【作者】 吴再新；

【导师】 贺国京；

【作者基本信息】 中南大学 ， 桥梁与隧道工程， 2007， 博士

【摘要】 大跨度组合体系箱梁具有型式新颖、造价经济、受力合理等特点，传统简化分析方法已不能适应该类桥型结构设计的要求，必须进行仿真分析研究。本文以宜万铁路线宜昌长江大桥为工程背景，对大跨度组合体系箱梁仿真分析的计算理论及其应用方法进行了深入细致的研究。首先，从约束变分原理出发，采用转动与线位移独立插值的位移模式，首次提出适用于大跨度组合体系箱梁结构分析的板段元能量变分原理，并建立相应的板段元列式。通过数值算例和模型试验，验证板段元法的精度与效率。进一步，利用板段元方法对宜昌长江大桥的静、动力特性进行深入细致的仿真分析。为改善箱形主梁横向受力特性，提出多种改进方案并进行相应的参数研究，从而揭示“刚梁柔拱”组合体系桥梁结构的受力特性。最后，分析研究了宜昌长江大桥的抗震性能。主要研究内容如下：1．提出基于平板壳元基本假定的箱梁结构计算理论。从平板壳元的基本假定出发，提出与箱梁结构变形特征相适应的应变位移关系，基于能量变分原理建立箱梁顶、底及腹板的刚度方程。为精确模拟横隔板对箱梁结构受力的影响并使横隔板元与顶、底及腹板单元位移模式协调，本文从约束变分原理出发，对横隔板单元部分线位移及角位移沿板宽方向采用独立插值的位移模式，提出一类新的横隔板单元列式方法，从而形成箱梁结构分析的板元解析法。该方法中各类单元位移模式能够保持较好的协调，精度与效率比一般平板壳元更高，且能较好模拟横隔板对箱梁结构受力特性的影响。另外，为使板元解析法与常规有限单元位移模式协调，本文建立了板元解析法与常规单元连接的约束方程，编制了相应计算程序，使板元解析法可应用于一般箱型直梁的静力分析。2．提出一类应用于箱梁组合结构体系仿真分析的板段元方法。在板元解析计算理论基础上，深入分析单元节点自由度的物理概念以及单元精度和效率提高的实质。基于约束变分原理，利用常规板壳单元节点自由度建立新的板段元位移模式。该位移模式在充分反映箱梁结构受力特征的基础上，对部分单元线位移及角位移采用独立插值函数形式，使得板段元在保持板元解析法精度及效率的基础上，提高了适应性。进一步，通过建立替代剪切应变场，使得板段元刚度矩阵在进行精确数值积分时，避免了剪切自锁和零能模式，从而形成适用于大跨度组合体系箱梁结构分析的板段元能量变分原理及相应的有限元列式。最后，编制板段元计算程序并进行数值算例及模型试验验证。板段元法具有精度及效率较高且与常规单元位移模式协调等优点，可方便地应用于大跨度组合桥梁结构体系的仿真分析。3．宜昌长江大桥静力特性仿真分析。宜昌长江大桥具有结构型式新颖、受力性能良好等特点。本文采用独立开发的板段元计算程序对该桥成桥阶段的受力状态进行了全桥仿真分析。首先，通过平面施工过程分析得到桥跨结构在成桥状态的总体受力特性。然后，以此为初始状态，对大桥在二期恒载及活载作用下的结构受力行为进行空间仿真分析。仿真分析工作主要包括箱梁腹板传力途径研究、顶底板剪力滞后效应研究、横框弯曲应力研究等。最后，针对箱梁横框应力状态较为不利的特点，提出多种可行的改进方案，对各种方案的优点与不足进行了深入细致的参数研究。揭示横隔板(横梁)的受力机理，分析横隔板对箱形主梁的影响方式和作用效果，同时对比研究横隔板(横梁)对箱梁横框弯曲正应力的影响规律。4．宜昌长江大桥的动力特性仿真分析。首先，推导了板段元的协调质量矩阵，引入里兹向量叠加法求解大型动力特性方程组的部分特征解问题，提高了求解速度，从而成功地将板段元法应用于结构的动力特性计算。然后，对宜昌长江大桥的动力特性进行深入细致的仿真分析。仿真分析工作包括脊梁模型与板段元模型的对比验证分析，二期恒载对大桥动力特性的影响分析，桩土共同作用的不同模拟方式对结构计算频率及振型顺序的影响分析等。5．宜昌长江大桥的抗震性能分析。首先，从整体上分析宜昌长江大桥的抗震受力特征。其次，根据桥址处场地土特性合成人工地震波，分析确定大桥的抗震分析参数。然后，采用反应谱和时程分析两类方法对大桥进行地震响应分析。揭示了大质量法的基本原理及实质，并将其应用于宜昌长江大桥非一致激励时程响应分析。在时程分析时根据场地土对应的地震视波速计入行波效应的影响。最后，通过不同计算方法、不同地震作用方向下大桥地震响应的比较分析，深入研究宜昌长江大桥主梁、主拱以及桥墩的抗震性能。6．刚梁柔拱组合体系桥梁结构的设计建议。通过对宜昌长江大桥深入细致的静、动力仿真分析，掌握该类刚梁柔拱组合体系桥梁的结构受力特征，进一步对结构设计提出合理建议。其主要内容包括箱梁横向弯曲应力改进方案的选择、结构动力特性的计算方法、结构抗震性能的薄弱环节等。本文工作为确保宜昌长江大桥在施工及运营阶段的安全提供了帮助，所提出的板段元方法可应用于大跨度组合体系箱梁的仿真分析，具有较好的实用价值及广阔的应用前景。更多还原

