大型渡槽的二维半流固耦合模型及其工程应用研究
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摘要
本文针对现有各类模型的局限性及存在的问题，提出了大型渡槽的二维半流固耦合模型。以简支U型渡槽为研究对象，采用二维半流固耦合模型进行了静力和动力数值计算分析，通过与三维模型计算结果进行对比分析，证明了该二维半流固耦合模型在渡槽的动、静力分析中均可获得较好的计算结果。通过对受到横向地震荷载的多跨联合大型渡槽进行流固耦合分析，研究了梁式渡槽槽身在横向地震荷载下的扭转效应。以支撑不等高的三跨大型梁式渡槽作为研究对象，研究了其在水平正交双向地震作用下的结构响应分析。本文进行了以下研究工作，并得到了一些有意义的结论：
（1）提出大型渡槽的二维半流固耦合模型。大型渡槽的二维半流固耦合模型是在已有的大型渡槽的流固耦合建模方法的基础上，针对目前不同计算模型存在的缺陷，在流固耦合理论以及结构动力学理论的基础上，按照平面问题与空间问题相结合的方法，提出的一种更好的流固耦合模型。本模型可有效降低非线性流固耦合求解的方程自由度，使得运算效率极大地提高，适用于实际工程应用中的多跨联合渡槽大规模求解。
（2）采用二维半流固耦合模型对大型渡槽进行了静力计算分析。以简支U型渡槽为研究对象，采用二维半流固耦合模型进行了静力数值计算分析。本文提出的二维半流固耦合模型，在静力作用下，可很好地模拟三维渡槽结构的槽身以及支撑的位移以及内力，也可以很好地模拟三维渡槽结构的壳槽内内水压力，并可以很好地反映耦合作用的三维效应。因此，本文模型可以满足工程实践中渡槽静力计算的精度要求。合理地设置二维流固耦合片的数目可以达到良好的静力模拟效果。
（3）采用二维半流固耦合模型对大型渡槽进行了动力计算分析。以简支U型渡槽为研究对象，在静力分析基础上，采用二维半流固耦合模型进行了动力数值计算分析。本文提出的二维半流固耦合模型，在动力作用下，可较好地模拟三维渡槽结构的槽身以及支撑的位移以及内力变化规律，也可以较好地模拟三维渡槽结构的壳槽内内水压力变化规律，并可以较好地反映耦合作用的三维效应。因此，本文模型可以满足工程实践中渡槽动力计算的精度要求；而且，本文提出的二维半流固耦合模型保持了较高的计算效率，便于工程利用。
（4）对大型渡槽的槽身地震扭转效应进行了研究。针对渡槽两端支撑刚度的不同、支撑条件的差异是否会导致渡槽的槽身结构发生不利的扭转问题进行研究。在不同地震波激励作用下，支撑刚度差异对槽身跨端扭矩的影响程度不同，在工程分析中，需要考虑不同地震激励荷载的周期特性差异。在渡槽的设计中，对于简支梁式渡槽，用来设计整个槽身的控制条件一般可以采用跨中截面的内力。在地震过程中，由于跨中截面的应力最大，以跨中截面的内力作为控制条件来设计整个槽身是可以满足抗震要求的。
（5）对大型渡槽槽身的水平双向地震响应进行了研究。以支撑不等高的三跨大型梁式渡槽作为研究对象，利用有限元分析软件ADINA，采用时程分析方法和流固耦合有限元计算方法，研究了其在水平正交双向地震作用下的结构响应。水平双向地震作用下，渡槽槽身的竖向位移和变形、竖向弯矩与横向地震动单独作用下的差别不大，受纵向地震动的影响较小。相比较纵向或横向地震动单独作用，在水平双向地震同时作用下，槽身截面最大主应力的增大较明显，因此，在进行槽身局部设计时，应该将水平双向地震作用纳入考虑。
This paper presents the2.5D fluid-structure interaction (FSI) model of aqueduct, due tothe limitations and problems of existing models. A simply supported U-shaped aqueduct isintroduced in the numerical analyses to study the2.5D FSI model and compare it with typical3D FSI models in the dynamic and static analysis of aqueduct. The results show that thismodel has good simulation results for dynamic and static analysis of aqueduct-water couplingsystem. And the torsion effect of a multi-span aqueduct body under the lateral seismicexcitation is studied by the numerical analysis of fluid-structure interaction. Finally, athree-span aqueduct with unequal height piers is introduced to study its structural responseunder the horizontal, orthogonal and bidirectional seismic action. The main work andconclusions in this paper are shown as follows:
（1）The2.5D fluid-structure interaction model of aqueduct is established. This model isbased on the existing modeling methods of aqueduct, structural dynamic analysis theory andfluid-structure interaction theory, combing plane problem with space problem. Comparedwith existing models, the2.5D FSI model of aqueduct can effectively reduce the orders ofnon-linear fluid-structure interaction equations to improve its computational efficiency, whichis practical in the large-scale calculation of multi-span aqueduct.
（2）The static structural response of large-scale aqueduct is analyzed with2.5D FSImodel. A simply supported U-shaped aqueduct is introduced in the static structural analysis.The numerical results show that under static loading, the2.5D FSI model presented in thispaper not only can well simulate the displacement and internal force of aqueduct body, butalso can well simulate the water pressure acting on the aqueduct interface wall and reflect the3D coupling effect. Therefore, the2.5D FSI model can meet the requirement of precision inthe static analysis of aqueduct, and can obtain good simulation results with appropriateselection of the amount of coupling planes.
（3）The dynamic structural response of large-scale aqueduct is analyzed with2.5D FSImodel. A simply supported U-shaped aqueduct is introduced in the dynamic structuralanalysis based on the above static analysis. The numerical results show that under dynamicloading, the2.5D FSI model presented in this paper not only can well simulate thedisplacement and internal force variation of aqueduct body, but also can well simulate thewater pressure variation acting on the aqueduct interface wall and reflect the3D couplingeffect. Therefore, the2.5D FSI model can meet the requirement of precision in the dynamic analysis of aqueduct, and it is time saving and practical in engineering applications.
（4）The torsion effect of large-scale aqueduct is studied. The study is focused onwhether the difference in the stiffness of piers and the support conditions of each span ofaqueduct causes bad torsion effect of aqueduct body. Though there is difference between theend supports’ stiffness of each span of aqueduct, the torques have little difference, whichmeans that the difference of supports’ stiffness has little influence on the torque internal forceof aqueduct body. In the design of a simply supported aqueduct, the mid-span section internalforce is usually adopted as the design threshold of the aqueduct body. During the earthquake,the mid-span section internal force is the maximum of internal force. Therefore therequirements of seismic safety for entire aqueduct body can be met if the mid-span sectioninternal force is adopted as the design threshold.
