薄壁箱梁混合单元及其在斜拉桥双重非线性分析中的应用研究
|
摘要
斜拉桥因其强大的跨越能力和优美的景观而得到人们的青睐。随着科学技术的进步和社会需求的增长，斜拉桥数量越来越多，跨度越来越大，结构形式也日益多样化。我国大江大河众多，斜拉桥在中国有着广阔的应用前景。斜拉桥是一种柔性结构体系，实践证明，设计计算中必须考虑几何非线性，如果作承载力分析，还必须考虑材料非线性。方案比选和初步设计中，经常要变更数据，计算工作量巨大，通用软件虽然功能非常强大，但很难在短时间内获得准确的结果。因此，迫切需要一种简单、实用且能满足工程要求的计算方法和软件为设计服务。斜拉桥主梁和主塔大多为薄壁箱梁结构，其受力状态非常复杂，经典梁理论很难正确反映其受力特性。本文对薄壁箱梁和斜拉索的分析理论和计算方法作了较为深入的研究，提出了新的计算理论和方法，并将其应用于斜拉桥非线性分析，主要取得如下创新性成果：
1、在广泛阅读国内外资料文献的基础上，对斜拉桥非线性特性、薄壁箱梁的计算理论和方法以及存在的问题作了较全面、深入的研究，确定以混合变分原理为本文薄壁箱梁单元的理论基础。
2、提出了基于Hellinger-Reissner混合变分原理的两节点空间非线性薄壁箱梁单元，推导了增量形式的几何非线性有限元方程、弹性刚度矩阵、几何刚度矩阵、初应力荷载阵等的计算公式。该单元考虑了薄壁箱梁的轴向变形、双向弯曲变形、剪切变形、约束扭转变形和截面畸变等因素，较全面地反映了箱梁的变形特征；编制了程序，给出了简单算例。结果表明，该单元简单有效正确。
3、提出了塑性削减应力当量荷载法，将上述两节点空间几何非线性薄壁箱梁单元发展到材料非线性问题，推导了适用于薄壁箱梁的弹塑性本构关系，塑性削减应力增量及其当量荷载增量、塑性削减应力及其当量荷载的计算公式，列出了计算步骤和计算方法。该法将塑性引起的结构刚度的削弱转化为当量荷载，简化了计算；编制了程序，给出了简单算例。结果表明，该法的计算理论和方法正确，简单可行。
4、提出了空间悬链线斜拉索单元，该单元严格按照斜拉索的自然几何形状建立；推导了缆索单元刚度矩阵和节点力列阵；给出了两类缆索问题的算法；考虑缆索与主梁相关节点之间的主从关系；编制了程序，给出了简单算例。结果表明，该缆索单元精确地模拟了斜拉索的几何非线性行为，计算结果真实可信。
5、将上述计算理论、计算方法和所编制程序综合起来，应用于两座单索面
斜拉桥的非线性分析计算，其中一座为钢一混凝土混合梁斜拉桥，另一座为预
应力混凝土斜拉桥，对该桥还作了成桥静载试验，本文分析计算结果与实测值
及通用软件的计算结果吻合良好，但本文的计算准备工作量和计算机时远小于
通用软件.计算结果还表明，钢斜拉桥的几何非线性效应比混凝土斜拉桥的几
何非线性效应更为明显。
实践表明，本文研究既有理论意义，又有实用价值。
关键词斜拉桥，薄壁箱梁，混合变分原理，塑性削减应力当量荷载，
悬链线斜拉索
Cable-stayed bridges get into good graces of people because of their great spanning capability and beautiful sight. With the development of scientific technology and increasing demands of the society, cable-stayed bridge has great increase in number and span; its structure form is increasingly diversiform. There are numerous rivers in China, which brings cable-stayed bridge a good future in application. As a kind of flexible structure, practice shows that geometry-nonlinear must be taken into account in the design and calculation of cable-stayed bridge. For carrying capability analysis, material nonlinear has to be taken into account, too. In the comparison of schemes and preliminary design, data are changed often, so that the amount of calculation work is huge. Though current software has powerful functions, it is still difficult to get accurate results in a short time. Therefore, there is an urgent need for a set of calculation methods and software for design of cable-stayed bridges, which should be simple, applied and able to meet engineering demands. The main girders and towers of cable-stayed bridges are usually thin-walled box girder structures, which have complex stress state. The classic beam theory has difficulty in reflecting the deformation characteristic of thin-walled box girders accurately. In this thesis, the author made an in-depth study of the analysis theories and calculation methods of thin-walled box girder and cable, put forward new calculation theory and methods, and applied them into the non-linear analysis of cable-stayed bridges. The main innovative achievements are listed in the following:1. On the basis of extensive reading, an in-depth study was made on the non-linear characteristic of cable-stayed bridges, the calculation theories and methods of thin-walled box girders, and the existing problems in the above -mentioned subjects; hybrid variation principle was fixed to be the theoretical basis of the thin-walled beam element of this paper.2. A two-node spatial non-linear thin-walled box girder element is
put forward, which is based on Hellinger-Reissner hybrid variation principle. The non-linear FEM (finite element method) equation, elastic rigidity matrix, geometry matrix and pre-stress load column matrix were formulated. In the element, axial deformation, double flexural, shear deformation, restraining torsion warping and section-distortion were all taken into account, which lead to a comprehensive reflection of deformation characteristic of thin-walled box girders. The corresponding program was designed, and some simple examples were given. The results of the examples show that the element is simple, accurate and effective.3. A method named equivalent load of cut-down plastic stress was put forward, which extended the above two-node spatial non-linear thin-walled hybrid beam element to material non-linear field. The plastic constructive equation suited for thin-walled box beam was derived, the increment of plastic cut-down stress and its resultant, the plastic cut-down stress and its resultant were formulated. The calculation steps were listed out. The method simplifies calculation by translates the impairment of structure rigidity, caused by plasticity, into an equivalent load. The corresponding program was designed, and some simple examples were given. The results of the examples show that the theory and the method are correct, simple and applicable.4. A spatial catenary cable element was brought forward, which was built strictly according to the natural geometric shape of cables. The rigidity matrix and node force column matrix of the cable element were formulated; the arithmetic of two kinds of cable problems was given; the master-slave relationship of the relative nodes between cable element and beam element was considered. Corresponding program was designed and some simple examples were given. The results of the examples show that the catenary cable element simulates the geometric non-linear behavior accurately, the results are actual and believable.5. All the above-mentione
