基于响应面法的钢空腹桁架结构优化设计  

Optimization design of steel vierendeel truss structure based on response surface method

作　　者：陈顺云 肖建春[1,2] 沈睿麟 杨行 盛夏 刘小龙 CHEN Shunyun;XIAO Jianchun;SHEN Ruilin;YANG Hang;SHENG Xia;LIU Xiaolong(0x09Research Center of Space Structures,Guizhou University,Guiyang 550025,Guizhou,China;Key Laboratory of Structural Engineering of Guizhou Province,Guizhou University,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州大学空间结构研究中心,贵州贵阳550025 [2]贵州大学贵州省结构工程重点实验室,贵州贵阳550025

出　　处：《建筑科学与工程学报》2024年第5期33-41,共9页Journal of Architecture and Civil Engineering

基　　金：国家自然科学基金项目(50978064,Z091015);贵州省自然科学基金项目(黔科合基础[2017]1036)。

摘　　要：为了提高钢空腹桁架结构的优化设计效率,提出采用基于响应面法的结构优化设计方法对钢空腹桁架进行优化设计。优化前根据虚功原理推导了空腹桁架的等效惯性矩和等效剪切刚度,采用等代实腹梁刚度法验证了有限元模型精度。通过Box-Behnken试验设计,获得66组有限元模拟的试验样本,建立Kriging响应面从而得到近似响应点。以结构质量最小化为目标,以规范允许的最大组合应力、最大挠度和构件宽厚比为约束条件,采用MOGA遗传算法对空腹桁架进行优化设计,得到Pareto最优候选解。结果表明:在各级荷载下,有限元计算值与等代实腹梁刚度法计算值的最大相对误差仅为5.6%,验证了用于优化设计的有限元模型的精度;优化设计后3组候选解中最优用钢量为6195.4 kg,与优化前相比节省用钢量约18%;对最优解的相关几何参数进行了有限元数值试验验证,优化后的构件宽厚比、最大组合应力、最大挠度和结构质量与数值试验结果吻合较好,偏差均在3%以内,表明基于响应面法的结构优化设计方法适用于钢空腹桁架结构多参数优化设计。To improve the optimization design efficiency of steel vierendeel truss structure,a structural optimization design method based on the response surface method was proposed to optimize the design of steel vierendeel truss.Before optimization,the equivalent inertia moment and equivalent shear stiffness of the vierendeel truss were derived according to the virtual work principle,and the accuracy of the finite element model was verified by the equivalent beam flexibility method.Through the Box-Behnken experimental design,totally 66 groups of finite element test samples were obtained,and Kriging response surface was established to obtain approximate response points.With the goal of minimizing structural quality and the constraints of maximum allowable combined stress,maximum deflection,and component width to thickness ratio,the MOGA genetic algorithm was used to optimize the design of the vierendeel truss,and the Pareto optimal candidate solution was obtained.The results show that under all levels of loads,the maximum relative error between the finite element calculation value and the equivalent stiffness method calculation value is only 5.6%,which verifies the accuracy of the finite element model used for optimization design.The optimal steel consumption of the three groups of candidate solutions after optimization is 6195.4 kg,which saves about 18%of the steel consumption compared with that before optimization.The geometric parameters related to the optimal solution are verified by finite element numerical tests.The width to thickness ratio,maximum combined stress,maximum deflection and structure quality of the optimized members are in good agreement with the numerical test results,and the deviation is within 3%,which shows that the structural optimization design method based on response surface method is suitable for the multi-parameter optimization design of steel vierendeel truss structures.

关 键 词：空腹桁架 BOX-BEHNKEN试验设计 Kriging响应面 优化设计 

分 类 号：TU328[建筑科学—结构工程]