（5）The horizontal and bidirectional seismic response of large-scale aqueduct is studied.A three-span aqueduct with unequal height piers is introduced to study its structural responseunder the horizontal, orthogonal and bidirectional earthquake action in the general finiteelement program ADINA, adopting the dynamic time-history method and fluid-structureinteraction numerical method. The results show that the vertical displacements, verticaldeformation and vertical moments of aqueduct body under the bidirectional seismic action arevery similar to those under the lateral seismic action alone, and are little influenced by thelongitudinal seismic action. Compared with longitudinal or lateral seismic action alone, underthe horizontal and bidirectional seismic action, the increase of the maximum values of sectionprincipal stress is obvious. Therefore, horizontal, orthogonal and bidirectional seismic actionshould be considered in the design of aqueduct.
（1）提出大型渡槽的二维半流固耦合模型。大型渡槽的二维半流固耦合模型是在已有的大型渡槽的流固耦合建模方法的基础上，针对目前不同计算模型存在的缺陷，在流固耦合理论以及结构动力学理论的基础上，按照平面问题与空间问题相结合的方法，提出的一种更好的流固耦合模型。本模型可有效降低非线性流固耦合求解的方程自由度，使得运算效率极大地提高，适用于实际工程应用中的多跨联合渡槽大规模求解。
（2）采用二维半流固耦合模型对大型渡槽进行了静力计算分析。以简支U型渡槽为研究对象，采用二维半流固耦合模型进行了静力数值计算分析。本文提出的二维半流固耦合模型，在静力作用下，可很好地模拟三维渡槽结构的槽身以及支撑的位移以及内力，也可以很好地模拟三维渡槽结构的壳槽内内水压力，并可以很好地反映耦合作用的三维效应。因此，本文模型可以满足工程实践中渡槽静力计算的精度要求。合理地设置二维流固耦合片的数目可以达到良好的静力模拟效果。
（3）采用二维半流固耦合模型对大型渡槽进行了动力计算分析。以简支U型渡槽为研究对象，在静力分析基础上，采用二维半流固耦合模型进行了动力数值计算分析。本文提出的二维半流固耦合模型，在动力作用下，可较好地模拟三维渡槽结构的槽身以及支撑的位移以及内力变化规律，也可以较好地模拟三维渡槽结构的壳槽内内水压力变化规律，并可以较好地反映耦合作用的三维效应。因此，本文模型可以满足工程实践中渡槽动力计算的精度要求；而且，本文提出的二维半流固耦合模型保持了较高的计算效率，便于工程利用。
（4）对大型渡槽的槽身地震扭转效应进行了研究。针对渡槽两端支撑刚度的不同、支撑条件的差异是否会导致渡槽的槽身结构发生不利的扭转问题进行研究。在不同地震波激励作用下，支撑刚度差异对槽身跨端扭矩的影响程度不同，在工程分析中，需要考虑不同地震激励荷载的周期特性差异。在渡槽的设计中，对于简支梁式渡槽，用来设计整个槽身的控制条件一般可以采用跨中截面的内力。在地震过程中，由于跨中截面的应力最大，以跨中截面的内力作为控制条件来设计整个槽身是可以满足抗震要求的。
（5）对大型渡槽槽身的水平双向地震响应进行了研究。以支撑不等高的三跨大型梁式渡槽作为研究对象，利用有限元分析软件ADINA，采用时程分析方法和流固耦合有限元计算方法，研究了其在水平正交双向地震作用下的结构响应。水平双向地震作用下，渡槽槽身的竖向位移和变形、竖向弯矩与横向地震动单独作用下的差别不大，受纵向地震动的影响较小。相比较纵向或横向地震动单独作用，在水平双向地震同时作用下，槽身截面最大主应力的增大较明显，因此，在进行槽身局部设计时，应该将水平双向地震作用纳入考虑。
This paper presents the2.5D fluid-structure interaction (FSI) model of aqueduct, due tothe limitations and problems of existing models. A simply supported U-shaped aqueduct isintroduced in the numerical analyses to study the2.5D FSI model and compare it with typical3D FSI models in the dynamic and static analysis of aqueduct. The results show that thismodel has good simulation results for dynamic and static analysis of aqueduct-water couplingsystem. And the torsion effect of a multi-span aqueduct body under the lateral seismicexcitation is studied by the numerical analysis of fluid-structure interaction. Finally, athree-span aqueduct with unequal height piers is introduced to study its structural responseunder the horizontal, orthogonal and bidirectional seismic action. The main work andconclusions in this paper are shown as follows:
（1）The2.5D fluid-structure interaction model of aqueduct is established. This model isbased on the existing modeling methods of aqueduct, structural dynamic analysis theory andfluid-structure interaction theory, combing plane problem with space problem. Comparedwith existing models, the2.5D FSI model of aqueduct can effectively reduce the orders ofnon-linear fluid-structure interaction equations to improve its computational efficiency, whichis practical in the large-scale calculation of multi-span aqueduct.
（2）The static structural response of large-scale aqueduct is analyzed with2.5D FSImodel. A simply supported U-shaped aqueduct is introduced in the static structural analysis.The numerical results show that under static loading, the2.5D FSI model presented in thispaper not only can well simulate the displacement and internal force of aqueduct body, butalso can well simulate the water pressure acting on the aqueduct interface wall and reflect the3D coupling effect. Therefore, the2.5D FSI model can meet the requirement of precision inthe static analysis of aqueduct, and can obtain good simulation results with appropriateselection of the amount of coupling planes.
（3）The dynamic structural response of large-scale aqueduct is analyzed with2.5D FSImodel. A simply supported U-shaped aqueduct is introduced in the dynamic structuralanalysis based on the above static analysis. The numerical results show that under dynamicloading, the2.5D FSI model presented in this paper not only can well simulate thedisplacement and internal force variation of aqueduct body, but also can well simulate thewater pressure variation acting on the aqueduct interface wall and reflect the3D couplingeffect. Therefore, the2.5D FSI model can meet the requirement of precision in the dynamic analysis of aqueduct, and it is time saving and practical in engineering applications.
（4）The torsion effect of large-scale aqueduct is studied. The study is focused onwhether the difference in the stiffness of piers and the support conditions of each span ofaqueduct causes bad torsion effect of aqueduct body. Though there is difference between theend supports’ stiffness of each span of aqueduct, the torques have little difference, whichmeans that the difference of supports’ stiffness has little influence on the torque internal forceof aqueduct body. In the design of a simply supported aqueduct, the mid-span section internalforce is usually adopted as the design threshold of the aqueduct body. During the earthquake,the mid-span section internal force is the maximum of internal force. Therefore therequirements of seismic safety for entire aqueduct body can be met if the mid-span sectioninternal force is adopted as the design threshold.
