虚拟层合单元在稳定型悬索桥分析中的应用
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摘要
本文用虚拟层合退化梁、板单元对稳定型悬索桥进行静动力分析。虚拟层合单元突破了传统有限元对于不同材料、构件须采用不同单元的限制,对于悬索桥的索塔、加劲梁等复杂结构,能用较少的单元进行模拟,并且仍能够仔细反映其内部各个构件的力学特征、几何尺寸、所在空间位置以及其对系统刚度、质量的贡献,实现了用微机进行悬索桥空间非线性分析。另外,虚拟层合单元保留了有限元法所具有的灵活性与程序统一性特点,可以适用于任意形状、任意内部构造、任意边界与载荷的结构系统分析,是一种非常适于复杂空间结构分析的有限元方法。
本文以墨江桥为工程背景,利用自行编制的虚拟层合单元程序,对全桥的受力特性进行分析。主要工作和成果如下：
1,回顾了中外悬索桥的发展历程,介绍了稳定型悬索桥的特点。分别阐述了悬索桥的三种设计计算理论。由于悬索桥具有强烈的几何非线性,在有限元中必须加以考虑,本文采用了Total-Lagrange增量解法。
2,介绍了虚拟层合单元相关理论。根据虚拟单元法的思想,构造了虚拟三维层合板壳单元、虚拟三维层合梁单元,借助有限元语言及FEPG系统,开发了vbeam、vshell程序,并通过经典算例验证了程序的正确性。
3,在稳定型悬索桥有限元分析中首次引入虚拟层合单元法。利用单元内部可分层分段,避免了传统有限元对于不同材料、构件须采用不同单元的限制,使得桥梁的空间结构分析变得方便可行。
4,对于求解土木工程这一类单元数多、且具有复杂空间结构的有限元分析问题,虚拟层合单元法的引入将有效地减少单元数目,提高计算效率。
5,根据墨江桥的实际情况建立稳定型悬索桥模型,在四种工况载荷作用下,利用自行编制的程序计算桥的位移、构件的内力、应力等。对计算结果进行分析总结,给出了稳定型悬索桥的受力特性。最后,为了给动力分析做准备,本文对桥梁进行了模态分析。
本文对稳定型悬索桥所做的静动力研究所得出的结论,可供稳定型悬索桥设计时参考。
In the thesis, to solve static and dynamic problem of the Stable Suspension Bridge (SSB), the computational method with virtual laminated beam and plate elements is used. Virtual laminated element breaks through the restriction of traditional finite element method that the different materials and components should adopt different elements. For the complicated structures such as the cable-tower, stiffening beam of the suspension bridge, it can perform simulation with fewer elements and still be able to closely reflect mechanical characteristics, geometric dimensions, spatials and contributions to system stiffness and quality of various components within them. Then the space nonlinearity analysis of the suspension bridge with computer can be realized. In addition, virtual laminated elements is a kind of Finite Element Method (FEM) which is suitable for the complex spatial structure analysis due to retainning the flexible and unitive features of FEM and being applied to the structured system analysis in arbitrary shape, internal structure and boundary condition.
This thesis is based on the engineering background of MoJiang Bridge.It uses the established virtual laminate elements program to analyze mechanical characters of the whole bridge. Main jobs and results are as follows:
1. This thesis reviews the development of suspension bridges home and abroad, introduces the characteristics of the SSB and expatiates the three design and calculation theories of the suspension bridge. It must be considered in FEM that the suspension bridge has the characteristics of intensive geometrical nonlinearity, so the Total-Lagrange increment solution is adopted in this thesis.
2. Related theories of virtual laminate elements are introduced. According to them,3D Virtual Laminated Plate-Shell Element and 3D Virtual Laminated Beam Element is formed. With finite element language and FEPG system, vbeam and vshell programs are developed, and those correctness are verified by the classical calculation example.
3. The virtual laminate element analysis method is introduced in FEM analysis of the SSB firstly. The characteristic that it can be layered and segmented inside the element can avoid the restrict of traditional finite element method that different materials and components should apply different elements.It also can make the spatial structure analysis of bridges become convenient and feasible.
4. Virtual laminate element method can reduce elements effectively and improve the efficiency of calculation in solving the analysis problems that are provided with many elements and complex spatial structures in civil engineering.
5. According to the actual situation of MoJiang Bridge, the model of the SSB is established. The displacement, internal forces, stresses and others of this bridge under four load cases are calculated by use of the established program. The mechanical characteristics of the SSB are shown after analysing and summarizing the results. Finally, this thesis make model analysis of the bridge preparing for dynamic analysis.
In designning, the conclusions made by the static and dynamic study of the SSB can provide reference.
