis. The accuracy and reliability of the STCCE were ver⁃ified using numerical analysis.