1、在广泛阅读国内外资料文献的基础上，对斜拉桥非线性特性、薄壁箱梁的计算理论和方法以及存在的问题作了较全面、深入的研究，确定以混合变分原理为本文薄壁箱梁单元的理论基础。
2、提出了基于Hellinger-Reissner混合变分原理的两节点空间非线性薄壁箱梁单元，推导了增量形式的几何非线性有限元方程、弹性刚度矩阵、几何刚度矩阵、初应力荷载阵等的计算公式。该单元考虑了薄壁箱梁的轴向变形、双向弯曲变形、剪切变形、约束扭转变形和截面畸变等因素，较全面地反映了箱梁的变形特征；编制了程序，给出了简单算例。结果表明，该单元简单有效正确。
3、提出了塑性削减应力当量荷载法，将上述两节点空间几何非线性薄壁箱梁单元发展到材料非线性问题，推导了适用于薄壁箱梁的弹塑性本构关系，塑性削减应力增量及其当量荷载增量、塑性削减应力及其当量荷载的计算公式，列出了计算步骤和计算方法。该法将塑性引起的结构刚度的削弱转化为当量荷载，简化了计算；编制了程序，给出了简单算例。结果表明，该法的计算理论和方法正确，简单可行。
4、提出了空间悬链线斜拉索单元，该单元严格按照斜拉索的自然几何形状建立；推导了缆索单元刚度矩阵和节点力列阵；给出了两类缆索问题的算法；考虑缆索与主梁相关节点之间的主从关系；编制了程序，给出了简单算例。结果表明，该缆索单元精确地模拟了斜拉索的几何非线性行为，计算结果真实可信。
5、将上述计算理论、计算方法和所编制程序综合起来，应用于两座单索面
斜拉桥的非线性分析计算，其中一座为钢一混凝土混合梁斜拉桥，另一座为预
应力混凝土斜拉桥，对该桥还作了成桥静载试验，本文分析计算结果与实测值
及通用软件的计算结果吻合良好，但本文的计算准备工作量和计算机时远小于
通用软件.计算结果还表明，钢斜拉桥的几何非线性效应比混凝土斜拉桥的几
何非线性效应更为明显。
实践表明，本文研究既有理论意义，又有实用价值。
关键词斜拉桥，薄壁箱梁，混合变分原理，塑性削减应力当量荷载，
悬链线斜拉索
Cable-stayed bridges get into good graces of people because of their great spanning capability and beautiful sight. With the development of scientific technology and increasing demands of the society, cable-stayed bridge has great increase in number and span; its structure form is increasingly diversiform. There are numerous rivers in China, which brings cable-stayed bridge a good future in application. As a kind of flexible structure, practice shows that geometry-nonlinear must be taken into account in the design and calculation of cable-stayed bridge. For carrying capability analysis, material nonlinear has to be taken into account, too. In the comparison of schemes and preliminary design, data are changed often, so that the amount of calculation work is huge. Though current software has powerful functions, it is still difficult to get accurate results in a short time. Therefore, there is an urgent need for a set of calculation methods and software for design of cable-stayed bridges, which should be simple, applied and able to meet engineering demands. The main girders and towers of cable-stayed bridges are usually thin-walled box girder structures, which have complex stress state. The classic beam theory has difficulty in reflecting the deformation characteristic of thin-walled box girders accurately. In this thesis, the author made an in-depth study of the analysis theories and calculation methods of thin-walled box girder and cable, put forward new calculation theory and methods, and applied them into the non-linear analysis of cable-stayed bridges. The main innovative achievements are listed in the following:1. On the basis of extensive reading, an in-depth study was made on the non-linear characteristic of cable-stayed bridges, the calculation theories and methods of thin-walled box girders, and the existing problems in the above -mentioned subjects; hybrid variation principle was fixed to be the theoretical basis of the thin-walled beam element of this paper.2. A two-node spatial non-linear thin-walled box girder element is
put forward, which is based on Hellinger-Reissner hybrid variation principle. The non-linear FEM (finite element method) equation, elastic rigidity matrix, geometry matrix and pre-stress load column matrix were formulated. In the element, axial deformation, double flexural, shear deformation, restraining torsion warping and section-distortion were all taken into account, which lead to a comprehensive reflection of deformation characteristic of thin-walled box girders. The corresponding program was designed, and some simple examples were given. The results of the examples show that the element is simple, accurate and effective.3. A method named equivalent load of cut-down plastic stress was put forward, which extended the above two-node spatial non-linear thin-walled hybrid beam element to material non-linear field. The plastic constructive equation suited for thin-walled box beam was derived, the increment of plastic cut-down stress and its resultant, the plastic cut-down stress and its resultant were formulated. The calculation steps were listed out. The method simplifies calculation by translates the impairment of structure rigidity, caused by plasticity, into an equivalent load. The corresponding program was designed, and some simple examples were given. The results of the examples show that the theory and the method are correct, simple and applicable.4. A spatial catenary cable element was brought forward, which was built strictly according to the natural geometric shape of cables. The rigidity matrix and node force column matrix of the cable element were formulated; the arithmetic of two kinds of cable problems was given; the master-slave relationship of the relative nodes between cable element and beam element was considered. Corresponding program was designed and some simple examples were given. The results of the examples show that the catenary cable element simulates the geometric non-linear behavior accurately, the results are actual and believable.5. All the above-mentione