本文以墨江桥为工程背景,利用自行编制的虚拟层合单元程序,对全桥的受力特性进行分析。主要工作和成果如下：
1,回顾了中外悬索桥的发展历程,介绍了稳定型悬索桥的特点。分别阐述了悬索桥的三种设计计算理论。由于悬索桥具有强烈的几何非线性,在有限元中必须加以考虑,本文采用了Total-Lagrange增量解法。
2,介绍了虚拟层合单元相关理论。根据虚拟单元法的思想,构造了虚拟三维层合板壳单元、虚拟三维层合梁单元,借助有限元语言及FEPG系统,开发了vbeam、vshell程序,并通过经典算例验证了程序的正确性。
3,在稳定型悬索桥有限元分析中首次引入虚拟层合单元法。利用单元内部可分层分段,避免了传统有限元对于不同材料、构件须采用不同单元的限制,使得桥梁的空间结构分析变得方便可行。
4,对于求解土木工程这一类单元数多、且具有复杂空间结构的有限元分析问题,虚拟层合单元法的引入将有效地减少单元数目,提高计算效率。
5,根据墨江桥的实际情况建立稳定型悬索桥模型,在四种工况载荷作用下,利用自行编制的程序计算桥的位移、构件的内力、应力等。对计算结果进行分析总结,给出了稳定型悬索桥的受力特性。最后,为了给动力分析做准备,本文对桥梁进行了模态分析。
本文对稳定型悬索桥所做的静动力研究所得出的结论,可供稳定型悬索桥设计时参考。
In the thesis, to solve static and dynamic problem of the Stable Suspension Bridge (SSB), the computational method with virtual laminated beam and plate elements is used. Virtual laminated element breaks through the restriction of traditional finite element method that the different materials and components should adopt different elements. For the complicated structures such as the cable-tower, stiffening beam of the suspension bridge, it can perform simulation with fewer elements and still be able to closely reflect mechanical characteristics, geometric dimensions, spatials and contributions to system stiffness and quality of various components within them. Then the space nonlinearity analysis of the suspension bridge with computer can be realized. In addition, virtual laminated elements is a kind of Finite Element Method (FEM) which is suitable for the complex spatial structure analysis due to retainning the flexible and unitive features of FEM and being applied to the structured system analysis in arbitrary shape, internal structure and boundary condition.
This thesis is based on the engineering background of MoJiang Bridge.It uses the established virtual laminate elements program to analyze mechanical characters of the whole bridge. Main jobs and results are as follows:
1. This thesis reviews the development of suspension bridges home and abroad, introduces the characteristics of the SSB and expatiates the three design and calculation theories of the suspension bridge. It must be considered in FEM that the suspension bridge has the characteristics of intensive geometrical nonlinearity, so the Total-Lagrange increment solution is adopted in this thesis.
2. Related theories of virtual laminate elements are introduced. According to them,3D Virtual Laminated Plate-Shell Element and 3D Virtual Laminated Beam Element is formed. With finite element language and FEPG system, vbeam and vshell programs are developed, and those correctness are verified by the classical calculation example.
3. The virtual laminate element analysis method is introduced in FEM analysis of the SSB firstly. The characteristic that it can be layered and segmented inside the element can avoid the restrict of traditional finite element method that different materials and components should apply different elements.It also can make the spatial structure analysis of bridges become convenient and feasible.
4. Virtual laminate element method can reduce elements effectively and improve the efficiency of calculation in solving the analysis problems that are provided with many elements and complex spatial structures in civil engineering.
5. According to the actual situation of MoJiang Bridge, the model of the SSB is established. The displacement, internal forces, stresses and others of this bridge under four load cases are calculated by use of the established program. The mechanical characteristics of the SSB are shown after analysing and summarizing the results. Finally, this thesis make model analysis of the bridge preparing for dynamic analysis.
In designning, the conclusions made by the static and dynamic study of the SSB can provide reference.
引文
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[3]屈本宁,刘北辰.索-梁混合有限元模式及其在索桥分析中的应用.计算结构力学及其应用.1990,7(4)：93-100
[4]屈本宁,文宏光.稳定型悬索桥的试验研究. 昆明理工大学学报,1998,23(1)：1-4
[5]屈本宁,何天淳.稳定型悬索桥与普通悬索桥固有振动比较研究.空间结构,1999,5(4)：39-46
[6]屈本宁,刘北辰.索桥在冲击荷载作用下的动态响应.昆明工学院学报,1992,17(2)：24-29
[7]屈本宁,刘北辰.悬索结构设计新构想及倒张拱钢索桥的设计计算.昆明工学院学报,1994,19(4)：83-89
[8]屈本宁,文宏光.稳定型悬索桥运输载荷通过时的非线性动态响应.昆明理工大学学报,2001,26(5)：8-13
[9]屈本宁.反张悬索桥简介.空间结构,1999,5(2)：63-64
[10]刘北辰.工程计算力学.北京：机械工业出版设,1994
[11]缪莉,稳定型悬索桥非线性有限元静动力计算[硕士学位论文],昆明,昆明理工大学,2002
[12]孙华安,稳定型悬索桥锚固系统的设计及数值模拟[硕士学位论文],昆明,昆明理工大学,2005
[13]郑玉国,基于优化理论的稳定型悬索桥有限元分析[硕士学位论文],昆明,昆明理工大学,2006
[14]黄坤,稳定型悬索桥力学控制微风方程研究[硕士学位论文],昆明,昆明理工大学,2006
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