（5）The horizontal and bidirectional seismic response of large-scale aqueduct is studied.A three-span aqueduct with unequal height piers is introduced to study its structural responseunder the horizontal, orthogonal and bidirectional earthquake action in the general finiteelement program ADINA, adopting the dynamic time-history method and fluid-structureinteraction numerical method. The results show that the vertical displacements, verticaldeformation and vertical moments of aqueduct body under the bidirectional seismic action arevery similar to those under the lateral seismic action alone, and are little influenced by thelongitudinal seismic action. Compared with longitudinal or lateral seismic action alone, underthe horizontal and bidirectional seismic action, the increase of the maximum values of sectionprincipal stress is obvious. Therefore, horizontal, orthogonal and bidirectional seismic actionshould be considered in the design of aqueduct.
引文
[1]灌溉与排水工程设计规范[S]．北京：中国计划出版社，1999
[2]水工建筑物抗震设计规范[S]．北京：中国水利水电出版社出版，1997
[3]水工建筑物抗震设计规范[S]．北京：中国电力出版社，2000
[4]周厚贵,马吉明,马金刚.国内外渡槽的发展与南水北调中线漕河渡槽[J].南水北调与水利科技,5(3)：14-17
[5]李珍照，王益敏，陈胜宏，何金平．中国水利百科全书（水工建筑物分册）[M]．北京：中国水利水电出版社，2004
[6] Eugene L．，Dennis P.E．Integration of computer systems for California aqueduct powerplant systems[J]．IEEE Transactions on Energy Convemion,1993，8(2)：93-113
[7] Shah J J．Construction of Gomti Aqueduct[J]. Indian Consrete．Journal，June，1986
[8] Golani B D．‘Rolling trusses’ as falsework for aqueduct and bridges．Indian ConcreteJouranl，January,1978
[9] Anon. Aqueduct Uses Prestressed Concrete Design.[J] World Construction, June.1984
[10] Connelly. David L., Perry．Roy J．First steps in aqueduct leak risk assessment[J]. Proc22Annu Conf Integr Water Res Plan21Century,1995．64l-644
[11]钟砥宁，边立明．东深供水改造工程渡槽伸缩缝止水设计与施工[J]．人民长江，2003，34(11)：34-36
[12]陆岸典，丁仕辉．大型U型薄壳渡槽预应力施工[J]．施工技术，2002，31(7)：18-19．
[13]何旭升，杜振坤等．东深供水改造工程渡槽伸缩缝止水研究[J]．水利水电技术，2002，33(5)：37-39
[14]邹正欣，朱军.东深供水改造工程现浇预应力U型薄壳渡槽有限元分析[J]．广东水利水电，2007，6：8-10
[15]赵瑜，白新理等．东深供水改造工程渡槽支承结构受力分析[J]．灌溉排水，2002，21(3)：53-55
[16]曾金鸿．东深供水改造工程渡槽伸缩缝新型止水结构设计与施工[J]．水利水电科学进展，2005，25(3)：35-37
[17]程瓦，潘登宇．大型双向预应力混凝土“U”型薄壳渡槽设计[J]．人民长江，2008，39(24)：38-40
[18]吴轶．大型梁式渡槽地震反应分析及设计方法研究[D]．广州：华南理工大学，2004
[19]吴轶，莫海鸿，杨春．大型矩形渡槽-水耦合体系的动力性能分析[J]．地震工程与工程振动，2004．24(4)：137-142
[20]吴轶，莫海鸿，杨春．排架-渡槽-水三维耦合体系地震响应分析[J]．水利学报，2005，36(3)：280-285
[21]吴轶,莫海鸿,杨春.大型渡槽动力设计方法研究[J].计算力学学报,2006,23(6):778-782
[22]吴轶,莫海鸿,杨春.大型拱式U型薄壳渡槽结构的模态分析[J].华南理工大学学报(自然科学版),2003,31(3):72-76
[23]吴轶,莫海鸿,杨春.三维排架渡槽中水的调频液体阻尼效应[J].水利学报,2005,(9):1115-1120
[24]张华忠，莫海鸿，刘春洋.大型梁式渡槽止水带纵轴向张开变位分析[J].广东土木与建筑,2003,(1):24-28
[25]徐梦华．大型渡槽梁壳流固耦合动力模型及其工程应用研究[D]．广州：华南理工大学，2004
[26]徐梦华，莫海鸿.大跨度梁式渡槽改进拟三维流固耦合模型的三维模拟效果分析[J].振动与冲击,2010,29(6):207-210
[27]徐梦华，莫海鸿.简支梁式渡槽考虑流固耦合的横向地震三维动力响应分析[J].工程抗震与加固改造，200931(5)：29-33
[28]符志远，段国学．大型“U”型薄壳预应力渡槽仿真结构试验[J]．人民长江，2004，35(8)：49-53
[29]王博．大型渡槽动力建模研究[J]．计算力学学报，2000,17(4):468-474
[30]徐建国，陈淮等．地震作用下大型渡槽结构动态应力计算方法研究[J]．水利学报，2002,7:79-82
[31]李遇春，楼梦麟等．大型梁式渡槽竖向地震作用估计[J]．土木工程学报，2003，36(2)：10-15
[32]徐建国，陈淮等．渡槽结构考虑流固耦合的横向地震响应研究[J]．工程力学，2004,21(6):197-202
[33]王博，陈淮等．考虑槽身与槽内水体流固耦合的渡槽地震反应计算[J]．水利水电科技进展，2005,25(3):5-7
[34]徐建国，陈淮等．考虑流固耦合的大型渡槽横向动力分析[J]．大连理工大学学报，2005,45(4):587-592
[35]徐建国，陈淮等．考虑流固动力相互作用的大型渡槽地震响应研究[J]．土木工程学报，2005,38(8):67-73
[36]徐建国，陈淮等．大型渡槽结构考虑流固耦合的动力建模研究[J]．南京理工大学学报，2005,29(6):639-644
[37]彭辉，刘德富等．南水北调中线漕河渡槽流固耦合机理研究[J]．灌溉排水学报，2006,25(5):75-77
[38]张林让，吴杰芳等．大型渡槽流固动力耦合效应试验研究[J]．南水北调与水利科技，2008,6(1):6-10
[39]张静娜，马文英等．大型联体式矩形渡槽流固耦合动力特性分析[J]．人民长江，2008,39(5):79-81
[40]徐建国，王博等．渡槽结构考虑流固耦合地震响应及求解敛散性[J]．人民长江，2008,39(6):51-53
[41]李遇春，楼梦麟等．大型渡槽的竖向地震效应分析[J]．地震工程与工程振动，2008,28(2):102-107
[42]王清云，张多新等．大型矩型水工渡槽三维流固耦合动力分析[J]．水利水运工程学报，2008,4:55-60
[43]袁吉栋，邢红芳等．考虑流固耦合的大型预应力渡槽地震反应分析[J]．人民长江，2009,40(5):7-10
[44]白新理，王丽芳等．考虑流固耦合的矩形渡槽动力分析[J]．华北水利水电学院学报，2009,30(5):33-36
[45]徐建国,王博.大型单墩渡槽流固耦合动力分析[J]．郑州大学学报(工学版),2009,30(4):128-132
[46]夏富洲,宋一乐等.大型渡槽隔震体系结构动力特性的试验研究[J]．南水北调与水利科技,2009,7(6):59-61
[47]张多新，王清云等．流固耦合系统位移-压力有限元格式在渡槽动力分析中的应用[J]．土木工程学报，2010,43(1):125-129
[48]徐建国,王博等.地震作用下大型渡槽结构纵向碰撞非线性分析[J]．地震工程与工程振动,2010,30(5):126-133
[49]蒋寅军,宋一乐.超大型渡槽抗震性能试验研究[J]．中国农村水利水电，2010，12:100-133
[50]邱流潮，张立翔.地震作用下拱坝一库水祸全振动动水压力分析[J]．水动力学研究与进展，2000,15(1):94-103
[51] Westergaard H M. Water pressures on dams during earthquakes[J]．Transcations, ASCE,1933,98:418-433
[52] R.W. Clough. Reservoir interaction effects on the dynamic response of archdams[J]．Proceeding of China-US Bilateral workshop on earthquake engineering,1982:58-84
[53] Fok,K-L., Chopra, A.K. Water compressibility in earthquake response of archdams[J]．Journalof Structural Engineering, ASCE,1987,113(5):958-975