引文
[1] 严国敏．现代斜拉桥．成都：西南交通大学出版社，2000，16
[2] 项海帆．高等桥梁结构理论．北京：人民交通出版社，2001，15～25
[3] 林元培．斜拉桥．北京：人民交通出版社，1997，161
[4] [美]陈惠发、A．E．萨里普 著．土木工程的材料本构方程．第一卷，第二卷，(余天庆、王勋文 译)．武汉：华中科技大学出版社，2001
[5] 李国豪．桥梁结构稳定与振动．北京：中国铁道出版社，1996
[6] 梁硕．大跨度混凝土斜拉桥局部与整体相关屈曲空间极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1999
[7] H. Sbakoarzadsh. Y. Q. Guo. J. L. Batoz. A Torsion Bending Element for Thin-Walled Beams With Open and Closed Cross Sections. Computers & Structures, 1995, 55(6): 621～635
[8] 颜全胜．大跨度钢斜拉桥极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1994
[9] 王勖成．有限单元法基本原理和数值方法．北京：清华大学出版社，1999，267～269
[10] 李存权．结构稳定和稳定内力．北京：人民交通出版社，2000
[11] 项海帆，李映．悬索桥按有限位移理论的空间非线性分析．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，913～919，926～928
[12] 朱晞，王克海．几何非线性对大跨度斜拉桥的影响．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，985～988
[13] 彭杰元，汪正兴．关于大跨度斜拉桥的非线性分析——武汉桥模型研究．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，972～978
[14] 李映，项海帆．悬索桥在侧向风载下的空间非线性分析．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，941～947
[15] 沈锐利，廖海黎．悬索桥静动力空间非线性计算有限元模型及其应用．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，935～940
[16] 王序森等著．桥梁工程．北京：中国铁道出版社，1995，489～493
[17] China, F. Jiang, W. W. Yang. Design of the Qi Ao Bridges. Structure Engineering International, 1998, 8(2):
[18] 江峰．淇澳大桥独柱式主塔横向受力分析．武汉城市建设学院学报，2001，18(1)：20～24
[19] 周述华，陈忻等．淇澳大桥成桥及施工状态气动弹性模型风洞试验研究．
[20] 钟新谷．单拱面预应力混凝土系杆拱桥极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1997
[21] 王荣辉．板桁组合钢梁非线性分析：[博士学位论文]．长沙：长沙铁道学院，1997
[22] 肖万伸．大跨度钢斜拉桥局部与整体相关屈曲极限承载力分析．：[博士学位论文]．长沙：长沙铁道学院，1999
[23] 盛兴旺．预应力混凝土斜交箱形梁分析理论与试验研究：[博士学位论文]．长沙：中南大学，2000
[24] 梁硕等．大跨度混凝土斜拉桥极限承载力分析综述．长沙：长沙交通学院学报，1997，9：39～46；
[25] 李俊升，贺到荣，刘玉海．斜拉桥极限跨度及分析．华东公路，1999，1：7～8
[26] 张汝清、詹先义编著．非线性有限元分析．重庆：重庆大学出版社，1990年
[27] 程庆国、潘家英、高路彬等．关于大跨度斜拉桥几何非线性问题．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992：
[28] 洪显诚．刘志英．精确的斜拉索等效弹性模量公式的推导．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992：
[29] 杨讯．沈志林．独塔单索面斜拉桥稳定性计算方法的探讨．铁道学报，2000，22(增刊)：4～7
[30] 张新军等．大跨度桥梁非线性空气静力和动力行为研究．桥梁建设，2001，6：4～7
[31] John F. Fleming, Nonlinear Static Analysis Of Cable-stayed Bridge Structures. Computers & Structures., 1979, 10: 621～635
[32] 龚仁明．超大跨度斜拉桥方案设计．同济大学学报，1999, 4：229～233
[33] Aly S. Nazmy & Ahmed M. Abdel-Ghaffar, Three-Dimensional Nonlinear Static Analysis Of Cable-stayed Bridges. Computers & Structures, 1990, 34.. 257～271
[34] Eric P. Kasper, Robert L. Taylor. A mixed-enhanced strain method Part Ⅰ: Geometrically linear problems. Computers & Structures, 2000, 34:237～250
[35] Eric P. Kasper, Robert L. Taylor. A mixed-enhanced strain method Part Ⅰ: Geometrically nonlinear problems. Computers & Structures, 2000, 34.. 237～250
[36] 特大跨径桥梁新设想．国外公路，2000，3：18～20
[37] 金增洪．介绍吉姆辛的未来长大桥概念．国外公路．2000年第3期．P8～14
[38] 星樊正明，宫田利雄．长大斜拉桥(中跨1000m)试设计．桥梁与基础，1990，2：5～22
[39] 潘家英等．大跨度斜拉桥活载非线性研究．土木工程学报，1993，26(1)：31～37
[40] 沈聚敏等．钢筋混凝土有限元与板壳极限分析．北京：清华大学出版社，1993
[41] 过镇海．混凝土的强度和变形——试验基础和本构关系．北京：清华大学出版社，1997
[42] 华孝良．桥梁结构非线性分析．北京：人民交通出版社，1997
[43] 匡震邦．非线性连续介质力学基础．西安：西安交通大学出版社，1989
[44] 程翔云．单索面索塔横桥向稳定分析．公路，1999，5：25～31
[45] 陈铁冰等．计入结构几何非线性影响时斜拉桥可跨度分析．同济大学学报，2000，28(4)：407～412
[46] Pao-Hsii Wang, Chiung-Guei Yang. Parametric Studies On Cable-Stayed Bridges. Computers & Structures, 1996, 60 (2): 243～260
[47] Tang Chia-Chih, Shu Hung-Shan, Wang Yang-Cheng. Stability Analysis of Steel Cable-Stayed Bridges. Structural Engineering and Mechanics, 2001, 11 (1): 35～48
[48] Shu Hung-Shan, Wang Yang-Cheng. Stability Analysis of Box-Girder Cable-Stayed Bridges. Journal of Bridge Engineering, 2001, 6 (1): 63～68
[49] Wang Yang-Cheng. Effect of Cable Stiffness on a Cable-Stayed Bridge. Structural Engineering and Mechanics, 1999, 8 (1): 27～38
[50] 叶英华，刁波．钢筋混凝土结构非线性理论综述．哈尔滨建筑工程学院学报，1995，1：127～131
[51] 苏善根等译．斜拉桥设计指南．国外公路，1993，13(2)：18～22
[52] 伏魁先，刘学信，黄华彪．斜拉桥面内整体失稳分析．铁道学报，1993，4：74～79
[53] 朱晞，陈兴冲．混凝土桥墩的非线性分析．铁道学报，1993，1：87～93
[54] 钱江等．带有单边约束斜拉桥非线性问题的参数二次规划法分析．土木工程学报，26(2)：39～47
[55] Yeong-Bin Yang and William McGuire. Stiffness Matrix For Geometic Nonlinear Analysis. Journal of Structural Engineering, ASCE, 1986, 112 (4): 853～905
[56] M. Como, A. Grimaldi, F. Maceri. Statical Behaviour Of Long-span Cable-Stayed Bridges. International Journal Of Solids and Structures, 1985, 21 (8): 831～850
[57] Demenico BRUNO. Angelo LEONARDI, Nonlinear Analysis of Cable-Stayed Bridges Eccentrically Loaded. IABSE Proceedings, P-103/86: 129～139
[58] S. P. Seif and W. H. Dilger. Nonlinear Analysis and Collapse Load of P/C cable-Stayed Bridges. Journal of Structural Engineering, ASCE, 1990, 116 (3): 829～849
[59] M. L. Gambhir, Barrington deV. Batchelor. Finite Elements for Cable Analysis. International Journal of Structures, 1986, 6 (63): 17～34
[60] J. L. Meek, S. Loganthan. Geometric and Material Nonlinear Behavior of Beam-Columns. Computers & Structures, 1990, 34 ( 1 ): 87～100
[61] GNarayanan, G.S.Krishnamoorthy. An Investigation of Geometric nonlinear Formulations for 3D Beam Elements. International Nonlinear Mechanics, 1990, 25 (6): 643～662
