超大跨径CFRP缆索悬索桥力学性能分析及优化设计
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摘要
随着碳纤维复合材料(CFRP)的在桥梁中的应用研究,其在超大跨悬索桥中的优势日益受到人们的重视。然而,国内外尚无此类桥梁建成,在初步设计时,没有具体的结构尺寸以及相互之间的关系可以借鉴,所以进行优化设计是很有必要的。本文仅对CFRP缆索悬索桥的一些基本尺寸参数对结构的静力性能和自振特性的影响进行了对比分析,然后通过零阶优化法和一阶优化法对其进行静力优化研究,以期得到合理的构造尺寸。
本文首先介绍了碳纤维复合材料(CFRP)的基本力学性能,系统地阐述了悬索桥计算理论,包括弹性理论、挠度理论以及有限位移理论为悬索桥的静、动力分析提供理论基础,还介绍了结构优化设计理论,包括它的分类、一般数学模型和算法。
其次,对CFRP缆索和钢缆索两种结构的理论极限跨径进行了对比,采用ANSYS软件建立有限元模型,对CFRP缆索悬索桥和钢缆索悬索桥分别进行恒载、汽车荷载以及温度作用的对比分析计算,得出在这些工况下,二者的力学性能差异。
然后,采用参数化有限元法(APDL)建立主跨2000m的三跨连续CFRP缆索悬索桥,并调整不同的参数,对比其在不同参数下的静、动力性能,分析这些参数对结构性能的影响。主要参数包括主缆尺寸、主缆垂度以及边中跨比。
最后,详细介绍了优化设计的方法和步骤,并采用零阶优化法和一阶优化法对此悬索桥进行了静力性能优化,并对优化前后的模型进行了静、动力性能对比分析,为超大跨悬索桥的优化提供一些具有一定参考价值的结论。
With the application study of the carbon fiber reinforced polymer (CFRP) in bridge structure, the superiority that CFRP is applied to super-span suspension bridge is increasingly highlighted for special attention to designer. However, there is none this kind of bridge completed both at home and abroad, and there is no detailed and exact construction size to use for reference in preliminary design stage, so it is necessary to make optimum design. Some influences of fundamental parameters on static and free vibration characteristics of suspension bridges with CFRP cables are analyzed comparatively, then optimum design of static characteristics by zero-order optimization method and first-order optimization method is carried out in this article to expect obtaining the reasonable construction size.
Firstly, the mechanical characteristics of CFRP and the calculation theories of suspension bridges, including elastic theory, deflection theory and finite displacement theory are introduced systematically in this article, which provides theoretical basis for the analysis of static and dynamic characteristic of suspension bridges. Besides, the construction optimum design theory including its categories, general mathematics model and mathematics is also introduced.
Secondly, the theoretic limitation span of continuous suspension bridges with CFRP cables or steel cables are compared. The performances of both bridges are calculated and analyzed comparatively by making use of ANSYS, when they are under dead load, vehicle load and temperature load separately. Then, the differences mechanical properties of them in these working conditions are arrived.
Thirdly, the static and dynamic performances of the 2000m-span and three-span continuous suspension bridges with CFRP cables are compared by making use of the ANSYS Parametric Design Language (APDL) through changing different parameters. The influence of these parameters are analyzed.The main parameters include the size and the sag of main cable, the ratio of side span to middle span.
Finally, the methodology and procedure of optimum design are detailed introduced, and the optimum design of static characteristics for suspension bridges making use of zero-order optimization method and first-order optimization method is carried out in this article. The static and dynamic characteristic of suspension bridges before and after optimum are analyzed comparatively, to provide a certain valuable conclusion to the optimum design of super-span suspension bridge.
本文首先介绍了碳纤维复合材料(CFRP)的基本力学性能,系统地阐述了悬索桥计算理论,包括弹性理论、挠度理论以及有限位移理论为悬索桥的静、动力分析提供理论基础,还介绍了结构优化设计理论,包括它的分类、一般数学模型和算法。
其次,对CFRP缆索和钢缆索两种结构的理论极限跨径进行了对比,采用ANSYS软件建立有限元模型,对CFRP缆索悬索桥和钢缆索悬索桥分别进行恒载、汽车荷载以及温度作用的对比分析计算,得出在这些工况下,二者的力学性能差异。
然后,采用参数化有限元法(APDL)建立主跨2000m的三跨连续CFRP缆索悬索桥,并调整不同的参数,对比其在不同参数下的静、动力性能,分析这些参数对结构性能的影响。主要参数包括主缆尺寸、主缆垂度以及边中跨比。
最后,详细介绍了优化设计的方法和步骤,并采用零阶优化法和一阶优化法对此悬索桥进行了静力性能优化,并对优化前后的模型进行了静、动力性能对比分析,为超大跨悬索桥的优化提供一些具有一定参考价值的结论。
With the application study of the carbon fiber reinforced polymer (CFRP) in bridge structure, the superiority that CFRP is applied to super-span suspension bridge is increasingly highlighted for special attention to designer. However, there is none this kind of bridge completed both at home and abroad, and there is no detailed and exact construction size to use for reference in preliminary design stage, so it is necessary to make optimum design. Some influences of fundamental parameters on static and free vibration characteristics of suspension bridges with CFRP cables are analyzed comparatively, then optimum design of static characteristics by zero-order optimization method and first-order optimization method is carried out in this article to expect obtaining the reasonable construction size.
