基于共旋坐标法的悬索桥几何非线性正装计算分析及软件开发

Geometric Nonlinear Forward Calculation Analysis and Software Development of Suspension Bridges Based on the Co-rotational Procedure

给出了基于共旋坐标法的几何非线性计算流程,推导了按共旋坐标法的梁杆单元在总体坐标系下的几何非线性切线刚度矩阵,经过比较证明了和Saafan给出的几何非线性切线刚度矩阵一致。同时单元切线刚度矩阵元素完全对称,并且可以用于直接组集总刚度矩阵,不需要经过旋转变换。根据无应力长度为未知量的成桥找形计算和已知无应力长度的几何非线性正装计算的互逆性,应用基于几何非线性正装计算算法开发的几何非线性分析程序,对含梁杆索混合单元的悬索结构进行了正装计算,其中梁单元和杆单元按共旋坐标法计算,主缆单元按只受拉的索单元计算。几何非线性正装计算的线形和内力跟成桥找形的结果能闭合,验证了找形所得线形的平衡状态以及几何非线性程序的正确性。

Based on co-rotational procedure,the geometrically nonlinear calculation procedures was introduced and the tangient stiffness matrix of beam and truss element in the global coordinate system was deduced in this paper,which was proved to be consistent with that deduced by Saafan by comparison.The element of tangient stiffness ma-trix is totally symetric and can be assembled directlly for total stiff matrix without rotation transformation.According to the mutual invesism of shape-finding analysis of the bridge and geometrically nonlinear forward calculation,as the former of which zero-stress lengths are known but the latter unknown,the geometrically nonlinear analysis programs developed by the algorithm of geometrically nonlinear forward analysis has been used to do forward analysis of suspension structures with hybrid elements of beam,truss and cable.And the beam and truss element was calculated by co-rotational procedure and the main cable element by tension-only cable element.The shape and inner force by geometrically nonlinear forward analysis closed with the result of shape-finding of the bridge,which the balance state of shape finding and the correctness of the programs have been verified.