[54] Fenves G L, Mojtahedi S and Reimer R B. Effect of contraction joints on earthquakeresponse of an arch dam[J]．Journal of Structural Engineering, ASCE,1992,118(4):1039-105
[55]郑哲敏.平板在流体作用下的振动[J]．力学学报，1958,2(1):11-16
[56]郑哲敏等.悬臂梁在一侧受有液体作用下的振动[J]．力学学报，1959,3(2):111-119
[57]王前信，王孝信.在不规则地震作用下刚性坝面动水压力的探讨[J]．地震工程研究报告集，第一集：153-161,1962
[58]王前信，王孝信.伸臂梁在一侧有水时的自振特性与地震荷载[J]．地震工程研究报告集，第一集：152-172,1962
[59]居荣初，曾心传.弹性结构与液体的祸联振动理论[M]．北京：地震出版社，1983
[60]宫维圣.码头和船闸建筑物的抗震[M]．北京:人民交通出版社,1993
[61] Housner G W. The Dynamic Pressure on Accelerated Fluid Containers[J]．Bulletion ofthe seismological of America,1957,47(1):15-35
[62] Housner G W. The Dynamic behavior of Water Tanks[J]．Bulletion of the seismologicalof America,1963,53(2):381-387
[63]徐建国.大型渡槽结构抗震分析方法及其应用[D]．大连：大连理工大学，2005.
[64]刘云贺,胡宝柱,闫建文,王克成. Housner模型在渡槽抗震计算中的适用性[J]．水利学报,2002(9):94-99
[65] Nakayama, T. and Washizu, K., The boundary element method applied to the analysis oftwo-dimensional nonlinear sloshing problems[J]．Int. J. Numer. Methods Engrg.1981,17:1631-1646
[66] Liu Z. and Huang Y., A new method for large amplitudes loshing problems[J]．J. Sound&Vi b.1994,175(2):185-195
[67]邵岩,赵兰浩,李同春.考虑流固耦合的渡槽动力计算方法综述.人民黄河.2005,27(11):55-56
[68] Noh CEL. A time-dependent two-space-dimension coupled Eulerian-Lagrangiancode[J]． In: Alder B, Fernbach S, eds. Methods in computational Physics3. New York:Academic Press,1964
[69] Thomas JR. Lagrangian-Eulerian Finite element formulation for in compressible viscousflows[J]．Computer Methods in applied Mechanics and Engineering,1981,29(3):329-349
[70] Wang CY, Moody F J, Shin Y W eds. Fluid-structure Interaction, Transient Thermal-hydraulics, and Structural Mechanics-1992[C]．ASME PVP Conf., June1992, NewOrleans LA, ASME, New York(l992)
[71] T. J. R. Hughes, Multiscale phenomena: Geren's function, the Dirichlet-to-Neumannformulation, subgrid scale models, bubbles and the origins of stabilizedformulations[J]．Comput. Methods Appl. Mech. Engrg.127(1995)387-401
[72] Okamoto, T. and Kawahara, M. Two-dimensional sloshing analysis by Lagrangian finiteelement method[J]．Int. J, Numer. Methods Fluids,1990,11:453-477
[73] D.W. Kelly, S. Nakazawa, O. C. Zienkiewiez and J. C. Heinrich, A note on upwindingand anisotropic balancing dissipation in finite element approximations to convectivedifusion problems[J]．Int. J. Numer. Methods Engrg.15(1980)1705-1711
[74] Fung Y C. An Intorduction to the Theory of Aeroelasticity[J]．J. Wiley and Sons, Inc.,New York(1955)
[75] J. Douglas and J. Wang, An absolutely stabilized finite element methods for the StrokesProblem[J]．Math. Comput.52(1989)495-508
[76] O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method[J]．4th edition,Vol.2(McGraw-Hill,1989)
[77] D. N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokesequations[J]．Calcolo21(1984)337-344
[78] I. Harari and T. J. R. Hughes, what are C and h？：Inequalities for the analysis anddesign of finite element methods[J]．Comput. Methods Appl. Mech. Engrg.97(1992)157-192
[79] Zienkiewicz O C, Chang C T, Betess P. Drained, Undrained, Consolidating andDynamics behaviour assumptions in soils, Limits of validity[J]．Geotechnique.30(1980):385-395
[80] Ramaswamy, B, Kawahara, M. Arbitrary Lagrangian-Eulerian finite element method forunsteady, convective, in compressible viscous free surface fluid flow[J]．Int. J Numer.Methods fluids.1987,7:1053-1075
[81] J. Douglas and T. F. Russell, Numerical methods for convection dominated difusionproblems based on combining the method of characteristics with finite element or finiteprocedures[J]．SIAM J. Numer. Anal.19(1982)871-885
[82] Paidoussis M P. Flow-induced instabilities of cylindrical structures[J]．Appl. Mech. Rech.Rev.,40,2(1987):163-175
[83] Brook AN, Hughes TJR. Streamline upwind petrov-Galerkin formulation for convectiondominated flows with particular emphasis on the incompressible Navier-stokesequations[J]．Computer Methods in Applied Mechanics and Engineering,1982,32(1-3):199-259
[84] Liu WK. Finite element procedure for fluid-structure interactions and application toliquid storage tanks[J]．Nuclear Engineering and Design,1981,65:221-238
[85] Liu WK, Hu YK. ALE finite element with hydrodynamic lubrication for metalforming[J]．Nuclear Engineering and Design,1992,138:1-10
[86] Chen S S, Fujita K, Au-Yang M K eds. Fluid-induced Vibration-1990[C]．ASME PVPConf. Nashville TN, ASME, New York(1990)
[87] T. J. R. Hughes, L. P. Franca and GM. Hulbert, A new finite element formulation forcomputational fluid dynamics: VIII. The Galerkin least-squares method foradvective-diffusivee quations[J]．Comput. Methods Appl. M ech. Engrg.73(1989)173-189
