索穹顶结构预应力多目标优化的小生境遗传算法
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摘要
根据索穹顶结构的柔性结构特点和力学特性,探索以质量最小、刚度最大和支座反力最小为目标函数,以预应力整体可行性准则、荷载态应力控制和位移限值为约束条件的多目标优化模型。结合自适应技术、预选择机制和共享函数小生境技术对传统遗传算法进行改进,利用加权系数法将多目标优化问题转换为单目标Pareto最优解问题。利用向量式有限元对不同预应力水平的结构进行静力分析。最后通过两个不同类型索穹顶算例,采用自编程序的计算结果证明所提出的方法是有效的,为索穹顶结构预应力优化分析提供了新的计算方法。
According to the flexibility and mechanical property of cable dome structures,a multi-objective optimization model was proposed. The minimum structural weight,maximum stiffness and minimum support reaction were taken as three optimal objectives of the model. The feasible integral structural prestressing,members load stress control and structure displacement limit were taken as three constraint conditions of the model. The traditional genetic algorithm was improved based on the adaptive technique,preselection niche mechanism and sharing function niche mechanism.The weighted coefficient method was applied to transform the multi-objective optimal problem to the singular objective Pareto optimal solution problem. Finally a self-compiled program was applied to solve two given examples. The analysis of optimization results proves the effectiveness and validity of the proposed computing method. The improved niche genetic algorithm provides a new computing method for the stress optimization of cable domes.
According to the flexibility and mechanical property of cable dome structures,a multi-objective optimization model was proposed. The minimum structural weight,maximum stiffness and minimum support reaction were taken as three optimal objectives of the model. The feasible integral structural prestressing,members load stress control and structure displacement limit were taken as three constraint conditions of the model. The traditional genetic algorithm was improved based on the adaptive technique,preselection niche mechanism and sharing function niche mechanism.The weighted coefficient method was applied to transform the multi-objective optimal problem to the singular objective Pareto optimal solution problem. Finally a self-compiled program was applied to solve two given examples. The analysis of optimization results proves the effectiveness and validity of the proposed computing method. The improved niche genetic algorithm provides a new computing method for the stress optimization of cable domes.
引文
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[4]吕晶,徐国彬,王月栋.鞍山体育中心劲-柔索张拉穹顶屋盖优化设计[J].北方交通大学学报,2004,28(1):28-31.(LV Jing,XU Guobin,WANG Yuedong.Optimal design of tension-compression cable dome on Anshan athletics center[J].Journal of Northern Jiaotong University,2004,28(1):28-31.(in Chinese))
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[10]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part I:basic procedure and a planar frame element[J].Journal of Mechanics,2004,20(2):113-122.
[11]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part II:plane solid elements[J].Journal of Mechanics,2004,20(2):123-132.
[12]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part III:convected material frame and examples[J].Journal of Mechanics,2004,20(2):133-143.
[13]朱明亮,董石麟.向量式有限元在索穹顶静力分析中的应用[J].工程力学,2012,29(8):236-242.(ZHU Mingliang,DONG Shilin.Application of vector form intrinsic finite element method to static analysis of cable domes[J].Engineering Mechanics,2012,29(8):236-242.(in Chinese))
[14]王小平,曹立明.遗传算法:理论、应用与软件实现[M].西安:西安交通大学出版社,2002:68-85.(WANG Xiaoping,CAO Liming.Genetic algorithmtheory,application and software implementation[M].Xi’an:Xi’an Jiaotong University Press,2002:68-85.(in Chinese))
[15]Srinivas M,Patnaik L M.Adaptive probabilities of crossover and mutation in GA[J].IEEE Trans on Systems,Man and Cybernetics,1994,24(4):656-667.
[16]江季松,叶继红.遗传算法在单层球壳质量优化中的应用[J].振动与冲击,2009,28(7):1-7.(JIANG Jisong,YE Jihong.Application of genetic algorithm in section optimization of a single layer dome[J].Journal of Vibration and Shock,2009,28(7):1-7.(in Chinese))
[17]曲晓宁,罗尧治,郑君华.基于改进遗传算法的预应力钢结构索张拉优化分析[J].工程力学,2009,26(9):131-137.(QU Xiaoning,LUO Yaozhi,ZHENG Junhua.Optimal analysis of tensioning cables for prestressed steel structure based on improved genetic algorithm[J].Engineering Mechanics,2009,26(9):131-137.(in Chinese))
[18]Deb K,Goldberg D E.An investigation of niche and species formation in genetic function optimization[C]//Proceedings of the Third ICGA.Burlington,MA:Morgan Kaufmann Publishers,1989:42-50.
