带刚臂和弹性段的平面组合索单元

Combined Planar Cable Element with Rigid Arms and Elastic Segments

为在斜拉桥的有限元模型中高效地模拟斜拉索,建立了带刚臂和弹性段的平面组合索单元.两个刚臂位于单元的端部,单元的节点分别与塔柱和主梁上的对应节点固接.索的钢套筒部分视为弹性段,中间索段视为弹性悬链线,弹性段的内力沿接点处弹性悬链线的切线方向.首先利用弹性悬链线的解析解建立了索体的投影方程和刚度矩阵;利用刚臂两端位移转换关系,对组合单元的节点力微分,得到了组合索单元的刚度矩阵.算例分析证明了公式推导及编程的正确性.

To efficiently simulate the stay cable in the FEM of cable-stayed bridges,a combined planar cable element with rigid arms and elastic segments was proposed.Two rigid arms were located in the two end regions.The two nodes of the element were fixed to the points on the column of the tower and the main beam respectively.The steel sleeves of the cable was taken as elastic truss,and the inner part was considered elastic catenary.The inner force in the elastic truss was tangent to the elastic catenary at the joint.Based on the analytical solution of the elastic catenary,the projection equations as well as the stiffness matrix of the cable body were obtained.Taking the relationship between displacements at the two ends of the rigid arm into account,the node forces of the element were differentiated,then the stiffness matrix of the combined cable element was obtained.The example analyses proved the correctness of the formula derivation and programming.