悬链线索元的协调方程式及其弦向刚度

Compatible equation and chord-direction stiffness expression of catenary cable element

基于精确的悬链线索元模型,本文推导了一种反映索原长和索张力水平分量之间关系的协调方程式,以及适用于动力松弛法找形分析的索元弦向刚度表达式.利用该协调方程式,无需迭代或仅采用简单的二分法便可以稳定快速地实现索原长与索力之间的换算.索元弦向刚度表达式可以在常规动力松弛法找形分析时考虑大垂度松弛索元的情况.

Based on the catenary cable element model,a new compatible equation which reflects the relationship between the unelongated cable length and the horizontal component of its tensile foce is put forward.Using the compatible equation,the conversion between the cable's unelongated length and its tensile force can be achieved rapidly and steadily in simple bichotomy,even without iteration.The chord-direction stiffness expression of catenary cable is also deduced on request of shape-finding with dynamic relaxation method.The two expressions can be adopted for both large-sag and prestressed cable element.