[62] 叶英华，刁波．钢筋混凝土结构非线性分析中的本构关系．哈尔滨建筑工程学院学报，1995，3：7～13
[63] 王娜等．网壳结构弹塑性大位移全过程分析．土木工程学报，1993，26(2)：19～28
[64] 梁硕．平板结构主梁混凝土斜拉桥非线性分析．中国公路学报，1998，11(1)：77～83
[65] 胡成．钢筋混凝土板的非线性有限元分析和计算．合肥工业大学学报(自然科学版)，1998，21(2)：88～90
[66] 汤广来，赵坤．全量式混凝土非线性本构模型分析．安徽建筑工业学院学报(自然科学版)，1998，6(3)：37～39
[67] 王志军，刘南科．混凝土结构非线性全过程分析中的迭代控制法研究．重庆建筑大学学报，1998，20(4)：14～20
[68] 蔡松柏，沈蒲生．一种高阶非线性钢筋混凝土平板单元．1998，30(3)：371～384
[69] 叶英华，刁波．钢筋混凝土构件在压弯扭作用下的截面非线性刚度矩阵．哈尔滨建筑大学学报，1996，29(2)：20～24
[70] 郭德发等．钢筋混凝土深梁非线性有限元分析．西安交通大学学报，1997，31(6)：84～88
[71] 惠卓，秦卫红，吕志涛．非线性空间有限元在钢筋砼分析中的应用．东南大学学报，1997，27(5)：58～63
[72] 姜庆远，田春，杨振宏．钢筋混凝土三维轴对称非线性有限元分析．哈尔滨工 业大学学报，1999，31(3)：118～121
[7
[73] 刘本玉，缪升，叶燎原．钢筋混凝土非线性分析中的几个问题．云南工业大学学报，1999，15(4)：1～4
[74] 巫海昌．汪基伟等．钢筋混凝土板的三维非线性有限元分析．河海大学学报，1999，27(3)：1～4
[75] 胡文发，黄鼎业．预应力混凝土框架结构的非线性分析．山东建筑工程学院学报，1999，14(4)：5～11
[76] 刁波，叶英华．任意截面钢筋混凝土偏压构件非线性稳定性分析的简化法．北方交通大学学报，1999，23(1)：24～29
[77] W. Kanok-Nukulchai, P. W. A. Yie, D. M. Brotton. Mathematical Modelling of Cable-Stayed Bridge, International Structural Engineeing, 1992, 2:
[78] W. Kanok-Nukulchai, Guan Hong. Nonlinear Modelling of Cable-Stayed Bridges. Joournal of Steel Structure Research, 1993, 26: 249～266
[79] Wang P. H, Tseng T C, Yang C. G. Initial Shape of Cable-Stayed Bridges,
[80] 潘家英，吴亮明，高路彬．大跨度斜拉桥活载非线性研究．土木工程学报，1993，26(1)：
[81] Z. Q. Chen and T. J. A. Agar, Geometric Nonlinear Analysis of Flexible Spatial Beam Structures. Comput. &. Struct., 1993, 49 (6): 1083～1094
[82] Z. Friedman & J. B. Kosmataka. An Improved Two-Node Timoshenko Beam Finite Element. Comput. &. Struct., 1993, 47 (3): 473～481
[83] Wei-Xin Ren & Makoto Obata, Elastic-Plastic Seismic Behavior Of Long Span Cable-Stayed Bridges. Journal Of Bridge Enigineering/August, 1999
[84] Wei-Xin Ren. Ultimate Behavior Of Long Span Cable-Stayed Bridges. Journal Of Bridge Enigineering/February, 1999
[85] G. Alfano, F. Marotti de Sciarra and L. Rosati. Automatic Analysis Of Multicell Thin-Walled Sections. Comput. &. Struct., 1996, 59 (4): 641～655
[86] B. Kerman & P. Waldron. Analysis Of Continuous Box Girder Bridges Including the Effects Of Distortion. Comput. &. Struct., 1993, 47 (3): 427～440
[87] Z. P. Szewczyk & A. K. Noor, A Hybrid Neurocomputing/Numerical Strategy for Nonlinear Structural Analysis. Comput. &. Struct., 1996, 58 (4): 661～677
[88] 倪元增，钱寅泉著．弹性薄壁梁桥分析．北京：人民交通出版社，2000
[89] 张元海．一种考虑不规则支承地薄壁箱梁单元．铁道学报，1995，17(2)：112～117
[90] 王荣辉，曾庆元．薄壁箱梁空间计算的板梁单元法．铁道学报，1999，21(5)：94～98
[91] 徐艳秋，许克宾，刘凤奎．复合受力下混凝土箱梁抗扭承载力计算方法与试验研究．中国公路学报，2000，13(3)：36～40
[92] 韦成龙，曾庆元．薄壁曲线箱梁考虑翘曲、畸变和剪滞效应的空间分析．土木工程学报，2000，33(6)：81～87
[93] 程仁元．郑振飞．白塔大桥箱梁效应分析．福州大学学报(自然科学版)，2000，28．增刊：94～98
[94] 赵国恩．淇澳大桥2~#墩0~#块箱梁混凝土缺陷修补的分析及处理．广东公路交通，2000，4：37～39
[95] 韦成龙，刘小燕，曾庆元．一种剪力滞效应分析的薄壁箱梁单元．长沙交通学院学报，2000，16(2)：57～61
[96] 张启伟，张士铎．单索面斜拉桥箱梁恒载剪力滞效应分析．中国公路学报，1997，10(1)：39～42
[97] Lin, W. Y. & Hsiao, K. M. Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams. Computer Methods in Applied Mechanics and Engineering, 2001, 190 (45): 6023-6052
[98] Shen, Z. Y. & Ding, K, New theory of thin-walled beams involved the effects of shear deformation. Proceedings of the Asian Pacific Conference on Computational Mechanics, Publ by A. A. Balkema, 1991, Dec 11-13: 65-71
[99] Musat, Sorin D. & Epureanu, Bogdan I.. Study of warping torsion of thin-walled beams with closed cross-section using macro-elements. Communications in Numerical Methods in Engineering, John Wiley & Sons Ltd, 1996, 12 (12): 873-884 1069-8299
[100] Kermani, B. & Waldron, P. Analysis of continuous box girder bridges including the effects of distortion. Computers and Structures, 1993, 47 (3): 427-440
[101] Shu, Hung-Shan & Wang, Yang-Cheng. Stability analysis of box-girder cable-stayed bridges. Journal of Bridge Engineering, 2001, 6 (1): 1084-0702
[102] Luo, Q. Z. & Li, Q. S. Shear lag of thin-walled curved box girder bridges (University of Foshan). Journal of Engineering Mechanics, 2000, 126 (10): 1111-1114
[103] Luo, Q. Z. Tang, J. Li, Q. S. Negative shear lag effect in box girders with varying depth. Journal of Structural Engineering, 2001, 127 (10): 1236-1239
[104] Noor, Ahmed K. Hadian, M. Jafar Andersen, Carl M., Hybrid analytical technique for nonlinear vibration analysis of thin-walled beams, Journal of Engincering Mechanics, 1993, 119 (4): 786-800
[105] Miodrag, Sekulovic, & Pujevic, Branislav, Nonlinear analysis of reinforced concrete thin-walled beams and frames, Computers and Structures, 1989, 32 (3-4): 861-870
[106] K. Noor, Ahmed, Peters, Jeanne M. Min, Byung-Jin Mixed finite clement models for free vibrations of thin-walled beams, Finite Elements in Analysis and Design, 1989, 5 (4): 291-305
[107] 邹立华．单索面钢筋混凝土斜拉桥的非线性分析．兰州铁道学院学报(自然科学版)，2000，19(4)：63～67
[108] 辛克贵，刘钺强，杨国平．大跨度斜拉桥恒载非线性静力分析．清华大学学报(自然科学版)，2002，42(6)：818～821
[109] 钟新谷，曾庆元．箱形梁的研究．湘潭矿业学院学报，2001，19(3)：68～73
[110] 周世军．钢筋混凝土箱形梁的极限承载力分析．铁道学报，1997，19(2)：73～79
[111] 吴文清．叶见曙．杨效中等．薄壁箱梁剪力滞效应研究理论的若干问题讨论．桥梁建设，2001，6：53～57
[112] 混凝土箱梁桥的近似分析．原载美国《Journal Of Structural Engineering》(孙连祖．陶庆玲译)，1988，114(7)1644～1657
