基于拓扑优化的U形梁优化设计  

U-beam optimization design based on topology optimization

作　　者：蒋田勇 涂志杰 赵杰 张家滨 JIANG Tianyong;TU Zhijie;ZHAO Jie;ZHANG Jiabin(School of Civil Engineering,Changsha University of Science and Technology,Changsha,Hunan 410114,China;Jiangxi Traffic Engineering Development Co.,Ltd.,Nanchang,Jaingxi 331000,China)

机构地区：[1]长沙理工大学土木工程学院,湖南长沙410114 [2]江西交通工程开发有限公司,江西南昌331000

出　　处：《公路交通科技》2025年第2期111-118,共8页Journal of Highway and Transportation Research and Development

基　　金：国家自然科学基金项目(52378123);国家杰出青年科学基金项目(52425802)。

摘　　要：【目标】为减小某磁浮轨道交通工程项目中U形梁自重并提升其耐久性,对其进行优化设计。【方法】应用超高性能混凝土(UHPC)代替原U形梁中的普通混凝土,选择并设计UHPC基结构,以体积限值为约束条件,应变能最小为优化目标,采用Abaqus优化模块对UHPC基结构进行拓扑优化。为避免以往拓扑优化中人为主观设置体积限值造成反复计算而导致效率低,利用UHPC与C55普通混凝土的弹性模量比值及截面惯性矩与面积间的关系确定体积限值。UHPC基结构经过拓扑优化后得到初始设计截面,基于初始设计截面尺寸调整原U形梁尺寸得到新U形梁截面。使用Abaqus建立新U形梁和原U形梁的有限元模型,对比分析两种梁的自重和力学性能。【结果】与原U形梁相比,新U形梁自重减少了31.7%,第一、二阶弯曲振型对应的固有频率分别增加了18.5%和24.2%,最不利荷载作用下跨中挠度减少了21%,正截面抗弯性能提升了12%,斜截面抗裂性能提升了46%。【结论】优化设计得到的新U形梁在力学性能提升的前提下,其自重大幅减少,耐久性显著提升;同时,也表明了利用两种混凝土的弹性模量比值及截面惯性矩与面积间的关系确定的体积限值是有效的。研究设计成果可为后期U形梁优化设计研究和应用提供借鉴和参考。[Objective]To reduce the U-beam dead weight for a maglev rail transit project and improve its durability,the U-beam optimization design was carried out.[Method]The ultra-high performance concrete(UHPC)was used to replace the ordinary concrete in the original U-beam.The UHPC base structure was selected and designed.Taking the volume limit as the constraint,and the minimum strain energy as the optimization objective.The topology optimization on UHPC base structure was conducted by using the Abaqus optimization module.To avoid the low efficiency,caused by the repeated calculation due to the subjectively set volume limit,in the previous topology optimization,the volume limit was determined by using the elastic modulus ratio of UHPC and C55 ordinary concrete,and by using the relation between the section moment of inertia and the area.The initial designed section of UHPC base structure was obtained after topology optimization.The novel U-beam section was obtained by adjusting the original U-beam size based on the initial designed section size. Abaqus was used to establish and simulate the finite element model of novel andoriginal U-beams. The dead weight and mechanical properties of two beams were compared and analyzed.[Result] Compared with the original U-beam, the dead weight of novel U-beam is reduced by 31. 7%. Thenatural frequencies corresponding to the first and second bending modes are increased by 18. 5% and 24. 2%respectively. The mid-span deflection under adverse load is reduced by 21%. The bending performance ofnormal section is increased by 12%. The cracking performance of inclined section is increased by 46%.[Conclusion] Under the premise of improving mechanical properties, the optimized U-beam dead weight issignificantly reduced, and the durability is greatly improved. It also indicates that the volume limit iseffective, which is determined by using the elastic modulus ratio and the relation between section moment ofinertia and area. The study and design results can provide a reference for the later study

关 键 词：桥梁工程 新U形梁 拓扑优化 UHPC 基结构 体积限值 

分 类 号：U24[交通运输工程—道路与铁道工程]