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为解决应用抛物线索元进行索结构几何非线性分析时锚固点的刚性连接问题,在参考已有研究的基础上,进行了带刚臂的平面抛物线索元研究。将锚固点的刚性连接视为刚臂,根据受力后刚臂两端节点力之间和位移之间全量和增量的关系,利用微分方法导出两端带任意刚臂的平面抛物线索元切线刚度矩阵显式表达式;同时给出了考虑温度变化的节点力计算方法,提供了详细的计算步骤;编制了相应的几何非线性计算程序,对经典大垂度单索、带刚臂的平面桁架和索梁混合结构进行了几何非线性分析。研究结果表明:相对于已有文献方法,该算法具有同样的计算精度,且在计算效率及求解问题的非线性程度上有较大的优势,为索结构进行几何非线性精细分析提供了有力工具。
In order to solve the problem of rigid connection of anchor points in the nonlinear geometric analysis of cable structure using parabola, a planar parabolic cable element with rigid arms is studied based on the existing research. The rigid connection of anchorage point is regarded as a rigid arm. According to the relationship between total forces and displacements between the two ends of the rigid arm after the force is applied, the tangent of the plane parabolic element with arbitrary arm at both ends is derived by using the differential method Stiffness matrix expression is given. At the same time, the calculation method of nodal force considering temperature change is given and detailed calculation steps are provided. Corresponding geometric nonlinear calculation program is compiled, The geometric nonlinear analysis of truss and cable beam hybrid structures. The results show that the proposed algorithm has the same computational accuracy as the existing literature methods and has great advantages in computational efficiency and non-linearity of solving the problem, thus providing a powerful tool for geometric non-linear fine analysis of cable structures .