两种新单元在悬索桥有限元计算中的应用

Application of Two New Elements to Finite Element Calculation of Suspension Bridge

为实现索与鞍座间接触非线性计算,开发了可用于悬索桥有限元计算的2种新单元:鞍座单元和锚跨单元,其中鞍座单元用于主缆和塔顶鞍座的接触非线性计算,锚跨单元用于锚跨分散索股及边跨主缆与散索鞍的接触非线性计算。根据空间悬链线理论及索与鞍座的几何关系,推导出精确的单元节点力。以增量代替微分,根据刚度矩阵的定义,推导出单元的切线刚度矩阵。编制了包含2种新单元在内的悬索桥几何非线性有限元程序。计算表明:2种新单元计算精度高、收敛速度较快,解决了悬索桥索与鞍座间接触非线性的计算难题。

To realize the calculation of contact nonlinearity between the main cable and sad dies, two new elements, the saddle element and anchor span element that can be applied to the fi nite element calculation of suspension bridge, have been developed. Of the two new elements, the saddle element is applicable to the calculation of contact nonlinearity between the main cable and tower saddle while the anchor span element is applicable to the calculation of contact nonlinearity between the anchor span splay main cable strands, the side span main cable and splay saddle. In accordance with the spatial catenary theory and the geometric relation between the main cable and saddles, the accurate element nodal forces are deduced. At the same time, by substituting the dif- ferential with the increment, the element tangent stiffness matrix is deduced, depending on the de{inition of the stiffness matrix. A calculation program including the two new elements that can satisfy the geometric nonlinear analysis of suspension bridge is complied. The application of the new elements to the calculation shows that the elements have high calculation accuracy, rapid convergence rate and the calculation problem of contact nonlinearity between the main cable and saddles of suspension bridge has hence been resolved.