[88] O. Pironnrau, on the transport-diffusion aplorithm and its application to theNavier-Strokes equations[J]．Numer. Math.38(1982)309-332
[89] Liu, Z. and Huang, Y, A new method for large amplitude sloshing problems[J]．J.Sound&Vib.1994,175(2):185-195
[90] Zienkiewics O C. Coupled problems and their numerical solution in: Lewis R W, BetessP, Hinton E eds[J]．Numeircal Methods in Coupled Systems. John Wiley and Sons Ltd,New York(1984)
[91] F. Shakib and T. J. R. Hughes, A new finite element formulation for computational fluiddynamics: IX. Fourier Analysis of space-time Galerkin least-squaresalgorithms[J]．Comput. Methods Appl. Mech. Engrg.87(1991)35-58
[92] L. Franca, S. L. Frey and T. J. R Hughes, Stabilized finite element methods: I.Application to the advective-diffusive model[J]．Comput. Methods Appl. Mech. Engrg.95(1992)253-276
[93] R. Codina, Numerical solution of the incompressible Navier-Strokes equations wi thCoriolis forces based on the discretization of the total time derivative[J]．CIMNE Report,Num.102,1996
[94] R. Codina, A discontinuity-capturing cross wind-dissipation for the finite elementsolution of the convection-difusione quation[J]．Comput. Methods Appl. Mech. Engrg.110(1993)325-342
[95] R. E. Bank and B. D. Welfert, A comparison between the mini-element and the Petrov-Galerkin formulations for the generalized Stokes problem[J]．Comput. Methods Appl.Mngrg.83(1990)61-68
[96] Zienkiewicz O C， Betess P. Fluid-structure dynamic in teraction and wave forces, anintroduction to numerical treatment[J]．Int. J. Num. Meth. Engrg.,13,1(1978):1-16
[97] Ramaswamy, B., Kawahara, M. and Nakayama T. Lagrangian finite element method forthe analysis of two-dimensional sloshing problems[J]．Int. J. Numer. Methods fluids,1986,6:659-670
[98] F. Shakib, T. J. R. Hughes and Z. Johan,. A new finite element formulation forcomputational fluid dynamics: X. The compressible Euler and Navier-Strokesequations[J]．Comput. Methods Appl. Mech. Engrg.89(1991)141-219
[99] P. G. Ciarletand P. A. Raviart, Maximum principle and uniform convergence for thefinite element method[J]．Comput. Methods Appl. Mech. Engrg.2(1973)17-31
[100] J. von Neumann and R. D. Richtmyer, A method for the numerical calculation ofhydrodynamical shocks[J]．J. Appl. Phys.21(1950)232
[101] Johnson W. Recent developments in the dynamics of advanced rotorsystems[J]．Vertion,10,1(1986):73-107
[102] L. P. France and C. Farhat, Bubble functions prompt unusual stabilized finite elementmethods[J]．Comput Methods Appl. Mech. Engrg.123(1994)299-308
[103] C. Baiocchi, F. Brezzi and L. P. Franca, Virtual bubbles and Galerkin-least-squares typemethods[J]．Comput. Methods Appl. Mech. Engrg.105(1993)125-141
[104] Huerta A, Liu WK. Viscous flow with large free surface motion[J]．Computer Methodsin Applied Mechanics and Engineering,1988,69(3):277-324
[105] Hirt GW, Amsden AA, Cook JL. An arbitary Lagrangian-Eulerian computing methodfor all flow speeds[J]．J Comp Phys,1974,14(3):227-253
[106] Liu WK, Chang H, Belytscko T. Arbitary Lagrangian-Eulerian Petrov-Galerkin finiteelement for nonlinear continua[J]．Computer Methods in Applied Mechanics andEngineering,1988,68(3):259-310
[107] Liu WK, chen JS. Adaptive ALE finite element with particular reference to externalwork rate on frictional interface[J]．Computer Methods in Applied Mechanics andEngineering,1991,93:189-216
[108] A. N. Brooks and T. J. R. Hughes, Streamline upwind petrov-Galerkin formation forconvective dominated flows with particular emphasis on the incompressibleNavier-Strokese quations[J]．Comput. Methods Appl. Mech. Engrg.32(1982)199-259
[109]刘云贺.流体一固体动力耦合理论及水利工程应用[D].西安:西安交通大学，2001
[110] RAMASWAMYB, Kawahara M, Nakayama T. Lagrangian finite element method forthe analysis of two-dimensional sloshing problems [J]. Int. J. Numer. Methods Fluids,1986,6:659～670
[111] RAMASWAMYB, Kawahara M. Arbitrary Lagrangian-Eulerian finite element methodfor unsteady, convective, incompressible viscous free surface fluid flow [J]. Int. J.Numer. Methods Fluids,1987,7:1053～1075
[112] NAKAYAMA T, Washizu K, The boundary element method applied to the analysis oftwo-dimensional nonlinear sloshing problems [J]. Int. J. Numer. Methods Engrg,1981.17:1631～1646
[113] CHEN W, Haroun M A, Liu F. Large amplitude liquid shloshing in seismically excitedtanks [J]. Earthquake Engrg. Struct. Dyn.,1996,25:653～669
[114]王博，陈淮，徐建国，黄亮.大型渡槽结构抗震分析理论及其应用[M].北京:科学出版社,2013
[115]高平，魏德敏，徐梦华.大型渡槽槽身的地震扭转效应研究[J].水力发电学报，2013,29(6):207-210
[116]石诚.考虑双向水平地震作用的结构抗震分析与设计若干问题研究[M].重庆大学，2004
[117]建筑抗震设计规范[S].北京：中国建筑工业出版社，2010
[118]公路桥梁抗震设计细则[S].北京：人民交通出版社，2008
