基于响应面法对桁架结构形状的优化设计  

Optimal design for truss structure shape based on response surface method

作　　者：陈洪武[1] 彭聪聪[1] 田铖[1] 王立原[1] CHEN Hong-wu;PENG Cong-cong;TIAN Cheng;WANG Li-yuan(College of Engineering Science and Tchnology,Shanghai Ocean University,Shanghai 201306,China)

机构地区：[1]上海海洋大学工程学院,上海201306

出　　处：《工程设计学报》2018年第4期457-464,共8页Chinese Journal of Engineering Design

基　　金：国家自然科学基金资助项目(51075258)

摘　　要：针对数学非线性回归问题,需不断改进设计模型和设计参数,从而使得设计效果达到最佳。求解约束条件下体积最小问题时经常用响应面法进行优化,即利用函数关系拟合仿真模型,采用筛选试验来确定优化方向。为了优化经典10杆桁架结构的形状,基于响应面法,编写并运行APDL(ANSYS parametric design language,参数化设计语言)程序,得到各桁架的初始应力和体积。以节点纵坐标值的改变来反映形状的变化,各因子设置三水平并编码为-1,0,1,通过响应面法(response surface method,RSM)进行寻优并调整中心点和水平。基于调整后的水平,先找到最佳邻域,再用优化软件在最佳邻域内求解桁架在许应力下体积的最优解,最后将确定好的节点纵坐标值回代到APDL程序中验证是否满足约束条件,若满足,则此时的体积为最优解。结果表明:利用响应面法优化桁架杆的迭代次数仅为3次,它能快速定位最优解,降低了前期设计成本。通过对比文献[9]可知响应面法对结构的形状优化更为有效,能快速定位出设计试验方案,在工程应用中对于寻找在约束条件下的最佳配比设计有着高效性。In view of the problem of mathematical nonlinear regression,it is necessary to continu-ously improve the design model and design parameters,so that the design effect is the best.The response surface method is often used to optimize the minimum volume problem under the con-straint conditions,which means that the simulation model is fitted by the function relation and the optimization direction is determined by the screening test.In order to optimize the shape of the classic 10-bar truss structure?based on the response surface,the APDL(ANSYS parametric design language)program was written and run,and the initial stress and volume of the truss were obtained.The change of node coordinates was used to reflect the change of shape.Each fac-tor was set at three levels and encoded as一1?0 and 1?and the center and level were adjusted by response surface method(RSM).Based on the adjusted level,the best neighborhood was found,and then the optimal solution of the volume under the allowable stress in the best neighborhood was solved by the optimization software.Finally,the determined node vertical coordinate value was returned to the APDL program to verify whether the constraint condition was satisfied.If it was satisfied,the volume was the best solution at this time.The results indicated that the itera-tions number was only 3 times when using the response surface method,which could quickly lo-cate the optimal solution and reduce the previous design cost.By comparing the experimental de-sign method in literature[9],it was found that the RSM was more efficient in optimizing the shape of the structure.In engineering applications?it is efficient to locate the design test program and find the best matching design under constraint conditions.

关 键 词：响应面法 水平调整 最佳邻域 最优解 

分 类 号：TH113.1[机械工程—机械设计及理论]