基于响应面法的钢管混凝土组合桁梁桥多尺度有限元模型修正

为建立适用于钢管混凝土桥梁的高效、高精度有限元分析模型，提出一种基于响应面法的全桥多尺度有限元模型修正方法。首先以一座钢管混凝土组合桁梁桥为工程背景建立包含全桥、组合桁梁桥面板以及钢管混凝土桁架杆件3个尺度的ABAQUS全桥多尺度有限元模型。在考虑钢管混凝土结构的特点和施工误差的基础上选取桥面板混凝土弹模、厚度，桁架弦杆内混凝土弹模，钢材弹模以及加载车辆荷载5个影响因素作为待修正参数；根据实桥试验条件选择中跨跨中挠度、下弦空管弦杆应力、墩顶钢管混凝土弦杆应力、墩顶受压腹杆应力以及桥面板顺桥向应力5个目标函数。其次采用中心复合设计方法生成了待修正参数的样本集，并将每组参数样本代入有限元模型进行计算。进而采用响应面法建立待修正结构参数和目标函数的2次多项式函数关系，结合参数显著性分析得到响应面方程。最后结合实桥试验结果对多尺度有限元模型3个尺度上的结构参数进行同步修正。结果表明：修正后的参数变化情况与依托工程的实际施工情况相符；采用修正后的参数建立的多尺度有限元模型计算值与实桥试验结果吻合良好；修正后的有限元模型具有较高的精度，可真实反映实际工程中桥梁结构的受力状态。该修正方法可为桥梁结构运营期间的健康监测、状态评估、损伤检测提供可靠的分析手段。

Multi-scale Finite Element Model Updating of CFST Composite Truss Bridge Based on Response Surface Method

In order to propose a finite element model (FEM) of a concrete-filled steel tubular (CFST) bridge with high efficiency and accuracy, an updating method combined with field test and multi-scale FEM was presented. Firstly, a multi-scale ABAQUS FEM of a CFST composite truss bridge was developed based on practical engineering. The FEM model included three scale levels:the whole bridge, deck of the composite girder, and members of the CFST truss. The elastic modulus and thickness of the concrete deck, elastic modulus of the truss chord, elastic modulus of steel, and the loads of loading vehicles were chosen as the five updating parameters by considering the structural characteristics and construction errors of CFST structures. Deflection at mid-span, stress of the hollow bottom chord member, stress of the CFST bottom chord member at the pier top, stress of the compression brace at the pier top, and longitudinal stress of the deck were chosen as the five objective functions by considering the conditions of the field test. Secondly, the central composite design method was applied to generate a sample set of updating parameters, and each sample was imported into the FEM for calculation. The response surface method was then used to establish the second-order polynomial function between the updating parameters and objective function. The response surface equation was also obtained by parameter significance analysis. Finally, the structural parameters of the three scale levels from the multi-scale FEM were updated synchronously based on the bridge field test. The results show that the updated parameters coincided well with the conditions of practical bridge construction. The calculated results of the updated multi-scale FEM agreed with the field test results. The updated FEM has higher accuracy, which can truly reflect the mechanical behavior of bridge structures in practical engineering. The proposed updating method provides a reasonable analytical method for health monitoring, state assessment, and damage detection during the operation stage of bridge structures.