[119]中国水利水电科学研究院主编,《水工建筑物抗震设计规范》（征求意见稿2013）
[120]杜晓伟，陈淮，孙国钧，王博.大型双槽渡槽地震反应分析[J].世界地震工程，2003，19(2):23-26
[121]李遇春，楼梦麟，尚伟，朱军.大型渡槽抗震分析中流体的位移有限元模式[J].水利学报，2003，2:93-97
[122]王博，李杰.大型渡槽结构地震响应分析[J].土木工程学报，2001，34(3):29-34
[123]莫海鸿，张华忠，刘春洋，吴轶.大型梁式U形渡槽槽身结构动内力分析[J].华南理工大学学报（自然科学版），2003，31(9):82-85
[124]李遇春，楼梦麟.强震下流体对渡槽槽身的作用[J].水利学报，2000，3:46-52
[125]王青沙.山西某大跨复合拱式渡槽支撑结构的稳定与地震响应分析[M].太原理工大学，2011
[126]裴欢.山西某大跨钢管混凝土拱式渡槽结构静动力分析[M].太原理工大学，2013
[127]冯云田，李明瑞．复杂结构的弹性地震反应分析[J]．地震工程与工程振动，1991，11(1):78-87
[2]水工建筑物抗震设计规范[S]．北京：中国水利水电出版社出版，1997
[3]水工建筑物抗震设计规范[S]．北京：中国电力出版社，2000
[4]周厚贵,马吉明,马金刚.国内外渡槽的发展与南水北调中线漕河渡槽[J].南水北调与水利科技,5(3)：14-17
[5]李珍照，王益敏，陈胜宏，何金平．中国水利百科全书（水工建筑物分册）[M]．北京：中国水利水电出版社，2004
[6] Eugene L．，Dennis P.E．Integration of computer systems for California aqueduct powerplant systems[J]．IEEE Transactions on Energy Convemion,1993，8(2)：93-113
[7] Shah J J．Construction of Gomti Aqueduct[J]. Indian Consrete．Journal，June，1986
[8] Golani B D．‘Rolling trusses’ as falsework for aqueduct and bridges．Indian ConcreteJouranl，January,1978
[9] Anon. Aqueduct Uses Prestressed Concrete Design.[J] World Construction, June.1984
[10] Connelly. David L., Perry．Roy J．First steps in aqueduct leak risk assessment[J]. Proc22Annu Conf Integr Water Res Plan21Century,1995．64l-644
[11]钟砥宁，边立明．东深供水改造工程渡槽伸缩缝止水设计与施工[J]．人民长江，2003，34(11)：34-36
[12]陆岸典，丁仕辉．大型U型薄壳渡槽预应力施工[J]．施工技术，2002，31(7)：18-19．
[13]何旭升，杜振坤等．东深供水改造工程渡槽伸缩缝止水研究[J]．水利水电技术，2002，33(5)：37-39
[14]邹正欣，朱军.东深供水改造工程现浇预应力U型薄壳渡槽有限元分析[J]．广东水利水电，2007，6：8-10
[15]赵瑜，白新理等．东深供水改造工程渡槽支承结构受力分析[J]．灌溉排水，2002，21(3)：53-55
[16]曾金鸿．东深供水改造工程渡槽伸缩缝新型止水结构设计与施工[J]．水利水电科学进展，2005，25(3)：35-37
[17]程瓦，潘登宇．大型双向预应力混凝土“U”型薄壳渡槽设计[J]．人民长江，2008，39(24)：38-40
[18]吴轶．大型梁式渡槽地震反应分析及设计方法研究[D]．广州：华南理工大学，2004
[19]吴轶，莫海鸿，杨春．大型矩形渡槽-水耦合体系的动力性能分析[J]．地震工程与工程振动，2004．24(4)：137-142
[20]吴轶，莫海鸿，杨春．排架-渡槽-水三维耦合体系地震响应分析[J]．水利学报，2005，36(3)：280-285
[21]吴轶,莫海鸿,杨春.大型渡槽动力设计方法研究[J].计算力学学报,2006,23(6):778-782
[22]吴轶,莫海鸿,杨春.大型拱式U型薄壳渡槽结构的模态分析[J].华南理工大学学报(自然科学版),2003,31(3):72-76
[23]吴轶,莫海鸿,杨春.三维排架渡槽中水的调频液体阻尼效应[J].水利学报,2005,(9):1115-1120
[24]张华忠，莫海鸿，刘春洋.大型梁式渡槽止水带纵轴向张开变位分析[J].广东土木与建筑,2003,(1):24-28
[25]徐梦华．大型渡槽梁壳流固耦合动力模型及其工程应用研究[D]．广州：华南理工大学，2004
[26]徐梦华，莫海鸿.大跨度梁式渡槽改进拟三维流固耦合模型的三维模拟效果分析[J].振动与冲击,2010,29(6):207-210
[27]徐梦华，莫海鸿.简支梁式渡槽考虑流固耦合的横向地震三维动力响应分析[J].工程抗震与加固改造，200931(5)：29-33
[28]符志远，段国学．大型“U”型薄壳预应力渡槽仿真结构试验[J]．人民长江，2004，35(8)：49-53
[29]王博．大型渡槽动力建模研究[J]．计算力学学报，2000,17(4):468-474
[30]徐建国，陈淮等．地震作用下大型渡槽结构动态应力计算方法研究[J]．水利学报，2002,7:79-82
[31]李遇春，楼梦麟等．大型梁式渡槽竖向地震作用估计[J]．土木工程学报，2003，36(2)：10-15
[32]徐建国，陈淮等．渡槽结构考虑流固耦合的横向地震响应研究[J]．工程力学，2004,21(6):197-202
[33]王博，陈淮等．考虑槽身与槽内水体流固耦合的渡槽地震反应计算[J]．水利水电科技进展，2005,25(3):5-7
[34]徐建国，陈淮等．考虑流固耦合的大型渡槽横向动力分析[J]．大连理工大学学报，2005,45(4):587-592
[35]徐建国，陈淮等．考虑流固动力相互作用的大型渡槽地震响应研究[J]．土木工程学报，2005,38(8):67-73
[36]徐建国，陈淮等．大型渡槽结构考虑流固耦合的动力建模研究[J]．南京理工大学学报，2005,29(6):639-644
[37]彭辉，刘德富等．南水北调中线漕河渡槽流固耦合机理研究[J]．灌溉排水学报，2006,25(5):75-77
[38]张林让，吴杰芳等．大型渡槽流固动力耦合效应试验研究[J]．南水北调与水利科技，2008,6(1):6-10
[39]张静娜，马文英等．大型联体式矩形渡槽流固耦合动力特性分析[J]．人民长江，2008,39(5):79-81
[40]徐建国，王博等．渡槽结构考虑流固耦合地震响应及求解敛散性[J]．人民长江，2008,39(6):51-53
[41]李遇春，楼梦麟等．大型渡槽的竖向地震效应分析[J]．地震工程与工程振动，2008,28(2):102-107
[42]王清云，张多新等．大型矩型水工渡槽三维流固耦合动力分析[J]．水利水运工程学报，2008,4:55-60
[43]袁吉栋，邢红芳等．考虑流固耦合的大型预应力渡槽地震反应分析[J]．人民长江，2009,40(5):7-10
[44]白新理，王丽芳等．考虑流固耦合的矩形渡槽动力分析[J]．华北水利水电学院学报，2009,30(5):33-36
[45]徐建国,王博.大型单墩渡槽流固耦合动力分析[J]．郑州大学学报(工学版),2009,30(4):128-132
[46]夏富洲,宋一乐等.大型渡槽隔震体系结构动力特性的试验研究[J]．南水北调与水利科技,2009,7(6):59-61
[47]张多新，王清云等．流固耦合系统位移-压力有限元格式在渡槽动力分析中的应用[J]．土木工程学报，2010,43(1):125-129
[48]徐建国,王博等.地震作用下大型渡槽结构纵向碰撞非线性分析[J]．地震工程与工程振动,2010,30(5):126-133
[49]蒋寅军,宋一乐.超大型渡槽抗震性能试验研究[J]．中国农村水利水电，2010，12:100-133
[50]邱流潮，张立翔.地震作用下拱坝一库水祸全振动动水压力分析[J]．水动力学研究与进展，2000,15(1):94-103
[51] Westergaard H M. Water pressures on dams during earthquakes[J]．Transcations, ASCE,1933,98:418-433
[52] R.W. Clough. Reservoir interaction effects on the dynamic response of archdams[J]．Proceeding of China-US Bilateral workshop on earthquake engineering,1982:58-84
[53] Fok,K-L., Chopra, A.K. Water compressibility in earthquake response of archdams[J]．Journalof Structural Engineering, ASCE,1987,113(5):958-975
[54] Fenves G L, Mojtahedi S and Reimer R B. Effect of contraction joints on earthquakeresponse of an arch dam[J]．Journal of Structural Engineering, ASCE,1992,118(4):1039-105
[55]郑哲敏.平板在流体作用下的振动[J]．力学学报，1958,2(1):11-16
[56]郑哲敏等.悬臂梁在一侧受有液体作用下的振动[J]．力学学报，1959,3(2):111-119
[57]王前信，王孝信.在不规则地震作用下刚性坝面动水压力的探讨[J]．地震工程研究报告集，第一集：153-161,1962
[58]王前信，王孝信.伸臂梁在一侧有水时的自振特性与地震荷载[J]．地震工程研究报告集，第一集：152-172,1962
[59]居荣初，曾心传.弹性结构与液体的祸联振动理论[M]．北京：地震出版社，1983
[60]宫维圣.码头和船闸建筑物的抗震[M]．北京:人民交通出版社,1993