[19]Goldberg D E,Richardson J.Genetic algorithms with sharing for multimodal function optimization[C]//Proceeding of the Second International Conference on Genetic Algorithms.Hillsdale,MI:Lawrence Erlbaum Associates Inc.,1987:41-49.
[20]周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社,1999:74-78,130-138.(ZHOU Ming,SUN Shudong.Genetic algorithms:theory and application[M].Beijing:National Defence Industry Press,1999:74-78,130-138.(in Chinese))
[21]雷英杰,张善文,李续武,等.MATLAB遗传算法工具箱及应用[M].西安:西安电子科技大学出版社,2004:22-31.(LEI Yingjie,ZHANG Shanwen,LI Xuwu,et al.MATLAB GA toolbox and its application[M].Xi’an:Xidian University Press,2004:22-31.(in Chinese))
[22]崔逊学.多目标进化算法及其应用[M].北京:国防工业出版社,2006:77-114.(CUI Xunxue.Multiobjective evolutionary algorithms and their applications[M].Beijing:National Defense Industry Press,2006:77-114.(in Chinese))
[23]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33-37.(YUAN Xingfei,DONG Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33-37.(in Chinese))
[24]董石麟,梁昊庆.肋环人字型索穹顶受力特性及其预应力态的分析法[J].建筑结构学报,2014,35(6):102-108.(DONG Shilin,LIANG Haoqing.Mechanical characteristics and analysis of prestressing force distribution of herringbone ribbed cable dome[J].Journal of Building Structures,2014,35(6):102-108.(in Chinese))
[2]陈联盟,袁行飞,董石麟.Kiewitt型索穹顶结构自应力模态分析及优化设计[J].浙江大学学报(工学版),2006,40(1):73-77.(CHEN Lianmeng,YUAN Xingfei,DONG Shilin.Selfstress mode analysis and optimal design of Kiewitt domes[J].Journal of Zhejiang University(Engineering Science),2006,40(1):73-77.(in Chinese))
[3]陈联盟.Kiewitt型索弯顶结构的理论分析和试验研究[D].杭州:浙江大学,2005:35-46.(CHEN Lianmeng.Theoretical and experimental research of Kiewitt domes[D].Hangzhou:Zhejiang University,2005:35-46.(in Chinese))
[4]吕晶,徐国彬,王月栋.鞍山体育中心劲-柔索张拉穹顶屋盖优化设计[J].北方交通大学学报,2004,28(1):28-31.(LV Jing,XU Guobin,WANG Yuedong.Optimal design of tension-compression cable dome on Anshan athletics center[J].Journal of Northern Jiaotong University,2004,28(1):28-31.(in Chinese))
[5]陈联盟,董石麟,袁行飞,等.多整体自应力模态索穹顶结构优化设计[J].建筑结构,2008,38(2):35-38.(CHEN Lianmeng,DONG Shilin,YUAN Xingfei,et al.Optimal design of cable-domes with multi-overall selfstress modes[J].Building Structure,2008,38(2):35-38.(in Chinese))
[6]Holland J H.Adaptation in natural and artificial systems[M].Cambridge:MIT Press,1975:1-23.
[7]De Jong K A.An analysis of the behavior of a class of genetic adaptive systems[D].Ann Arbor:University of Michigan,1975:1-32.
[8]伞冰冰,武岳,卫东,等.膜结构的多目标形态优化[J].土木工程学报,2008,41(9):1-7.(SAN Bingbing,WU Yue,WEI Dong,et al.Multi-objective optimization of membrane structures[J].China Civil Engineering Journal,2008,41(9):1-7.(in Chinese))
[9]牟在根,梁杰,隋军,等.基于小生境遗传算法的单层网壳结构优化设计研究[J].建筑结构学报,2006,27(2):115-119.(MU Zaigen,LIANG Jie,SUI Jun,et al.Study of optimum design of single layer dome structures based on niche genetic algorithm[J].Journal of Building Structures,2006,27(2):115-119.(in Chinese))
[10]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part I:basic procedure and a planar frame element[J].Journal of Mechanics,2004,20(2):113-122.