Firstly, the mechanical characteristics of CFRP and the calculation theories of suspension bridges, including elastic theory, deflection theory and finite displacement theory are introduced systematically in this article, which provides theoretical basis for the analysis of static and dynamic characteristic of suspension bridges. Besides, the construction optimum design theory including its categories, general mathematics model and mathematics is also introduced.
Secondly, the theoretic limitation span of continuous suspension bridges with CFRP cables or steel cables are compared. The performances of both bridges are calculated and analyzed comparatively by making use of ANSYS, when they are under dead load, vehicle load and temperature load separately. Then, the differences mechanical properties of them in these working conditions are arrived.
Thirdly, the static and dynamic performances of the 2000m-span and three-span continuous suspension bridges with CFRP cables are compared by making use of the ANSYS Parametric Design Language (APDL) through changing different parameters. The influence of these parameters are analyzed.The main parameters include the size and the sag of main cable, the ratio of side span to middle span.
Finally, the methodology and procedure of optimum design are detailed introduced, and the optimum design of static characteristics for suspension bridges making use of zero-order optimization method and first-order optimization method is carried out in this article. The static and dynamic characteristic of suspension bridges before and after optimum are analyzed comparatively, to provide a certain valuable conclusion to the optimum design of super-span suspension bridge.
引文
[1]雷俊卿,郑明珠,徐恭义.悬索桥设计[M].北京：人民交通出版社,2002
[2]严国敏,周世忠.现代悬索桥[M].北京：人民交通出版社,2002
[3]马学起.悬索桥的构造选择[J].西安公路交通大学学报,2000,20(2)：52-54
[4]钱冬生,陈仁福.大跨悬索桥的设计与施工[M].成都：西南交通大学出版社,1999：63-68
[5]杨汉文.悬索桥结构受力特征及设计计算理论比较[J].交通科技,2005,3：44-46
[6]楼庄鸿.近年来悬索桥发展的若干趋势[J].公路交通科技,1999,16(3)：35-39
[7]Haijun Wang, Yukitake Shioi, AkiraHasegawa, Endo Takanori:"Displacement Charac-teristics of Compound Bridge of Suspension Bridgesand Cable-stayed Bridges" Session-Conceptual De-sign:Trend and Innovative, IABSE Conference onCable-Supported Bridges-Challenging TechnicalLimits, Seoul, Korea June 12-14,2001.
[8]金增洪.悬索和斜拉复合桥梁的位移特征[J].中外公路,2003,23(1)：47-50
[9]张新军,张丹.吊拉组合体系桥的研究进展[J].浙江工业大学学报,2007,35(5)：553-558
[10]梅葵花,吕志涛.CFRP在超大跨悬索桥和斜拉桥中的应用前景[J].桥梁建设,2002,2：75-78
[11]宋香娥,雷俊卿.悬索桥发展中的问题与挑战[C].中国公路学会桥梁和结构工程分会2005年全国桥梁学术会议论文集：258-161
[12]梅葵花.CFRP拉索斜拉桥的研究[D].南京：东南大学,2005
[13]郑宏宇,梅葵花,吕志涛.CFRP缆索体系悬索桥的优势及可行性研究[J].桥梁建设,2006,4：7-10
[14]Nik Winkler,Pascal Klein. "Carbon Fiber Products(CFP)-A Construction Material for the Next Century".Proceedings of the 13th FIP Congress,1988:69-72.
[15]"Building Better Bridges with CFRP".Reinforced Plasitcs. March,1998:44-47.
[16]Francesco Lanza di Scalea, Vistasp M. Karbhari, Frieder Seible. "The Ⅰ-5/Gilman Advanced Technology Bridge Project".Proceedings of SPIE,2000, Vol.3988:10-17.