[113] 石现峰，梁志广，李建中．大跨度预应力混凝土斜拉桥的空间非线性分析．《工程力学》增刊，1999：064～068；
[114] 贺拴海，刘志文，宋一凡．斜拉桥的极限承载力分析．中国公路学报，2000，13(3)：53～57
[115] 胡隽．许克宾．斜拉桥结构非线性分析的数值方法．338～342
[116] 谢旭，黄剑源．关于大跨度钢斜拉桥极限承载力特性的研究．第十三届全国桥梁学术会议论文集．上海：同济大学出版社，1998，211～218
[117] 周念先，周世忠．特大跨径桥梁走势．中国公路，2002，7：59～62
[118] 彭卫等．箱形梁桥的空间有限元分析．工程设计CAD与智能建筑，2002，6：46～49
[119] 杨允表，朱鸿蕾．关于大跨度单索面斜拉桥抗风与抗扭分析．中国市政工程，2001年，1：30～32
[120] 张启伟，张士铎．单索面斜拉桥箱梁恒载剪力滞效应分析．中国公路学报， 1997，10(1)：39～43
[1
[121] 刘腾喜．罗松南．斜拉桥拉索锚区箱梁的空间应力分析．湖南大学学报，1996，23(4)：2～45
[122] 张士铎，张启伟．单索面斜拉桥剪力滞效应．江西科学，1996，14(1)：1～6
[123] 金增洪 编译．日本多多罗大桥简介．国外公路．1999，19(4)：8～13
[124] 安琳，丁大钧．香港青马大桥简介．桥梁建设．1997，3：22～26
[125] 华有恒．试论香港汀九斜拉桥设计构思的特色和探讨．桥梁建设，1997，3：27～33
[126] 陈秉玲．国内外大跨径桥梁发展概况．城市道桥与防洪，1997，2：33～40
[127] 本州四国连络桥建设概况．国外公路，1996，16(6)：39～41
[128] 杨允表，黄剑源．广义有限条法分析多室箱梁的剪滞效应．桥梁建设．1995，4：40～45；
[129] 梁立农，马春生．番禺大桥主跨斜拉桥设计．华南理工大学学报(自然科学版)，1999，27(6)：20～28
[130] 上官萍，房贞政，卓卫东．塔梁墩固结斜拉桥受力分析．福州大学学报(自然科学版)，1999，27(3)：19～22
[131] 曾庆元．薄壁箱形梁计算的板梁框架法．铁道学报，1981，3(2)：92～104
[132] 曾庆元．三跨连续变截面薄壁双室箱形梁计算的有限元法．长沙铁道学院学报，1981，2：34～48
[133] R. Kouhia. On Kinematical Relations Of Spatial Framed Structures. Computers & Structures, 1991, 40 (3): 1185～1191
[134] Raid Karoumi. Some Modeling Aspects In The Nonlinear Finite Element Analysis Of Cable Supported Bridges. Computers & Structures, 1999, 71: 397～412
[135] Jeppe Jonsson. Determination Of Shear Stresses, Warping Functions And Section Properties Of Thin-walled Beams Using Finite Elements. Computers & Structures, 1998, 68: 393～410
[136] D. W. Chen, F. T. K. Au, L. G. Tham, P. K. K. Lee. Determination Of Initial Cable Forces In Prestressed Concrete Cable-stayed Bridges for Given deck profiles using the force equilibrium method. Computers & Structures, 2000, 74: 1～9
[137] H. R. Ronagh, M. A. Bradford, M. M. Attard. Nonlinear analysis of thin-walled members of variable cross-section, Part Ⅰ: theory. Computers & Structures, 2000, 77: 285～299
[1
[138] H.R.Ronagh, M.A.Bradford, M.M.Attard. Nonlinear analysis of thin-walled members of variable cross-section, Part Ⅰ: Application. Computers & Structures, 2000, 77: 301～313
[139] Aleksandar Prokic. Computer program for determination of geometrical properties of thin-walled beams with open-closed section. Computers & Structures, 2000, 74: 705～715
[140] A.H.Peyrot and A.M.Goulois. Analysis of cable structures. Computers & Structures, 1979, 10: 805～813
[141] T.Y. Chang, A.F. Saleeb and W. Graf. On the mixed formulation of a 9-node Lagrange shell element. Comput. Methods Appl. Mech. Engrg. 1989, 73: 259-281
[142] A. F. Saleeb and T. Y. Chang. On the hybrid mixed formulation of C~0 curved beams. Comput. Methods Appl. Mech. Engrg, 1987, 60: 95-121
[143] A. F. Saleeb and A. S. Gendy. Shear-flexible models for spatial buckling of thin-walled curved beams. Int. J. Number. Methods Engrg, 1991, 31: 729-757
[144] 张士铎，邓小华，王文州著．箱形薄壁梁剪力滞效应．北京：人民交通出版社，1998
[145] W Kanok-Nukulchai, Guan hong. Nonlinear Modeling of Cable-Stayed Bridges. J. Structure Steel Research, 1993, 26: 249-266
[146] S. Goto. Tangent Stiffness Equation of Flexible Cable and Some Considerations, Proc. Of JSCE. No. 270. Feb. P41-49.1978;
[147] H Nakai, T. Kitada, R. Ohminami, T. Nishimura. Elasto-Plastic and Finite Displacement Analysis of Cable-Stayed Bridge. Mem. Fac. Eng. Osaka Univ. 1985, 26: 251-271
[148] 铁道部大桥工程局．单室箱形梁的扭转及截面畸变．国外桥梁．1975．(6)：
[149] Yiu PkA. Brotton DM. Computation of fabrication dimensions for cable-stayed bridges[J]. The Structure Engineer, 1988, 66(15): 237～243
[150] Levinson DA.. Kane TR. A usable solution of the hanging cable problem[J]. Computers and Structures. 1993, 46(5): 821～844
[151] Ali HM. Abdel-Ghaffar AM. Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings [J]. Computers and structures, 1995, 54(3): 461～492.
[152] O'Brien T. Francis AJ. Cable movements under two-dimensional loading [J]. Journal of Structural Engineering, 1964, 90(ST3): 89-123
[153] O'Brien T. General solution of suspended cable problems [J]. Journal of Structural Engineering, 1967, 93(ST1): 1-26
[154] Peyrot AH, Goulois AM. Analysis of cable structures [J]. Computers can Structures. 1981. 14 (3-4):
[155] Jayaraman HB, Knudson WC. A curved dement for the analysis of cable structures [J]. Computers & Structures, 1981, 14(3-4): 325～333
[156] 梁鹏，肖汝诚．斜拉索分析理论及特性研究．第十六届全国桥梁学术会议论文集．上海：同济大学出版社，2004：470～480
[157] 尼尔斯J．吉姆辛著．金增洪译．缆索支承桥梁—概念与设计．北京：人民交通出版社，2002
[158] 党发宁，荣廷玉，孙训方．有限元广义混合法及其应用．西安理工大学学报，1999，15(4)：25～30
[159] 党发宁，李宁，荣廷玉．广义混合变分原理及其有限元法．自然科学进展，2002，12(3)：250～254
[160] 党发宁，荣廷玉，孙训方．薄板有限元广义混合法及克服病态问题研究．应用力学学报，2000，17(2)：105～109
[161] 党发宁，荣廷玉，孙训方．Reissner板问题的有限元广义混合法．计算力学学报，2000，17(2)：218～222
[162] 朱伯芳．有限单元法原理与应用．北京：水利电力出版社，1979
[163] S. N. Atluri, R. H. Gallagher, Zienkiewicz. F. R. S. Hybrid and Mixed Finite Element Methods. Chichester. New York. Brisbane. Toronto. Singapore, JOHN WILEY & SONS, 1983
[164] K. Washizu. Variational methods in elasticity and plasticity. New York: Pergamon Press, Third edition,1992
[165] T. J. R. Hughes. The finite element method. New Jersey: Prentice-Hall. Inc., 1987