【Abstract】 Long-span composite box bridges are characterized by their innovative configuration, economical construction and favorable mechanics. As assumptions and simplifications are usually introduced in general analysis methods, for the design of this type of bridges, simulation analysis methods are inevitably needed. This thesis, with Yi-Chang Yangtze Railway Bridge (YCYRB) as an engineering background, is focused deeply on the computational theory and its application with respect to simulation analysis techniques. Firstly, based on the generalized variational method, a new plate displacement model with independent interpolation functions of linear displacement from angular rotation is presented. Accordingly, a Plate Segment Element Variational Method (PSEVM) and Plate Segment Element Method (PSEM) are established for the first time which could be applied in the simulation analysis of composite box bridges. Furthermore, a program for PSEM is developed and its efficiency and precision is verified by a numerical model and a Plexiglas’s physical model test. Secondly, by using PSEM, the static and dynamic characteristics of YCYRB are studied thoroughly. Many proposals for the improvement of transverse flexible norm stress in box girder are presented and a corresponding parameters analysis is completed. The mechanics of bridges composed by stiff girder and tender arch are investigated deeply. At last, the anti-seismic properties of YCYRB are discussed generally in this thesis. The main research work is listed as follows:1. New computation theories for box girder are presented based on the assumptions of plate element.At first, based on the presumptions of plate element, new geometrical equations are proposed in this thesis according to deformation characteristics of box girder. And stiffness matrices for web and top/bottom plate of box girder are derived on the basis of variational method. To simulate accurately the influence of diaphragms on mechanics of box girder and guarantee continuity of displacement models between elements, independent interpolation functions of angular rotation from linear displacement are established and corresponding diaphragm element formulations are developed based on generalized variational method. Thus an Analytic Method based on Plate element (AMP) for box girder is presented. Generally speaking, the precision and efficiency of AMP is better than traditional plate element because of its appropriate and compatible displacement models. Moreover, the influence of diaphragms on mechanics of box girder could be reflected more accurately than existed methods. To guarantee the continuity of displacement models between AMP and other traditional elements, some possible constraint equations are discussed in this thesis.2. A new PSEM is proposed which could be applied in the simulation analysis of composite box bridges with box girder.Firstly, Degrees Of Freedom (DOF) of AMP along with their essence are analyzed and the choice of these DOFs is made according to their significations. Furthermore, with the application of generalized variational method, a new displacement model for PSEM is built which adopts only the DOFs of traditional plate elements. The PSEM displacement model, besides the more accurate reflection of box girder’s mechanics as well as the same precision and efficiency compared to ASM, is characterized by its independent interpolation functions of angular rotation from that of linear displacement. Thus SSEM has better adaptiveness than AMP when applied in simulation analysis of box girder. Moreover, a substitute shear strain model is introduced to avoid shear lock when the exact numerical integration of stiffness matrix is performed. Thus the PSEVM is established and its corresponding PSEM is proposed. Finally the program for SSEM is developed and verified in this thesis. Such advantages as high efficiency and better precision of PSEM make its application in the simulation analysis of long span composite box bridges more convenient than AMP.3. A simulation analysis on the static characteristics of YCYRB is preformed.For the innovative configuration of YCYRB, an entire simulation model is built and analyzed based on the PSEM program developed in this paper. Firstly, a plane analysis considering the influence of construction phases is performed to achieve the primary properties of YCYRB at the time when the box-girder is closed up. Further, taking it as the initial state of spatial simulation analysis, the behavior and characteristics of YCYRB under deck load as well as live load is investigated thoroughly. These are mainly about the manner of load transmission with respect to webs of the box girder, the shear lag of top/bottom plate of box girder and the rules of transverse normal stress due to flexural deformation. Besides these, to improve the disadvantages of transverse stress state according to design project, several substitute projects are proposed and corresponding design parameters analysis are performed. Thus the mechanics of diaphragm is revealed and the behavior and effect of diaphragm influence on box girder are compared thoroughly.4. A simulation analysis on the dynamic characteristics of YCYRB is preformed.At fist, the mass matrix for SSEM is derived. And to achieve quickly partial eigenvalues from large-scale characteristic dynamical equations, Ritz-Vector Superposition Method is introduced, thus the application of PSEM in the dynamic properties analysis of composite box bridges is. practical. And then the dynamic characteristics analysis of YCYRB is preformed in this paper. These includes the comparison of results between SSEM and traditional chine-like models, the influence analysis of deck mass and different pile-soil models on dynamic properties of YCYRB.5. The anti-seismic properties of YCYRB are investigated.Firstly, the preliminary anti-seismic properties of YCYRB are discussed, an artificial earthquake wave is synthesized according to the site-soil properties of YCYRB and the choice of parameters relating to anti-seismic analysis is made. Successively, the earthquake response of YCYRB is calculated separately by response spectrum method and time-history method. When taking into account the influence of multi-excitation due to traveling-wave effect which depends on the velocity of earthquake wave near the site soil, Large Mass Method (LMM) is introduced. Thus the time history analysis of YCYRB under earthquake action is more convenient than others methods. At last, by the comparison of results from different methods as well as different directions of earthquake action, the anti-seismic properties of YCYRB’s components such as beams, arches and piers are discussed generally in this thesis.6. Some helpful advice for the design of composite box bridges with stiff girder and tender arch is made in this thesis.By the simulation analysis of YCYRB, the mechanics of this type of bridges composed by stiff girder and tender arch is revealed generally and some helpful advice for the design is made suitably. These include the choice of improvement projects for transverse bending stress, the computing methods for dynamic properties as well as the unfavorable positions of YCYRB under seismic action. The work in this thesis could be useful for the safety of YCYRB in construction and operation stages. And the proposed PSEM could be applied in the simulation analysis of long span composite box bridges. As a result, Practical merits and wide applications could be achieved in the future.更多还原