[17]王光远,董明耀.结构优化设计[M].北京：高等教育出版社,1987
[18]汪树玉,刘国华,包志仁.结构优化设计的现状与进展[J].基建优化,1999,20(4)：3-14
[19]禹智涛,韩大建.基于可靠度的桥梁结构优化设计[J].广东工业大学学报,2002,19(3)：50-55
[20]周孟波,刘自明,王邦楣.悬索桥手册[M].北京：人民交通出版社,2003
[21]杨汉文.悬索桥结构受力特征及设计计算理论比较[J].交通科技,2005,3：44-46
[22]傅强.悬索桥几何非线性影响因素分析[J].上海公路.1997
[23]侯贯泽,刘树堂,简国威.工程结构优化设计理论与方法[J].钢结构,2009,24(8)：30-33
[24]汪树玉,刘国华,包志仁.结构优化设计的现状与进展-续[J].基建优化,1999,20(5)：3-7
[25]Arora J S, Haug E J. Methods of Design Sensitivity Analysis in Structural Optimization[J]. AIAA Journal,1979,19(9):970-974
[26]肖尚宏.形状优化中关键技术的研究与实现[D].武汉：华中科技大学,1993
[27]蔡新,郭兴文,张旭明.工程结构优化设计[M].北京：中国水利水电出版社,2003
[28]王跃方,孙焕纯.离散变量桁架结构的布局优化设计[J].大连理工大学学报1995,35(5)：458-462
[29]谭中富,张作泉.关于桁架结构布局优化理论和方法的探讨[J].科技通报,1995,11(3)：167-170
[30]David W B, Liu Xiaojian. On Simultaneous Optimization of Smart Structures:Part Ⅱ:Algorithms and Examples[J]. Comput Methods Appl Mech Engrg,2000,184:25-37
[31]王波.钢桁架拱桥优化设计研究[D].重庆：重庆交通大学.2009
[32]赵长军,黄弘读,徐兴.大跨索桁桥静力优化研究[J].公路.2003,4：8-14
[33]张炳华,侯旭.土建结构优化设计(第二版)[M].上海：同济大学出版社,1998
[34]蔡新,郭兴文,张旭明.工程结构优化设计[M].北京：中国水利水电出版.2003
[35]L. Schmit. A Structural Design by Systematic Synthesis. Conf. On Electronic Computation, ASCE[M].New York.1960
[36]孙国正.优化设计及应用(第二版)[M].北京：人民交通出版.2000.1
[37]李炳威.结构优化设计[M].北京：人民交通出版社,1986
[38]许素强,夏人伟.桁架拓扑优化的遗传算法[J].计算结构力学及其应用.1994,11(4)：36-45
[39]阎平凡.人工神经网络-模型、分析与应用[M].合肥：安徽教育出版社,1993
[40]焦李成.神经网络系统理论[M].西安：西安电子科技大学出版社,1990
[41]马文刚.大跨径CFRP缆索悬索桥静动力性能分析[D].长安大学,2006
[42]郑宏宇.CFRP缆索悬索桥基本性能及若干关键技术研究[D].南京：东南大学,2007
[43]肖汝诚,贾丽君,王小同.确定大跨径悬索桥主缆成桥线形的虚拟梁法[J].计算力学学报,1999,16(1)
[44]郭永强,刘炎海,徐勐.不同单元形式对悬索桥受力分析的影响[J].甘肃科学学报,2005(3)：118-121
[45]罗喜恒,肖汝诚,项海帆.基于精确解析解的索单元[J].同济大学学报(自然科学版),2005(4)：445-450
[46]周青松.人行悬索桥参数分析与优化设计[D].杭州：浙江大学.2010
[47]邓杨芳.优化理论及ANSYS程序在桥梁优化设计中的应用研究[D].重庆：重庆交通大学.2009
[48]中交公路规划设计院.公路悬索桥设计规范(报批稿)[S].北京：人民交通出版社,2002
[2]严国敏,周世忠.现代悬索桥[M].北京：人民交通出版社,2002
[3]马学起.悬索桥的构造选择[J].西安公路交通大学学报,2000,20(2)：52-54
[4]钱冬生,陈仁福.大跨悬索桥的设计与施工[M].成都：西南交通大学出版社,1999：63-68
[5]杨汉文.悬索桥结构受力特征及设计计算理论比较[J].交通科技,2005,3：44-46
[6]楼庄鸿.近年来悬索桥发展的若干趋势[J].公路交通科技,1999,16(3)：35-39
[7]Haijun Wang, Yukitake Shioi, AkiraHasegawa, Endo Takanori:"Displacement Charac-teristics of Compound Bridge of Suspension Bridgesand Cable-stayed Bridges" Session-Conceptual De-sign:Trend and Innovative, IABSE Conference onCable-Supported Bridges-Challenging TechnicalLimits, Seoul, Korea June 12-14,2001.
