基于索长迭代的斜拉桥整体线形优化实用算法

孟繁增

doi:10.19713/j.cnki.43-1423/u.T20222384

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基于索长迭代的斜拉桥整体线形优化实用算法

桥梁隧道与结构 | 更新时间：2023-12-05

- 基于索长迭代的斜拉桥整体线形优化实用算法
- Practical algorithm for optimizing the integral geometrical shape of cable-stayed bridges based on cable length iteration
- 铁道科学与工程学报 2023年20卷第11期页码：4266-4276
- 作者机构：
  
  1.中国铁路设计集团有限公司土建工程设计研究院，天津 300308
- 作者简介：
  
  孟繁增(1988—)，男，河北衡水人，高级工程师，从事桥梁设计研究；E-mail：mengfanzeng@crdc.com
- 基金信息：
  
  中国国家铁路集团有限公司科技研究开发计划项目(K2021G013);中国铁路设计集团有限公司科技开发课题(2020YY240604;2021B240633)
- DOI：10.19713/j.cnki.43-1423/u.T20222384
  中图分类号：
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孟繁增.基于索长迭代的斜拉桥整体线形优化实用算法[J].铁道科学与工程学报,2023,20(11):4266-4276.

MENG Fanzeng.Practical algorithm for optimizing the integral geometrical shape of cable-stayed bridges based on cable length iteration[J].Journal of Railway Science and Engineering,2023,20(11):4266-4276.
孟繁增.基于索长迭代的斜拉桥整体线形优化实用算法[J].铁道科学与工程学报,2023,20(11):4266-4276. DOI： 10.19713/j.cnki.43-1423/u.T20222384.

MENG Fanzeng.Practical algorithm for optimizing the integral geometrical shape of cable-stayed bridges based on cable length iteration[J].Journal of Railway Science and Engineering,2023,20(11):4266-4276. DOI： 10.19713/j.cnki.43-1423/u.T20222384.

摘要

针对密索体系斜拉桥整体线形优化问题，提出一种基于索长迭代的实用算法。该算法以无应力索长作为施调量，以主梁和主塔的位移值作为受调量，以锚点位移误差在斜拉索方向上的投影值作为修正值，代入索长-位移等代矩阵进行逐步逼近的正向迭代计算。首先，采用单索结构阐述算法原理，进行理论验证，并推广至密索结构；然后，进一步给出算法的具体实现方法并编制程序；最后，采用某无砟轨道斜拉桥进行应用验证。研究结果表明：算法收敛于理论解，收敛速度与梁索刚度比有关，当梁索刚度比,k,2,/,k,1,≤1.01时，迭代3～5次其误差降低至5%以内。随着迭代次数的增加，位移残差单调递减并逐渐稳定，索长调整量逐渐逼近于零位移法最小二乘解，证明了本文算法的收敛稳定性。当由混合梁、辅助墩等引起主梁刚度差异或局部变化时，本文解的均匀性优于零位移法最小二乘解。迭代18次，用时1.99 s即可得到一组合理的索长调整量，主梁及主塔线形偏差小于5.0 mm，线形平顺，索力均匀合理。本文算法可快速提供一系列接近零位移(或目标线形)的索长调整解，几何关系清晰，线形与索力均匀，实用性强，可应用于密索体系斜拉桥设计和施工控制中的线形优化调索。

Abstract

A practical algorithm based on cable length iteration was proposed for the integral geometrical shape optimization of a cable-stayed bridge with a multi-cable system. The proposed algorithm considered the unstressed cable length as the adjusting quantity, the displacements of the main girder and the main tower as the adjusted quantities and the projection value of the displacement error of the anchor point on the side of the cable as the correction value and then substitutes them into the cable length-displacement equivalent matrix for iterative forward calculations. The principle of the algorithm is explained for a single-cable structure, theoretically verified and then extended to a multi-cable structure. The implementation of the algorithm was presented, and programming was completed. Finally, a ballastless track cable-stayed bridge was used to verify the application of the algorithm. The algorithm converged to the theoretical solutions for single-cable structures, and the convergence rate was related to the beam-to-cable stiffness ratio. When the stiffness ratio,k,2,/,k,1, is ≤ 1.01, the error is reduced to 5% or below after 3～5 iterations. The study of 300 000 iterations of the multi-cable structure shows that as the number of iterations increases, the residual displacement decreases monotonously and gradually stabilises, and the cable length adjustment gradually approaches the least square solution of the zero displacement method. This confirms the convergence stability of the proposed algorithm. When the difference in stiffness or the local change is caused by a hybrid girder or an auxiliary pier, the uniformity of the solution in this paper is better than the least square solution of the zero displacement method. As verified in actual application, a reasonable set of cable length adjustment quantities can be obtained in 1.99 s with 18 iterations, the geometrical shape deviation of the main girder and the main tower is less than 5.0 mm, and a smooth geometrical shape, as well as uniform and reasonable cable tension values, can be obtained. The proposed algorithm can quickly provide a series of cable length adjustments close to zero displacement (or to the target alignment). Given its clear geometrical relationship, uniform geometrical shape and cable force and practical applications, the algorithm can be applied for integral geometrical shape optimization in the design and construction control of a cable-stayed bridge with a multi-cable system.

关键词

索长迭代斜拉桥线形优化实用算法

Keywords

cable length iterationcable-stayed bridgeintegral geometrical shape optimizationpractical algorithm

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