[166] D. R. J. Owen. E. Hinton. Finite Elemnets In Plasticity: Theory and Practice, Swansea, U. K: Pineridge Press Limited, 1980
[167] 严宗达．塑性力学．天津：天津大学出版社，1988
[2] 项海帆．高等桥梁结构理论．北京：人民交通出版社，2001，15～25
[3] 林元培．斜拉桥．北京：人民交通出版社，1997，161
[4] [美]陈惠发、A．E．萨里普 著．土木工程的材料本构方程．第一卷，第二卷，(余天庆、王勋文 译)．武汉：华中科技大学出版社，2001
[5] 李国豪．桥梁结构稳定与振动．北京：中国铁道出版社，1996
[6] 梁硕．大跨度混凝土斜拉桥局部与整体相关屈曲空间极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1999
[7] H. Sbakoarzadsh. Y. Q. Guo. J. L. Batoz. A Torsion Bending Element for Thin-Walled Beams With Open and Closed Cross Sections. Computers & Structures, 1995, 55(6): 621～635
[8] 颜全胜．大跨度钢斜拉桥极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1994
[9] 王勖成．有限单元法基本原理和数值方法．北京：清华大学出版社，1999，267～269
[10] 李存权．结构稳定和稳定内力．北京：人民交通出版社，2000
[11] 项海帆，李映．悬索桥按有限位移理论的空间非线性分析．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，913～919，926～928
[12] 朱晞，王克海．几何非线性对大跨度斜拉桥的影响．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，985～988
[13] 彭杰元，汪正兴．关于大跨度斜拉桥的非线性分析——武汉桥模型研究．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，972～978
[14] 李映，项海帆．悬索桥在侧向风载下的空间非线性分析．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，941～947
[15] 沈锐利，廖海黎．悬索桥静动力空间非线性计算有限元模型及其应用．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992，935～940
[16] 王序森等著．桥梁工程．北京：中国铁道出版社，1995，489～493
[17] China, F. Jiang, W. W. Yang. Design of the Qi Ao Bridges. Structure Engineering International, 1998, 8(2):
[18] 江峰．淇澳大桥独柱式主塔横向受力分析．武汉城市建设学院学报，2001，18(1)：20～24
[19] 周述华，陈忻等．淇澳大桥成桥及施工状态气动弹性模型风洞试验研究．
[20] 钟新谷．单拱面预应力混凝土系杆拱桥极限承载力分析：[博士学位论文]．长沙：长沙铁道学院，1997
[21] 王荣辉．板桁组合钢梁非线性分析：[博士学位论文]．长沙：长沙铁道学院，1997
[22] 肖万伸．大跨度钢斜拉桥局部与整体相关屈曲极限承载力分析．：[博士学位论文]．长沙：长沙铁道学院，1999
[23] 盛兴旺．预应力混凝土斜交箱形梁分析理论与试验研究：[博士学位论文]．长沙：中南大学，2000
[24] 梁硕等．大跨度混凝土斜拉桥极限承载力分析综述．长沙：长沙交通学院学报，1997，9：39～46；
[25] 李俊升，贺到荣，刘玉海．斜拉桥极限跨度及分析．华东公路，1999，1：7～8
[26] 张汝清、詹先义编著．非线性有限元分析．重庆：重庆大学出版社，1990年
[27] 程庆国、潘家英、高路彬等．关于大跨度斜拉桥几何非线性问题．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992：
[28] 洪显诚．刘志英．精确的斜拉索等效弹性模量公式的推导．全国桥梁结构学术大会论文集．上海：同济大学出版社，1992：
[29] 杨讯．沈志林．独塔单索面斜拉桥稳定性计算方法的探讨．铁道学报，2000，22(增刊)：4～7
[30] 张新军等．大跨度桥梁非线性空气静力和动力行为研究．桥梁建设，2001，6：4～7
[31] John F. Fleming, Nonlinear Static Analysis Of Cable-stayed Bridge Structures. Computers & Structures., 1979, 10: 621～635
[32] 龚仁明．超大跨度斜拉桥方案设计．同济大学学报，1999, 4：229～233
[33] Aly S. Nazmy & Ahmed M. Abdel-Ghaffar, Three-Dimensional Nonlinear Static Analysis Of Cable-stayed Bridges. Computers & Structures, 1990, 34.. 257～271
[34] Eric P. Kasper, Robert L. Taylor. A mixed-enhanced strain method Part Ⅰ: Geometrically linear problems. Computers & Structures, 2000, 34:237～250
[35] Eric P. Kasper, Robert L. Taylor. A mixed-enhanced strain method Part Ⅰ: Geometrically nonlinear problems. Computers & Structures, 2000, 34.. 237～250
[36] 特大跨径桥梁新设想．国外公路，2000，3：18～20
[37] 金增洪．介绍吉姆辛的未来长大桥概念．国外公路．2000年第3期．P8～14
[38] 星樊正明，宫田利雄．长大斜拉桥(中跨1000m)试设计．桥梁与基础，1990，2：5～22
[39] 潘家英等．大跨度斜拉桥活载非线性研究．土木工程学报，1993，26(1)：31～37
[40] 沈聚敏等．钢筋混凝土有限元与板壳极限分析．北京：清华大学出版社，1993
[41] 过镇海．混凝土的强度和变形——试验基础和本构关系．北京：清华大学出版社，1997
[42] 华孝良．桥梁结构非线性分析．北京：人民交通出版社，1997
[43] 匡震邦．非线性连续介质力学基础．西安：西安交通大学出版社，1989
[44] 程翔云．单索面索塔横桥向稳定分析．公路，1999，5：25～31
[45] 陈铁冰等．计入结构几何非线性影响时斜拉桥可跨度分析．同济大学学报，2000，28(4)：407～412
[46] Pao-Hsii Wang, Chiung-Guei Yang. Parametric Studies On Cable-Stayed Bridges. Computers & Structures, 1996, 60 (2): 243～260
[47] Tang Chia-Chih, Shu Hung-Shan, Wang Yang-Cheng. Stability Analysis of Steel Cable-Stayed Bridges. Structural Engineering and Mechanics, 2001, 11 (1): 35～48
[48] Shu Hung-Shan, Wang Yang-Cheng. Stability Analysis of Box-Girder Cable-Stayed Bridges. Journal of Bridge Engineering, 2001, 6 (1): 63～68
[49] Wang Yang-Cheng. Effect of Cable Stiffness on a Cable-Stayed Bridge. Structural Engineering and Mechanics, 1999, 8 (1): 27～38
[50] 叶英华，刁波．钢筋混凝土结构非线性理论综述．哈尔滨建筑工程学院学报，1995，1：127～131
[51] 苏善根等译．斜拉桥设计指南．国外公路，1993，13(2)：18～22
[52] 伏魁先，刘学信，黄华彪．斜拉桥面内整体失稳分析．铁道学报，1993，4：74～79
[53] 朱晞，陈兴冲．混凝土桥墩的非线性分析．铁道学报，1993，1：87～93
[54] 钱江等．带有单边约束斜拉桥非线性问题的参数二次规划法分析．土木工程学报，26(2)：39～47
[55] Yeong-Bin Yang and William McGuire. Stiffness Matrix For Geometic Nonlinear Analysis. Journal of Structural Engineering, ASCE, 1986, 112 (4): 853～905
[56] M. Como, A. Grimaldi, F. Maceri. Statical Behaviour Of Long-span Cable-Stayed Bridges. International Journal Of Solids and Structures, 1985, 21 (8): 831～850
[57] Demenico BRUNO. Angelo LEONARDI, Nonlinear Analysis of Cable-Stayed Bridges Eccentrically Loaded. IABSE Proceedings, P-103/86: 129～139
[58] S. P. Seif and W. H. Dilger. Nonlinear Analysis and Collapse Load of P/C cable-Stayed Bridges. Journal of Structural Engineering, ASCE, 1990, 116 (3): 829～849
[59] M. L. Gambhir, Barrington deV. Batchelor. Finite Elements for Cable Analysis. International Journal of Structures, 1986, 6 (63): 17～34
[60] J. L. Meek, S. Loganthan. Geometric and Material Nonlinear Behavior of Beam-Columns. Computers & Structures, 1990, 34 ( 1 ): 87～100
[61] GNarayanan, G.S.Krishnamoorthy. An Investigation of Geometric nonlinear Formulations for 3D Beam Elements. International Nonlinear Mechanics, 1990, 25 (6): 643～662
[62] 叶英华，刁波．钢筋混凝土结构非线性分析中的本构关系．哈尔滨建筑工程学院学报，1995，3：7～13
