带刚臂的平面抛物线索元精细几何非线性分析

Refined geometric nonlinear analysis on plane parabolic cable element with rigid arms

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。

Based on the existing research, a plane parabolic cable element with rigid arms was proposed to solve the problem of rigid anchor connection. According to the characteristics of the forced rigid arm, the relationships of total amount and incremental for the displacement and the end force of ends of rigid arms in global coordinate system were presented by treating rigid link of anchorage point as rigid arm. Then by differential method, the explicit expressions of nonlinear tangent stiffness matrix of plane parabolic cable element with rigid arms in both ends were obtained. The nodal forces algorithm which considers temperature change was developed, and the detailed calculation procedures were presented. A finite element program based on the algorithm was developed. Three examples including classic single cable structure, plane truss structure with rigid arms, and hybrid structure of cable and beam were employed to perform plane geometrical nonlinear analysis. The results show that the developed algorithm has the same calculation accuracy as the existing algorithm, and it can improve computational efficiency and apply to higher nonlinear degree. It can provide a powerful tool for refined geometrical nonlinear analysis of cable structure. 2 tabs, 10 figs, 12 refs.