基于多目标优化的独柱墩直线梁桥抗倾覆加固

Anti-overturning Reinforcement for Single-column Pier Straight Beam Bridge Based on Multi-objective Optimization

针对倾覆风险较高的独柱墩直线连续梁桥,采用增设钢盖梁的方法对独柱墩进行加固,使独柱墩处的支承由原来的单支撑转变为三支撑,从而提高独柱墩直线梁桥的抗倾覆能力。为在提高其横向倾覆稳定系数的同时,尽可能地减小独柱墩受到的偏心弯矩作用,构建了以独柱墩原支座尺寸和钢盖梁新增支座间距为设计变量、以横向倾覆稳定系数和偏心弯矩安全系数为目标函数的多目标优化模型,然后基于Python联合NSGA-Ⅱ遗传算法与Abaqus建立的参数化有限元模型,求解该多目标优化模型的Pareto最优解集,利用博弈论综合赋权法计算目标函数的权重,再采用TOPSIS法计算Pareto最优解集中解的亲密度系数,从而选出最佳的加固设计方案。研究结果表明:采用增设钢盖梁的加固方法能够有效提高独柱墩直线梁桥的抗倾覆能力,采用初始方案加固后独柱墩直线梁桥的倾覆稳定系数提高了167%,满足规范要求;Python能将优化算法与Abaqus建立的桥梁有限元模型有效结合,得到分布均匀的Pareto最优解集;与未加固状态相比,优化后加固方案的倾覆稳定系数提高了201%;与初始加固方案相比,最佳优化加固方案的倾覆稳定系数提高37.25%,偏心弯矩安全系数提高4.04%。

Aiming at the single-column pier straight continuous beam bridge with high overturning risk,the method for adding steel cap beam was used to reinforce the single-column pier.The support at single-column pier was changed from the original single-support to three-support,so as to improve the anti-overturning ability of single-column pier straight beam bridge.To improve the lateral overturning stability coefficient and to reduce the eccentric bending moment of single-column pier as much as possible,the multi-objective optimization model was established.The original bearing size of single-column pier and the new bearing spacing of steel cap beam were as the design variables.The lateral overturning stability coefficient and the safety factor of eccentric bending moment were as the objective functions.Then,based on the parametric finite element model established and combined with Python,NSGA-II genetic algorithm and ABAQUS,the Pareto optimal solution set of the multi-objective optimization model was solved.The weight of objective function was calculated by using the game theory comprehensive weighting method.Then the TOPSIS method was used to calculate the intimacy coefficient of Pareto optimal solution set,so as to select the best reinforcement design scheme.The result indicates that the reinforcement method for adding steel cap beam can effectively improve the anti-overturning ability of single-column pier straight beam bridge.The overturning stability coefficient of single-column pier straight beam bridge increases by 167%after the initial scheme is adopted,which meets the requirements of relevant specification.Python can effectively combine the optimization algorithm with the finite element model of bridge established with ABAQUS to obtain a uniformly distributed Pareto optimal solution set.Compared with the unreinforced state,the overturning stability coefficient of the optimized reinforcement scheme increases by 201%.Compared with the initial reinforcement scheme,the overturning stability coefficient of optimal reinforcement scheme increases by 37.25%.The safety factor of eccentric bending moment increases by 4.04%.