波形腹板钢箱-混凝土箱梁桥的有限元模型修正

为了缩小波形钢腹钢箱-混凝土组合箱梁桥有限元值与实测值之间的偏差，提出了采用响应面法和Fmincon算法相结合的桥梁有限元模型修正方法. 以甘肃景中机场连接线的一座波形钢腹钢箱-混凝土组合箱梁桥为研究对象，首先对其进行静、动载试验，获得其弯曲振动频率、挠度及应变的实测值；其次分别采用实体和板壳模式的有限元建模获得该桥相应的弯曲振动频率、挠度及应变的计算值，通过与实测值对比分析后，选取较为精确的实体模式有限元模型作为修正的初始有限元模型；随后在合理选择设计参数的基础上，通过中心复合试验设计得到相应的结构响应，采用最小二乘法拟合得到结构响应和设计参数之间的二次多项式回归方程，并构造目标响应与相应响应实测值差值的目标函数；最后运用Fmincon算法对目标函数进行迭代计算，获得参数修正值及该桥的基准有限元模型. 研究结果表明:采用响应面法和Fmincon算法相结合的方法对波形钢腹钢箱-混凝土组合箱梁桥的有限元模型进行修正切实可行，具有修正过程简单、计算收敛速度快等特点，计算时间在0.25～0.75 s内，一阶弯曲振动频率相对误差由4.85%依据不同响应组合修正到1.62%～2.91%不等；通过对遗传算法和Fmincon算法的比较发现，Fmincon算法显著提高了模型修正效率，可为实际工程中该类桥梁的有限元建模分析及力学性能分析提供参考. 

Finite Element Model Updating of Box Girder Bridges with Corrugated Steel Webs

In order to reduce the error between the finite element values and measured values of the box girder bridge with corrugated steel webs, a bridge finite element model updating method using response surface method and Fmincon algorithm was presented, taking a box girder bridge with corrugated steel webs in the connecting line of Jingzhong airport in Gansu province, China as the research object. Firstly, static and dynamic load tests were carried out to obtain the measured values of bending vibration frequency, deflection and strain. Secondly, the calculated values of these parameters were obtained by the finite element modeling using solid and plate-shell elements, respectively. After comparison of the calculated values with the measured values, a more accurate solid finite element model was selected as the updated initial finite element model. Then, on the basis of reasonable selection of design parameters, the corresponding structural response was obtained through the central composite test design, the quadratic polynomial regression equation between the structural response and design parameters was obtained by least square method fitting, and the objective function of the difference between the measured value of the target response and the corresponding response was constructed. Finally, Fmincon algorithm was used to calculate the objective function iteratively, and the updated value of parameters and the baseline finite element model of the bridge were obtained. The results show that it is feasible to modify the finite element model of the composite box girder bridge with corrugated steel webs by combining the response surface method and the Fmincon algorithm, which has the characteristics of simple modification process and fast convergence speed. The calculation time was within 0.25–0.75 s, and the relative error of the first-order bending vibration frequency was updated from 4.85% to 1.62%–2.91% according to different response combinations. Through the comparison between Genetic algorithm and Fmincon algorithm, it was found that Fmincon algorithm improves the model updating efficiency significantly, which can provide reference for the finite element modeling analysis and mechanical performance analysis of this kind of bridges in engineering practices.