带刚臂的两节点精确悬链线索元的非线性分析

NONLINEAR ANALYSIS OF TWO -NODE ACCURATE CATENARY CABLE ELEMENT WITH ARBITRARY RIGID ARMS

为解决应用悬链线索元时锚固点的刚性连接问题,在应用悬链线基本方程导出的两节点悬链线索元的切线刚度矩阵基础上,推导出两端带任意刚臂的两节点精确悬链线索元的切线刚度矩阵显式表达式,并且分析了考虑索元初次张拉和成形使用两种条件下切线刚度矩阵的迭代求解技术。分析和算例表明,应用两端带任意刚臂的两节点精确悬链线索元可以很好地解决前述问题,且其有限元分析格式与不带刚臂的悬链线索元完全一致,而且当索元不带刚臂时该切线刚度矩阵可自动转化为相应的刚度矩阵,实用价值较强。

In order to solve the problem of rigid anchor connection when using catenary cable element, based on the tangent stiffness matrix of two-node catenary cable element deduced with catenary equations, a more exact expression of tangent stiffness matrix is derived for two-node catenary cable element with arbitrary rigid arms. The iteration technique for initial cable tension and cable erection is also analyzed. Analysis and numerical example demonstrate that the new catenary cable element can simulate the rigid connection successfully, and the FEM procedure of the new element is the same as the old one. The new tangent stiffness matrix may degenerate into the old one automatically if the catenary cable element has no rigid arms. The new element can be used in cable structures extensively.