摘要
考虑材料参数的不确定性以及设计变量多重约束条件的影响,提出了基于可靠性分析的钢板组合梁桥结构优化设计方法。首先,利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验组合方案,并通过有限元分析获取试验设计组合下的最大挠度响应值。基于获取的训练样本,构建能够表征结构最大挠度值与随机输入之间映射关系的Kriging代理模型。基于建立的代理模型,以钢结构截面积最小化为目标函数,建立符合规范要求与可靠度约束的优化数学模型,并采用一阶可靠性方法(first order reliability method,FORM),实现设计变量优化。通过比较具有相同设计变量上限,但下限分别为初始值的80%和70%两种优化设计方案,评估了两者在相同阈值以及不同阈值下设计变量的优化结果。最后对方案二在阈值为17 mm下的优化结果进行极限状态验算。结果表明:两个优化设计方案在阈值为17 mm下的优化结果更具合理性,并且方案二在同一阈值下具有更高的优化程度。随着阈值增加,优化程度增加,且腹板高度在较大阈值下对结果影响更大,而翼缘宽度在较小阈值下影响更大。
Considering the uncertainties of material parameters and the influence of multiple constraints of design variables,an optimization design method for steel plate composite girder bridge structures based on reliability analysis was proposed.Firstly,the Latin hypercube design(LHD)was utilized to construct experimental combination schemes,and the maximum deflection response values under the experimental design combination were obtained by finite element analysis.Based on the obtained training samples,a Kriging surrogate model was constructed to represent the mapping relationship between the maximum deflection value of the structure and random inputs.Based on the established surrogate model,an optimization mathematical model that met regulatory requirements and reliability constraints was established with the objective function of minimizing the cross-sectional area of steel structures.And the first order reliability method(FORM)was adopted to optimize design variables.By comparing two optimization design schemes with the same upper limits of design variables but lower limits of 80%and 70%of the initial value,the optimization results of the design variables under the same threshold and different thresholds were evaluated.Finally,the limit state verification was conducted for the optimization results of scheme 2 at a threshold of 17 mm.The results indicate that the optimization results of the two design schemes are more reasonable at a threshold of 17 mm,and the scheme 2 exhibits a higher degree of optimization at the same threshold value.As the threshold increases,the degree of optimization also increases,and the height of the web has a greater impact on the results at a larger threshold,while the width of the flange has a greater impact at a smaller threshold.
作者
王佐才
张德林
辛宇
WANG Zuocai;ZHANG Delin;XIN Yu(School of Civil Engineering,Hefei University of Technology,Hefei 230009,Anhui,China;Anhui Province Road and Bridge Inspection Engineering Research Center,Hefei 230009,Anhui,China)
出处
《重庆交通大学学报（自然科学版）》
CAS
CSCD
北大核心
2024年第8期1-9,共9页
Journal of Chongqing Jiaotong University(Natural Science)
基金
国家自然科学基金项目(52278301,52308310)。
关键词
桥梁工程
基于可靠性的优化设计
KRIGING模型
一阶可靠性方法
钢板组合梁桥
极限状态验算
bridge engineering
reliability-based optimization design
Kriging model
first order reliability method
steel plate composite girder bridge
limit state verification