[61] Housner G W. The Dynamic Pressure on Accelerated Fluid Containers[J]．Bulletion ofthe seismological of America,1957,47(1):15-35
[62] Housner G W. The Dynamic behavior of Water Tanks[J]．Bulletion of the seismologicalof America,1963,53(2):381-387
[63]徐建国.大型渡槽结构抗震分析方法及其应用[D]．大连：大连理工大学，2005.
[64]刘云贺,胡宝柱,闫建文,王克成. Housner模型在渡槽抗震计算中的适用性[J]．水利学报,2002(9):94-99
[65] Nakayama, T. and Washizu, K., The boundary element method applied to the analysis oftwo-dimensional nonlinear sloshing problems[J]．Int. J. Numer. Methods Engrg.1981,17:1631-1646
[66] Liu Z. and Huang Y., A new method for large amplitudes loshing problems[J]．J. Sound&Vi b.1994,175(2):185-195
[67]邵岩,赵兰浩,李同春.考虑流固耦合的渡槽动力计算方法综述.人民黄河.2005,27(11):55-56
[68] Noh CEL. A time-dependent two-space-dimension coupled Eulerian-Lagrangiancode[J]． In: Alder B, Fernbach S, eds. Methods in computational Physics3. New York:Academic Press,1964
[69] Thomas JR. Lagrangian-Eulerian Finite element formulation for in compressible viscousflows[J]．Computer Methods in applied Mechanics and Engineering,1981,29(3):329-349
[70] Wang CY, Moody F J, Shin Y W eds. Fluid-structure Interaction, Transient Thermal-hydraulics, and Structural Mechanics-1992[C]．ASME PVP Conf., June1992, NewOrleans LA, ASME, New York(l992)
[71] T. J. R. Hughes, Multiscale phenomena: Geren's function, the Dirichlet-to-Neumannformulation, subgrid scale models, bubbles and the origins of stabilizedformulations[J]．Comput. Methods Appl. Mech. Engrg.127(1995)387-401
[72] Okamoto, T. and Kawahara, M. Two-dimensional sloshing analysis by Lagrangian finiteelement method[J]．Int. J, Numer. Methods Fluids,1990,11:453-477
[73] D.W. Kelly, S. Nakazawa, O. C. Zienkiewiez and J. C. Heinrich, A note on upwindingand anisotropic balancing dissipation in finite element approximations to convectivedifusion problems[J]．Int. J. Numer. Methods Engrg.15(1980)1705-1711
[74] Fung Y C. An Intorduction to the Theory of Aeroelasticity[J]．J. Wiley and Sons, Inc.,New York(1955)
[75] J. Douglas and J. Wang, An absolutely stabilized finite element methods for the StrokesProblem[J]．Math. Comput.52(1989)495-508
[76] O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method[J]．4th edition,Vol.2(McGraw-Hill,1989)
[77] D. N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokesequations[J]．Calcolo21(1984)337-344
[78] I. Harari and T. J. R. Hughes, what are C and h？：Inequalities for the analysis anddesign of finite element methods[J]．Comput. Methods Appl. Mech. Engrg.97(1992)157-192
[79] Zienkiewicz O C, Chang C T, Betess P. Drained, Undrained, Consolidating andDynamics behaviour assumptions in soils, Limits of validity[J]．Geotechnique.30(1980):385-395
[80] Ramaswamy, B, Kawahara, M. Arbitrary Lagrangian-Eulerian finite element method forunsteady, convective, in compressible viscous free surface fluid flow[J]．Int. J Numer.Methods fluids.1987,7:1053-1075
[81] J. Douglas and T. F. Russell, Numerical methods for convection dominated difusionproblems based on combining the method of characteristics with finite element or finiteprocedures[J]．SIAM J. Numer. Anal.19(1982)871-885
[82] Paidoussis M P. Flow-induced instabilities of cylindrical structures[J]．Appl. Mech. Rech.Rev.,40,2(1987):163-175
[83] Brook AN, Hughes TJR. Streamline upwind petrov-Galerkin formulation for convectiondominated flows with particular emphasis on the incompressible Navier-stokesequations[J]．Computer Methods in Applied Mechanics and Engineering,1982,32(1-3):199-259
[84] Liu WK. Finite element procedure for fluid-structure interactions and application toliquid storage tanks[J]．Nuclear Engineering and Design,1981,65:221-238
[85] Liu WK, Hu YK. ALE finite element with hydrodynamic lubrication for metalforming[J]．Nuclear Engineering and Design,1992,138:1-10
[86] Chen S S, Fujita K, Au-Yang M K eds. Fluid-induced Vibration-1990[C]．ASME PVPConf. Nashville TN, ASME, New York(1990)
[87] T. J. R. Hughes, L. P. Franca and GM. Hulbert, A new finite element formulation forcomputational fluid dynamics: VIII. The Galerkin least-squares method foradvective-diffusivee quations[J]．Comput. Methods Appl. M ech. Engrg.73(1989)173-189
[88] O. Pironnrau, on the transport-diffusion aplorithm and its application to theNavier-Strokes equations[J]．Numer. Math.38(1982)309-332
[89] Liu, Z. and Huang, Y, A new method for large amplitude sloshing problems[J]．J.Sound&Vib.1994,175(2):185-195
[90] Zienkiewics O C. Coupled problems and their numerical solution in: Lewis R W, BetessP, Hinton E eds[J]．Numeircal Methods in Coupled Systems. John Wiley and Sons Ltd,New York(1984)