[63] 王娜等．网壳结构弹塑性大位移全过程分析．土木工程学报，1993，26(2)：19～28
[64] 梁硕．平板结构主梁混凝土斜拉桥非线性分析．中国公路学报，1998，11(1)：77～83
[65] 胡成．钢筋混凝土板的非线性有限元分析和计算．合肥工业大学学报(自然科学版)，1998，21(2)：88～90
[66] 汤广来，赵坤．全量式混凝土非线性本构模型分析．安徽建筑工业学院学报(自然科学版)，1998，6(3)：37～39
[67] 王志军，刘南科．混凝土结构非线性全过程分析中的迭代控制法研究．重庆建筑大学学报，1998，20(4)：14～20
[68] 蔡松柏，沈蒲生．一种高阶非线性钢筋混凝土平板单元．1998，30(3)：371～384
[69] 叶英华，刁波．钢筋混凝土构件在压弯扭作用下的截面非线性刚度矩阵．哈尔滨建筑大学学报，1996，29(2)：20～24
[70] 郭德发等．钢筋混凝土深梁非线性有限元分析．西安交通大学学报，1997，31(6)：84～88
[71] 惠卓，秦卫红，吕志涛．非线性空间有限元在钢筋砼分析中的应用．东南大学学报，1997，27(5)：58～63
[72] 姜庆远，田春，杨振宏．钢筋混凝土三维轴对称非线性有限元分析．哈尔滨工 业大学学报，1999，31(3)：118～121
[7
[73] 刘本玉，缪升，叶燎原．钢筋混凝土非线性分析中的几个问题．云南工业大学学报，1999，15(4)：1～4
[74] 巫海昌．汪基伟等．钢筋混凝土板的三维非线性有限元分析．河海大学学报，1999，27(3)：1～4
[75] 胡文发，黄鼎业．预应力混凝土框架结构的非线性分析．山东建筑工程学院学报，1999，14(4)：5～11
[76] 刁波，叶英华．任意截面钢筋混凝土偏压构件非线性稳定性分析的简化法．北方交通大学学报，1999，23(1)：24～29
[77] W. Kanok-Nukulchai, P. W. A. Yie, D. M. Brotton. Mathematical Modelling of Cable-Stayed Bridge, International Structural Engineeing, 1992, 2:
[78] W. Kanok-Nukulchai, Guan Hong. Nonlinear Modelling of Cable-Stayed Bridges. Joournal of Steel Structure Research, 1993, 26: 249～266
[79] Wang P. H, Tseng T C, Yang C. G. Initial Shape of Cable-Stayed Bridges,
[80] 潘家英，吴亮明，高路彬．大跨度斜拉桥活载非线性研究．土木工程学报，1993，26(1)：
[81] Z. Q. Chen and T. J. A. Agar, Geometric Nonlinear Analysis of Flexible Spatial Beam Structures. Comput. &. Struct., 1993, 49 (6): 1083～1094
[82] Z. Friedman & J. B. Kosmataka. An Improved Two-Node Timoshenko Beam Finite Element. Comput. &. Struct., 1993, 47 (3): 473～481
[83] Wei-Xin Ren & Makoto Obata, Elastic-Plastic Seismic Behavior Of Long Span Cable-Stayed Bridges. Journal Of Bridge Enigineering/August, 1999
[84] Wei-Xin Ren. Ultimate Behavior Of Long Span Cable-Stayed Bridges. Journal Of Bridge Enigineering/February, 1999
[85] G. Alfano, F. Marotti de Sciarra and L. Rosati. Automatic Analysis Of Multicell Thin-Walled Sections. Comput. &. Struct., 1996, 59 (4): 641～655
[86] B. Kerman & P. Waldron. Analysis Of Continuous Box Girder Bridges Including the Effects Of Distortion. Comput. &. Struct., 1993, 47 (3): 427～440
[87] Z. P. Szewczyk & A. K. Noor, A Hybrid Neurocomputing/Numerical Strategy for Nonlinear Structural Analysis. Comput. &. Struct., 1996, 58 (4): 661～677
[88] 倪元增，钱寅泉著．弹性薄壁梁桥分析．北京：人民交通出版社，2000
[89] 张元海．一种考虑不规则支承地薄壁箱梁单元．铁道学报，1995，17(2)：112～117
[90] 王荣辉，曾庆元．薄壁箱梁空间计算的板梁单元法．铁道学报，1999，21(5)：94～98
[91] 徐艳秋，许克宾，刘凤奎．复合受力下混凝土箱梁抗扭承载力计算方法与试验研究．中国公路学报，2000，13(3)：36～40
[92] 韦成龙，曾庆元．薄壁曲线箱梁考虑翘曲、畸变和剪滞效应的空间分析．土木工程学报，2000，33(6)：81～87
[93] 程仁元．郑振飞．白塔大桥箱梁效应分析．福州大学学报(自然科学版)，2000，28．增刊：94～98
[94] 赵国恩．淇澳大桥2~#墩0~#块箱梁混凝土缺陷修补的分析及处理．广东公路交通，2000，4：37～39
[95] 韦成龙，刘小燕，曾庆元．一种剪力滞效应分析的薄壁箱梁单元．长沙交通学院学报，2000，16(2)：57～61
[96] 张启伟，张士铎．单索面斜拉桥箱梁恒载剪力滞效应分析．中国公路学报，1997，10(1)：39～42
[97] Lin, W. Y. & Hsiao, K. M. Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams. Computer Methods in Applied Mechanics and Engineering, 2001, 190 (45): 6023-6052
[98] Shen, Z. Y. & Ding, K, New theory of thin-walled beams involved the effects of shear deformation. Proceedings of the Asian Pacific Conference on Computational Mechanics, Publ by A. A. Balkema, 1991, Dec 11-13: 65-71
[99] Musat, Sorin D. & Epureanu, Bogdan I.. Study of warping torsion of thin-walled beams with closed cross-section using macro-elements. Communications in Numerical Methods in Engineering, John Wiley & Sons Ltd, 1996, 12 (12): 873-884 1069-8299
[100] Kermani, B. & Waldron, P. Analysis of continuous box girder bridges including the effects of distortion. Computers and Structures, 1993, 47 (3): 427-440
[101] Shu, Hung-Shan & Wang, Yang-Cheng. Stability analysis of box-girder cable-stayed bridges. Journal of Bridge Engineering, 2001, 6 (1): 1084-0702
[102] Luo, Q. Z. & Li, Q. S. Shear lag of thin-walled curved box girder bridges (University of Foshan). Journal of Engineering Mechanics, 2000, 126 (10): 1111-1114
[103] Luo, Q. Z. Tang, J. Li, Q. S. Negative shear lag effect in box girders with varying depth. Journal of Structural Engineering, 2001, 127 (10): 1236-1239
[104] Noor, Ahmed K. Hadian, M. Jafar Andersen, Carl M., Hybrid analytical technique for nonlinear vibration analysis of thin-walled beams, Journal of Engincering Mechanics, 1993, 119 (4): 786-800
[105] Miodrag, Sekulovic, & Pujevic, Branislav, Nonlinear analysis of reinforced concrete thin-walled beams and frames, Computers and Structures, 1989, 32 (3-4): 861-870
[106] K. Noor, Ahmed, Peters, Jeanne M. Min, Byung-Jin Mixed finite clement models for free vibrations of thin-walled beams, Finite Elements in Analysis and Design, 1989, 5 (4): 291-305
[107] 邹立华．单索面钢筋混凝土斜拉桥的非线性分析．兰州铁道学院学报(自然科学版)，2000，19(4)：63～67
[108] 辛克贵，刘钺强，杨国平．大跨度斜拉桥恒载非线性静力分析．清华大学学报(自然科学版)，2002，42(6)：818～821
[109] 钟新谷，曾庆元．箱形梁的研究．湘潭矿业学院学报，2001，19(3)：68～73
[110] 周世军．钢筋混凝土箱形梁的极限承载力分析．铁道学报，1997，19(2)：73～79
[111] 吴文清．叶见曙．杨效中等．薄壁箱梁剪力滞效应研究理论的若干问题讨论．桥梁建设，2001，6：53～57
[112] 混凝土箱梁桥的近似分析．原载美国《Journal Of Structural Engineering》(孙连祖．陶庆玲译)，1988，114(7)1644～1657
[113] 石现峰，梁志广，李建中．大跨度预应力混凝土斜拉桥的空间非线性分析．《工程力学》增刊，1999：064～068；
[114] 贺拴海，刘志文，宋一凡．斜拉桥的极限承载力分析．中国公路学报，2000，13(3)：53～57