[11]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part II:plane solid elements[J].Journal of Mechanics,2004,20(2):123-132.
[12]Ting E C,Shih C,Wang Y K.Fundamentals of a vector form intrinsic finite element:part III:convected material frame and examples[J].Journal of Mechanics,2004,20(2):133-143.
[13]朱明亮,董石麟.向量式有限元在索穹顶静力分析中的应用[J].工程力学,2012,29(8):236-242.(ZHU Mingliang,DONG Shilin.Application of vector form intrinsic finite element method to static analysis of cable domes[J].Engineering Mechanics,2012,29(8):236-242.(in Chinese))
[14]王小平,曹立明.遗传算法:理论、应用与软件实现[M].西安:西安交通大学出版社,2002:68-85.(WANG Xiaoping,CAO Liming.Genetic algorithmtheory,application and software implementation[M].Xi’an:Xi’an Jiaotong University Press,2002:68-85.(in Chinese))
[15]Srinivas M,Patnaik L M.Adaptive probabilities of crossover and mutation in GA[J].IEEE Trans on Systems,Man and Cybernetics,1994,24(4):656-667.
[16]江季松,叶继红.遗传算法在单层球壳质量优化中的应用[J].振动与冲击,2009,28(7):1-7.(JIANG Jisong,YE Jihong.Application of genetic algorithm in section optimization of a single layer dome[J].Journal of Vibration and Shock,2009,28(7):1-7.(in Chinese))
[17]曲晓宁,罗尧治,郑君华.基于改进遗传算法的预应力钢结构索张拉优化分析[J].工程力学,2009,26(9):131-137.(QU Xiaoning,LUO Yaozhi,ZHENG Junhua.Optimal analysis of tensioning cables for prestressed steel structure based on improved genetic algorithm[J].Engineering Mechanics,2009,26(9):131-137.(in Chinese))
[18]Deb K,Goldberg D E.An investigation of niche and species formation in genetic function optimization[C]//Proceedings of the Third ICGA.Burlington,MA:Morgan Kaufmann Publishers,1989:42-50.
[19]Goldberg D E,Richardson J.Genetic algorithms with sharing for multimodal function optimization[C]//Proceeding of the Second International Conference on Genetic Algorithms.Hillsdale,MI:Lawrence Erlbaum Associates Inc.,1987:41-49.
[20]周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社,1999:74-78,130-138.(ZHOU Ming,SUN Shudong.Genetic algorithms:theory and application[M].Beijing:National Defence Industry Press,1999:74-78,130-138.(in Chinese))
[21]雷英杰,张善文,李续武,等.MATLAB遗传算法工具箱及应用[M].西安:西安电子科技大学出版社,2004:22-31.(LEI Yingjie,ZHANG Shanwen,LI Xuwu,et al.MATLAB GA toolbox and its application[M].Xi’an:Xidian University Press,2004:22-31.(in Chinese))
[22]崔逊学.多目标进化算法及其应用[M].北京:国防工业出版社,2006:77-114.(CUI Xunxue.Multiobjective evolutionary algorithms and their applications[M].Beijing:National Defense Industry Press,2006:77-114.(in Chinese))
[23]袁行飞,董石麟.索穹顶结构整体可行预应力概念及其应用[J].土木工程学报,2001,34(2):33-37.(YUAN Xingfei,DONG Shilin.Application of integrity feasible prestressing to tensegrity cable domes[J].China Civil Engineering Journal,2001,34(2):33-37.(in Chinese))
[24]董石麟,梁昊庆.肋环人字型索穹顶受力特性及其预应力态的分析法[J].建筑结构学报,2014,35(6):102-108.(DONG Shilin,LIANG Haoqing.Mechanical characteristics and analysis of prestressing force distribution of herringbone ribbed cable dome[J].Journal of Building Structures,2014,35(6):102-108.(in Chinese))