改进Gibbs-Poole-Stockmeyer算法加速车-桥耦合振动分析的应用研究  

Application Research on Improving Gibbs-Poole-Stockmeyer Algorithm to Accelerate Vehicle-bridge Coupling Vibration Analysis

作　　者：刘修平 韩万水[1] 杨干 袁阳光 刘博 苏宁 LIU Xiu-ping;HAN Wan-shui;YANG Gan;YUAN Yang-guang;LIU Bo;SU Ning(School of Highway,Chang'an University,Xi'an 710064,Shaanxi,China;School of Civil Engineering,Xi'an University of Architecture and Technology,Xi'an 710055,Shaanxi,China;Shaanxi Transportation Holding Group Co.Ltd.,Xi'an 710000,Shaanxi,China)

机构地区：[1]长安大学公路学院,陕西西安710064 [2]西安建筑科技大学土木工程学院,陕西西安710055 [3]陕西交通控股集团建设管理公司,陕西西安710000

出　　处：《中国公路学报》2025年第2期164-174,共11页China Journal of Highway and Transport

基　　金：国家重点研发计划项目(2021YFB1600300);国家自然科学基金项目(52308200);陕西省自然科学基础研究计划项目(2023-JC-YB-321)。

摘　　要：为应对千米级双层随机车流-桥梁耦合振动高效分析需求,从降低桥梁子系统存储量和运算成本的角度出发,提出了一种基于改进Gibbs-Poole-Stockmeyer算法的车-桥耦合振动分析加速方法。首先,通过结构离散化模型对改进的Gibbs-Poole-Stockmeyer算法进行测试,验证方法的准确性;其次,将改进方法用于超千米跨度双层钢桁桥梁模型的存储优化分析,同时融入现有分析系统开展随机车流过桥响应分析,最后进行计算效率对比。研究结果表明:改进Gibbs-Poole-Stockmeyer算法在获得的带宽等于已有研究方法的前提下,节点编号过程中不需回溯;所提方法对大跨度双层钢桁桥梁模型存储空间占用有较大改善,刚度矩阵最大带宽和一维变带宽存储数组长度明显减小;同等计算条件下,改进后的分析系统在进行瞬态分析及处理高流量车辆-桥梁耦合振动分析方面,相较于现有分析系统,计算效率均有着较大的提升;所提方法使得现有分析系统的大规模有限元模型处理能力和计算效率得到了大幅提高。In this study,a method for accelerating the vehicle-bridge coupling vibration analysis based on an improved Gibbs-Poole-Stockmeyer algorithm was proposed to address the efficient analysis requirements of kilometer-scale dual-layer random vehicle-bridge coupled vibrations to reduce the storage and computational costs of the bridge subsystem.First,the improved Gibbs-Poole-Stockmeyer algorithm was tested using a structural discretization model to verify its accuracy.Subsequently,the improved method was applied to optimize the storage analysis of a super-long-span dual-layer steel-truss bridge model,while incorporating the existing analysis system for random vehicle flow over a bridge response analysis.Finally,the calculation efficiencies were compared.The results show that when the same bandwidth is obtained as in existing research methods,the improved Gibbs-Poole-Stockmeyer algorithm can achieve a lower tree width without the need for backtracking during node numbering.The proposed method improves the storage space of the long-span dual-layer steel-truss bridge model,and the maximum bandwidth of the stiffness matrix and the length of the one-dimensional variable-bandwidth storage array are significantly reduced.Under equivalent computational conditions,the improved analysis system significantly improves computational efficiency in performing transient analysis and handling high-traffic vehicle-bridge coupled vibration analysis compared to existing analysis systems.The proposed method significantly increases the processing capacity and computational efficiency of existing analysis systems for large-scale finite element models.

关 键 词：桥梁工程 车-桥耦合振动 数值分析 Gibbs-Poole-Stockmeyer算法 刚度矩阵带宽 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]