[115] 胡隽．许克宾．斜拉桥结构非线性分析的数值方法．338～342
[116] 谢旭，黄剑源．关于大跨度钢斜拉桥极限承载力特性的研究．第十三届全国桥梁学术会议论文集．上海：同济大学出版社，1998，211～218
[117] 周念先，周世忠．特大跨径桥梁走势．中国公路，2002，7：59～62
[118] 彭卫等．箱形梁桥的空间有限元分析．工程设计CAD与智能建筑，2002，6：46～49
[119] 杨允表，朱鸿蕾．关于大跨度单索面斜拉桥抗风与抗扭分析．中国市政工程，2001年，1：30～32
[120] 张启伟，张士铎．单索面斜拉桥箱梁恒载剪力滞效应分析．中国公路学报， 1997，10(1)：39～43
[1
[121] 刘腾喜．罗松南．斜拉桥拉索锚区箱梁的空间应力分析．湖南大学学报，1996，23(4)：2～45
[122] 张士铎，张启伟．单索面斜拉桥剪力滞效应．江西科学，1996，14(1)：1～6
[123] 金增洪 编译．日本多多罗大桥简介．国外公路．1999，19(4)：8～13
[124] 安琳，丁大钧．香港青马大桥简介．桥梁建设．1997，3：22～26
[125] 华有恒．试论香港汀九斜拉桥设计构思的特色和探讨．桥梁建设，1997，3：27～33
[126] 陈秉玲．国内外大跨径桥梁发展概况．城市道桥与防洪，1997，2：33～40
[127] 本州四国连络桥建设概况．国外公路，1996，16(6)：39～41
[128] 杨允表，黄剑源．广义有限条法分析多室箱梁的剪滞效应．桥梁建设．1995，4：40～45；
[129] 梁立农，马春生．番禺大桥主跨斜拉桥设计．华南理工大学学报(自然科学版)，1999，27(6)：20～28
[130] 上官萍，房贞政，卓卫东．塔梁墩固结斜拉桥受力分析．福州大学学报(自然科学版)，1999，27(3)：19～22
[131] 曾庆元．薄壁箱形梁计算的板梁框架法．铁道学报，1981，3(2)：92～104
[132] 曾庆元．三跨连续变截面薄壁双室箱形梁计算的有限元法．长沙铁道学院学报，1981，2：34～48
[133] R. Kouhia. On Kinematical Relations Of Spatial Framed Structures. Computers & Structures, 1991, 40 (3): 1185～1191
[134] Raid Karoumi. Some Modeling Aspects In The Nonlinear Finite Element Analysis Of Cable Supported Bridges. Computers & Structures, 1999, 71: 397～412
[135] Jeppe Jonsson. Determination Of Shear Stresses, Warping Functions And Section Properties Of Thin-walled Beams Using Finite Elements. Computers & Structures, 1998, 68: 393～410
[136] D. W. Chen, F. T. K. Au, L. G. Tham, P. K. K. Lee. Determination Of Initial Cable Forces In Prestressed Concrete Cable-stayed Bridges for Given deck profiles using the force equilibrium method. Computers & Structures, 2000, 74: 1～9
[137] H. R. Ronagh, M. A. Bradford, M. M. Attard. Nonlinear analysis of thin-walled members of variable cross-section, Part Ⅰ: theory. Computers & Structures, 2000, 77: 285～299
[1
[138] H.R.Ronagh, M.A.Bradford, M.M.Attard. Nonlinear analysis of thin-walled members of variable cross-section, Part Ⅰ: Application. Computers & Structures, 2000, 77: 301～313
[139] Aleksandar Prokic. Computer program for determination of geometrical properties of thin-walled beams with open-closed section. Computers & Structures, 2000, 74: 705～715
[140] A.H.Peyrot and A.M.Goulois. Analysis of cable structures. Computers & Structures, 1979, 10: 805～813
[141] T.Y. Chang, A.F. Saleeb and W. Graf. On the mixed formulation of a 9-node Lagrange shell element. Comput. Methods Appl. Mech. Engrg. 1989, 73: 259-281
[142] A. F. Saleeb and T. Y. Chang. On the hybrid mixed formulation of C~0 curved beams. Comput. Methods Appl. Mech. Engrg, 1987, 60: 95-121
[143] A. F. Saleeb and A. S. Gendy. Shear-flexible models for spatial buckling of thin-walled curved beams. Int. J. Number. Methods Engrg, 1991, 31: 729-757
[144] 张士铎，邓小华，王文州著．箱形薄壁梁剪力滞效应．北京：人民交通出版社，1998
[145] W Kanok-Nukulchai, Guan hong. Nonlinear Modeling of Cable-Stayed Bridges. J. Structure Steel Research, 1993, 26: 249-266
[146] S. Goto. Tangent Stiffness Equation of Flexible Cable and Some Considerations, Proc. Of JSCE. No. 270. Feb. P41-49.1978;
[147] H Nakai, T. Kitada, R. Ohminami, T. Nishimura. Elasto-Plastic and Finite Displacement Analysis of Cable-Stayed Bridge. Mem. Fac. Eng. Osaka Univ. 1985, 26: 251-271
[148] 铁道部大桥工程局．单室箱形梁的扭转及截面畸变．国外桥梁．1975．(6)：
[149] Yiu PkA. Brotton DM. Computation of fabrication dimensions for cable-stayed bridges[J]. The Structure Engineer, 1988, 66(15): 237～243
[150] Levinson DA.. Kane TR. A usable solution of the hanging cable problem[J]. Computers and Structures. 1993, 46(5): 821～844
[151] Ali HM. Abdel-Ghaffar AM. Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings [J]. Computers and structures, 1995, 54(3): 461～492.
[152] O'Brien T. Francis AJ. Cable movements under two-dimensional loading [J]. Journal of Structural Engineering, 1964, 90(ST3): 89-123
[153] O'Brien T. General solution of suspended cable problems [J]. Journal of Structural Engineering, 1967, 93(ST1): 1-26
[154] Peyrot AH, Goulois AM. Analysis of cable structures [J]. Computers can Structures. 1981. 14 (3-4):
[155] Jayaraman HB, Knudson WC. A curved dement for the analysis of cable structures [J]. Computers & Structures, 1981, 14(3-4): 325～333
[156] 梁鹏，肖汝诚．斜拉索分析理论及特性研究．第十六届全国桥梁学术会议论文集．上海：同济大学出版社，2004：470～480
[157] 尼尔斯J．吉姆辛著．金增洪译．缆索支承桥梁—概念与设计．北京：人民交通出版社，2002
[158] 党发宁，荣廷玉，孙训方．有限元广义混合法及其应用．西安理工大学学报，1999，15(4)：25～30
[159] 党发宁，李宁，荣廷玉．广义混合变分原理及其有限元法．自然科学进展，2002，12(3)：250～254
[160] 党发宁，荣廷玉，孙训方．薄板有限元广义混合法及克服病态问题研究．应用力学学报，2000，17(2)：105～109
[161] 党发宁，荣廷玉，孙训方．Reissner板问题的有限元广义混合法．计算力学学报，2000，17(2)：218～222
[162] 朱伯芳．有限单元法原理与应用．北京：水利电力出版社，1979
[163] S. N. Atluri, R. H. Gallagher, Zienkiewicz. F. R. S. Hybrid and Mixed Finite Element Methods. Chichester. New York. Brisbane. Toronto. Singapore, JOHN WILEY & SONS, 1983
[164] K. Washizu. Variational methods in elasticity and plasticity. New York: Pergamon Press, Third edition,1992
[165] T. J. R. Hughes. The finite element method. New Jersey: Prentice-Hall. Inc., 1987
[166] D. R. J. Owen. E. Hinton. Finite Elemnets In Plasticity: Theory and Practice, Swansea, U. K: Pineridge Press Limited, 1980
[167] 严宗达．塑性力学．天津：天津大学出版社，1988