基于截面优化的张弦桁架形状参数分析
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摘要
为了探讨张弦桁架矢高、垂度与最小结构质量的相互关系,确定出不同跨度的最优矢高、垂度,采用Fibonacci搜索法编写了以矢高、垂度为变量的张弦桁架形状优化程序。在编写Fibonacci搜索法程序中引入了动态搜索区,以有效提高搜索效率和保证精度要求。分别对不同跨度的张弦桁架矢高、垂度进行分析。结果表明:最优矢高、垂度都随着跨度的增加而几乎呈线性增加;不同跨度下的矢高、垂度与最小结构质量的关系曲线大致呈抛物线形状;当垂跨比为0.07时,各跨度的最优矢跨比出现在0.132～0.159之间;当矢跨比在0.14左右时,各跨度的最优垂跨比出现在0.07左右;最优的矢跨比与垂跨比之和为0.22,此时结构的质量最小。
In order to study the relations among rise,sag,and the minimum structure weight of truss string structure,and to find the optimum rise and sag for different spans,the optimization program of truss string structure had been written in terms of rise and sag by using Fibonacci search method.The dynamic search range was introduced to improve the efficiency and guarantee the precision.Shape parameters of rise and sag for different spans of truss string structure were analyzed.Results indicate that the optimum rise and sag almost linearly increase with span;these relation curves among rise,sag and minimum structure weight are parabola;the optimum rise-span ratio is between 0.132 and 0.159 when the sag-span ratio is 0.07;the optimum sag-span ratio is about 0.07 when the rise-span ratio is about 0.14;when the sum of the rise-span ratio and the sag-span ratio is 0.22,the structure weight is the least.
In order to study the relations among rise,sag,and the minimum structure weight of truss string structure,and to find the optimum rise and sag for different spans,the optimization program of truss string structure had been written in terms of rise and sag by using Fibonacci search method.The dynamic search range was introduced to improve the efficiency and guarantee the precision.Shape parameters of rise and sag for different spans of truss string structure were analyzed.Results indicate that the optimum rise and sag almost linearly increase with span;these relation curves among rise,sag and minimum structure weight are parabola;the optimum rise-span ratio is between 0.132 and 0.159 when the sag-span ratio is 0.07;the optimum sag-span ratio is about 0.07 when the rise-span ratio is about 0.14;when the sum of the rise-span ratio and the sag-span ratio is 0.22,the structure weight is the least.
引文
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[12]高亮,刘健新,张丹.桁架桥主梁三分力系数试验[J].长安大学学报:自然科学版,2012,32(1):52-56.GAO Liang,LIU Jian-xin,ZHANG Dan.Experimen-tal Study on Three-component Force Coefficients ofTruss Girder Cross-section[J].Journal of Chang'anUniversity:Natural Science Edition,2012,32(1):52-56.
[2]杨睿.预应力张弦梁结构的形态分析及新体系的静力性能研究[D].杭州:浙江大学,2001.YANG Rui.Shape Analysis of Prestressed BSS andStudy of Mechanical Behavior for a New System[D].Hangzhou:Zhejiang University,2001.
[3]陈侃.预应力张弦拱结构的理论分析和受力特性研究[D].杭州:浙江大学,2000.CHEN Kan.Theoretical Analysis and MechanicsProperty Study of Prestressed Beam String Structure[D].Hangzhou:Zhejiang University,2000.
[4]马美玲.张弦梁结构找形和受力性能研究[D].杭州:浙江大学,2004.MA Mei-ling.Study of Form-finding and MechanicalBehavior for Beam String Structure[D].Hangzhou:Zhejiang University,2004.
[5]曹春阳,刘红艳,董锦坤.离散变量结构优化的斐波那契算法[J].辽宁工学院学报,2005,25(1):34-36.CAO Chun-yang,LIU Hong-yan,DONG Jin-kun.Fi-bonacci Design Method for Structure Optimizationwith Discrete Variables[J].Journal of Liaoning Insti-tute of Technology,2005,25(1):34-36.
[6]SUBASI M,YILDIRIM N,YILDIZ B.An Improve-ment on Fibonacci Search Method in OptimizationTheory[J].Applied Mathematics and Computation,2004,147(3):893-901.
[7]YILDIZ B,KARADUMAN E.On Fibonacci SearchMethod with k-Lucas Numbers[J].Applied Mathe-matics and Computation,2003,143(2/3):523-531.
[8]王秀丽,刘永周.矢跨比和垂跨比对张弦立体桁架性能的影响分析[J].空间结构,2005,11(1):35-39.WANG Xiu-li,LIU Yong-zhou.Influences of Rise-to-span Ratio and Sag-to-span Ratio on the PrestressedSpatial Truss String Structure[J].Spatial Structures,2005,11(1):35-39.
[9]姚国红,刘树堂,康丽萍.单榀张弦桁架结构各因数的影响分析[J].河南科技大学学报:自然科学版,2008,29(2):65-70.YAO Guo-hong,LIU Shu-tang,KANG Li-ping.Influ-ence Analysis of Factors of Single Truss String Struc-ture[J].Journal of Henan University of Science&Technology:Natural Science,2008,29(2):65-70.
[10]柯友华,陈波.张弦桁架结构的非线性地震响应及其参数分析[J].钢结构,2010,25(3):37-44.KE You-hua,CHEN Bo.The Nonlinear Seismic Re-sponse and Parametric Analysis of Truss StringStructure[J].Steel Construction,2010,25(3):37-44.
[11]韩万水,王涛,李永庆,等.大跨钢桁架悬索桥有限元模型实用修正方法[J].交通运输工程学报,2011,11(5):18-27.HAN Wan-shui,WANG Tao,LI Yong-qing,et al.Practical Updating Method of Finite Element Modelfor Long-span Steel Truss Suspension Bridge[J].Journal of Traffic and Transportation Engineering,2011,11(5):18-27.
[12]高亮,刘健新,张丹.桁架桥主梁三分力系数试验[J].长安大学学报:自然科学版,2012,32(1):52-56.GAO Liang,LIU Jian-xin,ZHANG Dan.Experimen-tal Study on Three-component Force Coefficients ofTruss Girder Cross-section[J].Journal of Chang'anUniversity:Natural Science Edition,2012,32(1):52-56.
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