箱拱桥梁地震反应分析的新方法研究
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摘要
首先利用薄壁箱梁理论及样条有限点法建立了样条箱拱段单元的刚度矩阵、阻尼矩阵及质量矩阵,这种单元考虑了箱拱的拉压、弯曲、扭转、剪力滞、扭翘及畸翘等特性;其次利用QR法(秦荣的方法)建立了箱拱桥梁的动力模型,将三维问题变为一维问题求解;然后利用样条加权残数法建立了求解动力模型的无条件稳定算法,从而提出了箱拱桥梁地震反应分析的新方法。计算结果表明,此法不仅未知量数目少,计算时间省,而且精度高。
The stiffness matrix,damping matrix and massive matirix of a spline box arch segment element are built by thin-walled box girder theory and spline finite point method,considering the charactistics of extension,compression,flexure,torsion,torsional warpage,distorsional warpage and shear lag deflection.The dynamic model for analysis of box arch bridges is built by Qin Rong method,this procedure decomposes three dimensional problem into one dimensional problem.Then the unconditionally stable algorithm for the solving of the dynamic equations is formed by the method of spline weighted residual,which formed a whole new set of method to analyze the seismic response of box arch bridges.With few unknown quantities and less computation time,the numerical results of this new method are in good agreement with an exact solution.
The stiffness matrix,damping matrix and massive matirix of a spline box arch segment element are built by thin-walled box girder theory and spline finite point method,considering the charactistics of extension,compression,flexure,torsion,torsional warpage,distorsional warpage and shear lag deflection.The dynamic model for analysis of box arch bridges is built by Qin Rong method,this procedure decomposes three dimensional problem into one dimensional problem.Then the unconditionally stable algorithm for the solving of the dynamic equations is formed by the method of spline weighted residual,which formed a whole new set of method to analyze the seismic response of box arch bridges.With few unknown quantities and less computation time,the numerical results of this new method are in good agreement with an exact solution.
引文
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[11]王建军.箱形拱桥静力分析与动力分析的QR法[D].南宁:广西大学,2004.Wang Jianjun.QR-method for static and dynamic analysis of box arch bridges[D].Nanning:Guangxi University,2004.(in Chinese)
[12]秦荣.计算结构力学[M].第1版.北京:科学出版社,2001.Qin Rong.Computational structural mechanics[M].1st ed.Beijing:Science Press,2001.(in Chinese)
[2]秦荣.计算结构动力学[M].第1版.桂林:广西师范大学出版社,1997.Qin Rong.Computational structural dynamics[M].1st ed.Guilin:Guangxi Normal University Press,1997.(in Chinese)
[3]程进,江见鲸,肖汝城.大跨度钢拱桥极限承载力分析[J].工程力学,2003,20(2):7―10.Cheng Jin,Jiang Jianjin,Xiao Rucheng.Ultimateload-carrying capacity of long-span steel arch bridges[J].Engineering Mechanics,2003,20(2):7―10.(in Chinese)
[4]刘雪峰.大跨度钢箱提篮拱桥自振特性分析与试验研究[D].长沙:长沙理工大学,2004.Liu Xuefeng.The natural vibration feature analysis and experimental investigation of long span steel box handle-basket arch bridge[D].Changsha:Changsha University of Science and Technology.(in Chinese)
[5]Vlasov V Z.Thin-walled elastic beams[M].2nd ed.Jerusalem,Israel Program for Scientific Translation,1961.
[6]Umanskii A A.Mechanical engineering[M].Moscow,1948,V01.1,Part2.
[7]李国豪.大曲率薄壁箱梁的扭转和弯曲[J].土木工程学报,1987,20(1):65―67.Li Guohao.The torsion and bending of large curvature thin-walled box girder[J].China Civil Engineering Journal,1987,20(1):65―67.(in Chinese)
[8]李乔.闭口薄壁杆件翘曲函数的研究[J].西南交通大学学报,1993,28(6):1―6.Li Qiao.Investigation of warping functions of thin walled bars with closed cross section[J].Journal of Southwest Jiaotong Universtiy,1993,28(6):1―6.(in Chinese)
[9]Luo Q Z,Wu Y M,Li Q S.A finite segment model for shear lag analysis[J].Engineering Structures,2004,26:2113―2124.
[10]秦荣,王建军,张云峰.箱拱桥梁分析中的样条箱拱段子域[C].第14届全国结构工程会议论文集.山东,烟台,2005:367―373.Qin Rong,Wang Jianjun,Zhang Yunfeng.Spline box arch subdomain in the analysis of box arch bridge[C].Proceeding of14th National Structural Engineering.Yantai,Shangdong,2005:367―373.(in Chinese)
[11]王建军.箱形拱桥静力分析与动力分析的QR法[D].南宁:广西大学,2004.Wang Jianjun.QR-method for static and dynamic analysis of box arch bridges[D].Nanning:Guangxi University,2004.(in Chinese)
[12]秦荣.计算结构力学[M].第1版.北京:科学出版社,2001.Qin Rong.Computational structural mechanics[M].1st ed.Beijing:Science Press,2001.(in Chinese)
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