[8]金增洪.悬索和斜拉复合桥梁的位移特征[J].中外公路,2003,23(1)：47-50
[9]张新军,张丹.吊拉组合体系桥的研究进展[J].浙江工业大学学报,2007,35(5)：553-558
[10]梅葵花,吕志涛.CFRP在超大跨悬索桥和斜拉桥中的应用前景[J].桥梁建设,2002,2：75-78
[11]宋香娥,雷俊卿.悬索桥发展中的问题与挑战[C].中国公路学会桥梁和结构工程分会2005年全国桥梁学术会议论文集：258-161
[12]梅葵花.CFRP拉索斜拉桥的研究[D].南京：东南大学,2005
[13]郑宏宇,梅葵花,吕志涛.CFRP缆索体系悬索桥的优势及可行性研究[J].桥梁建设,2006,4：7-10
[14]Nik Winkler,Pascal Klein. "Carbon Fiber Products(CFP)-A Construction Material for the Next Century".Proceedings of the 13th FIP Congress,1988:69-72.
[15]"Building Better Bridges with CFRP".Reinforced Plasitcs. March,1998:44-47.
[16]Francesco Lanza di Scalea, Vistasp M. Karbhari, Frieder Seible. "The Ⅰ-5/Gilman Advanced Technology Bridge Project".Proceedings of SPIE,2000, Vol.3988:10-17.
[17]王光远,董明耀.结构优化设计[M].北京：高等教育出版社,1987
[18]汪树玉,刘国华,包志仁.结构优化设计的现状与进展[J].基建优化,1999,20(4)：3-14
[19]禹智涛,韩大建.基于可靠度的桥梁结构优化设计[J].广东工业大学学报,2002,19(3)：50-55
[20]周孟波,刘自明,王邦楣.悬索桥手册[M].北京：人民交通出版社,2003
[21]杨汉文.悬索桥结构受力特征及设计计算理论比较[J].交通科技,2005,3：44-46
[22]傅强.悬索桥几何非线性影响因素分析[J].上海公路.1997
[23]侯贯泽,刘树堂,简国威.工程结构优化设计理论与方法[J].钢结构,2009,24(8)：30-33
[24]汪树玉,刘国华,包志仁.结构优化设计的现状与进展-续[J].基建优化,1999,20(5)：3-7
[25]Arora J S, Haug E J. Methods of Design Sensitivity Analysis in Structural Optimization[J]. AIAA Journal,1979,19(9):970-974
[26]肖尚宏.形状优化中关键技术的研究与实现[D].武汉：华中科技大学,1993
[27]蔡新,郭兴文,张旭明.工程结构优化设计[M].北京：中国水利水电出版社,2003
[28]王跃方,孙焕纯.离散变量桁架结构的布局优化设计[J].大连理工大学学报1995,35(5)：458-462
[29]谭中富,张作泉.关于桁架结构布局优化理论和方法的探讨[J].科技通报,1995,11(3)：167-170
[30]David W B, Liu Xiaojian. On Simultaneous Optimization of Smart Structures:Part Ⅱ:Algorithms and Examples[J]. Comput Methods Appl Mech Engrg,2000,184:25-37
[31]王波.钢桁架拱桥优化设计研究[D].重庆：重庆交通大学.2009
[32]赵长军,黄弘读,徐兴.大跨索桁桥静力优化研究[J].公路.2003,4：8-14
[33]张炳华,侯旭.土建结构优化设计(第二版)[M].上海：同济大学出版社,1998
[34]蔡新,郭兴文,张旭明.工程结构优化设计[M].北京：中国水利水电出版.2003
[35]L. Schmit. A Structural Design by Systematic Synthesis. Conf. On Electronic Computation, ASCE[M].New York.1960
[36]孙国正.优化设计及应用(第二版)[M].北京：人民交通出版.2000.1
[37]李炳威.结构优化设计[M].北京：人民交通出版社,1986
[38]许素强,夏人伟.桁架拓扑优化的遗传算法[J].计算结构力学及其应用.1994,11(4)：36-45
[39]阎平凡.人工神经网络-模型、分析与应用[M].合肥：安徽教育出版社,1993
[40]焦李成.神经网络系统理论[M].西安：西安电子科技大学出版社,1990
[41]马文刚.大跨径CFRP缆索悬索桥静动力性能分析[D].长安大学,2006
[42]郑宏宇.CFRP缆索悬索桥基本性能及若干关键技术研究[D].南京：东南大学,2007
[43]肖汝诚,贾丽君,王小同.确定大跨径悬索桥主缆成桥线形的虚拟梁法[J].计算力学学报,1999,16(1)
[44]郭永强,刘炎海,徐勐.不同单元形式对悬索桥受力分析的影响[J].甘肃科学学报,2005(3)：118-121
[45]罗喜恒,肖汝诚,项海帆.基于精确解析解的索单元[J].同济大学学报(自然科学版),2005(4)：445-450
[46]周青松.人行悬索桥参数分析与优化设计[D].杭州：浙江大学.2010
[47]邓杨芳.优化理论及ANSYS程序在桥梁优化设计中的应用研究[D].重庆：重庆交通大学.2009
[48]中交公路规划设计院.公路悬索桥设计规范(报批稿)[S].北京：人民交通出版社,2002