悬索桥有限元计算的三节点空间鞍座单元

3-Node Sptial Saddle Element for Finite Element Calculation of Suspension Bridge

为了进行空间缆索悬索桥主缆与塔顶鞍座间接触非线性的计算,开发了包括塔顶鞍座及两侧主缆在内的三节点空间鞍座单元.基于空间悬链线理论及主缆与鞍座的几何关系,对单元进行状态求解,得到主缆与鞍座的切点位置及切点索力,根据静力平衡条件计算单元精确的节点力;由增量代替微分,根据切线刚度矩阵的定义计算单元刚度矩阵的元素.空间鞍座单元自动满足主缆与鞍座相切,通过修改一个参数可实现鞍座顶推的计算.计算表明:计算结果与数值解析解结果完全相同,收敛速度较快,在每次状态求解时,迭代次数在12次以内.

In order to solve the computational problem of nonlinear contact between main cable and saddle on tower top, a new 3-node spatial saddle element, including the saddle on tower top and both sides of the main cable, was produced. Based on the spatial catenary theory and the geometric relationship between main cable and saddle, the location of the tangent points and the cable force at the tangent points were obtained by solving the element state determination problem with known conditions. The accurate nodal force of the element was derived according to the static equilibrium. The elements of the tangent stiffness matrix were calculated based on its definition by replacing the differential with the increment. The new element could automatically satisfy the condition that the main cable is always tangent to the saddle, and thus the saddle jacking could be conveniently realized by modifying a parameter. Calculation shows that the new element has high calculation accuracy and convergence rate. The calculation results are the same with the numerical analytical solutions. The number of iterations is generally less than 12 in each element state solution.