[91] F. Shakib and T. J. R. Hughes, A new finite element formulation for computational fluiddynamics: IX. Fourier Analysis of space-time Galerkin least-squaresalgorithms[J]．Comput. Methods Appl. Mech. Engrg.87(1991)35-58
[92] L. Franca, S. L. Frey and T. J. R Hughes, Stabilized finite element methods: I.Application to the advective-diffusive model[J]．Comput. Methods Appl. Mech. Engrg.95(1992)253-276
[93] R. Codina, Numerical solution of the incompressible Navier-Strokes equations wi thCoriolis forces based on the discretization of the total time derivative[J]．CIMNE Report,Num.102,1996
[94] R. Codina, A discontinuity-capturing cross wind-dissipation for the finite elementsolution of the convection-difusione quation[J]．Comput. Methods Appl. Mech. Engrg.110(1993)325-342
[95] R. E. Bank and B. D. Welfert, A comparison between the mini-element and the Petrov-Galerkin formulations for the generalized Stokes problem[J]．Comput. Methods Appl.Mngrg.83(1990)61-68
[96] Zienkiewicz O C， Betess P. Fluid-structure dynamic in teraction and wave forces, anintroduction to numerical treatment[J]．Int. J. Num. Meth. Engrg.,13,1(1978):1-16
[97] Ramaswamy, B., Kawahara, M. and Nakayama T. Lagrangian finite element method forthe analysis of two-dimensional sloshing problems[J]．Int. J. Numer. Methods fluids,1986,6:659-670
[98] F. Shakib, T. J. R. Hughes and Z. Johan,. A new finite element formulation forcomputational fluid dynamics: X. The compressible Euler and Navier-Strokesequations[J]．Comput. Methods Appl. Mech. Engrg.89(1991)141-219
[99] P. G. Ciarletand P. A. Raviart, Maximum principle and uniform convergence for thefinite element method[J]．Comput. Methods Appl. Mech. Engrg.2(1973)17-31
[100] J. von Neumann and R. D. Richtmyer, A method for the numerical calculation ofhydrodynamical shocks[J]．J. Appl. Phys.21(1950)232
[101] Johnson W. Recent developments in the dynamics of advanced rotorsystems[J]．Vertion,10,1(1986):73-107
[102] L. P. France and C. Farhat, Bubble functions prompt unusual stabilized finite elementmethods[J]．Comput Methods Appl. Mech. Engrg.123(1994)299-308
[103] C. Baiocchi, F. Brezzi and L. P. Franca, Virtual bubbles and Galerkin-least-squares typemethods[J]．Comput. Methods Appl. Mech. Engrg.105(1993)125-141
[104] Huerta A, Liu WK. Viscous flow with large free surface motion[J]．Computer Methodsin Applied Mechanics and Engineering,1988,69(3):277-324
[105] Hirt GW, Amsden AA, Cook JL. An arbitary Lagrangian-Eulerian computing methodfor all flow speeds[J]．J Comp Phys,1974,14(3):227-253
[106] Liu WK, Chang H, Belytscko T. Arbitary Lagrangian-Eulerian Petrov-Galerkin finiteelement for nonlinear continua[J]．Computer Methods in Applied Mechanics andEngineering,1988,68(3):259-310
[107] Liu WK, chen JS. Adaptive ALE finite element with particular reference to externalwork rate on frictional interface[J]．Computer Methods in Applied Mechanics andEngineering,1991,93:189-216
[108] A. N. Brooks and T. J. R. Hughes, Streamline upwind petrov-Galerkin formation forconvective dominated flows with particular emphasis on the incompressibleNavier-Strokese quations[J]．Comput. Methods Appl. Mech. Engrg.32(1982)199-259
[109]刘云贺.流体一固体动力耦合理论及水利工程应用[D].西安:西安交通大学，2001
[110] RAMASWAMYB, Kawahara M, Nakayama T. Lagrangian finite element method forthe analysis of two-dimensional sloshing problems [J]. Int. J. Numer. Methods Fluids,1986,6:659～670
[111] RAMASWAMYB, Kawahara M. Arbitrary Lagrangian-Eulerian finite element methodfor unsteady, convective, incompressible viscous free surface fluid flow [J]. Int. J.Numer. Methods Fluids,1987,7:1053～1075
[112] NAKAYAMA T, Washizu K, The boundary element method applied to the analysis oftwo-dimensional nonlinear sloshing problems [J]. Int. J. Numer. Methods Engrg,1981.17:1631～1646
[113] CHEN W, Haroun M A, Liu F. Large amplitude liquid shloshing in seismically excitedtanks [J]. Earthquake Engrg. Struct. Dyn.,1996,25:653～669
[114]王博，陈淮，徐建国，黄亮.大型渡槽结构抗震分析理论及其应用[M].北京:科学出版社,2013
[115]高平，魏德敏，徐梦华.大型渡槽槽身的地震扭转效应研究[J].水力发电学报，2013,29(6):207-210
[116]石诚.考虑双向水平地震作用的结构抗震分析与设计若干问题研究[M].重庆大学，2004
[117]建筑抗震设计规范[S].北京：中国建筑工业出版社，2010
[118]公路桥梁抗震设计细则[S].北京：人民交通出版社，2008
[119]中国水利水电科学研究院主编,《水工建筑物抗震设计规范》（征求意见稿2013）
[120]杜晓伟，陈淮，孙国钧，王博.大型双槽渡槽地震反应分析[J].世界地震工程，2003，19(2):23-26
[121]李遇春，楼梦麟，尚伟，朱军.大型渡槽抗震分析中流体的位移有限元模式[J].水利学报，2003，2:93-97
[122]王博，李杰.大型渡槽结构地震响应分析[J].土木工程学报，2001，34(3):29-34
[123]莫海鸿，张华忠，刘春洋，吴轶.大型梁式U形渡槽槽身结构动内力分析[J].华南理工大学学报（自然科学版），2003，31(9):82-85
[124]李遇春，楼梦麟.强震下流体对渡槽槽身的作用[J].水利学报，2000，3:46-52
[125]王青沙.山西某大跨复合拱式渡槽支撑结构的稳定与地震响应分析[M].太原理工大学，2011
[126]裴欢.山西某大跨钢管混凝土拱式渡槽结构静动力分析[M].太原理工大学，2013
[127]冯云田，李明瑞．复杂结构的弹性地震反应分析[J]．地震工程与工程振动，1991，11(1):78-87