大跨度索拱组合体系非线性静动力性能研究
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摘要
随着轻质、高强、低阻尼索结构的出现,索拱组合体系在土木工程中具有广泛的应用,最早应用于体育馆等建筑结构中,在桥梁工程中的应用主要是作为大跨度拱桥施工过程中的临时受力结构体系,作为永久性受力结构体系在桥梁工程中应用仍处于探索阶段。本文以桥梁工程中广泛存在的索拱组合体系为工程背景,主要进行两个方面的研究:一是以国内第一座将索拱作为永久性受力结构体系的桥梁—湘江四大桥为研究对象,从非线性有限元法的基本原理出发,考虑几何和材料双重非线性,对索拱组合桥这一新型的桥梁结构形式的力学性能进行了深入的研究;二是以在采用缆索吊装施工方法的拱桥中广泛存在的临时索拱组合体系为研究对象,利用非线性动力学的基本理论,对索的参数共振和亚谐波共振以及索拱相互激励的内共振、分叉、混沌等非线性动力学行为进行了系统和深入的研究,工作主要研究内容如下:
第一章主要对索拱组合结构体系在土木工程中的应用进行了总结,特别对在桥梁工程中的应用进行了详细的阐述,从永久性的索拱组合体系和临时性的索拱组合体系两个方面,对该结构体系的研究方法、研究现状及进展进行了综述,介绍了本文的研究目的及研究内容。
第二章介绍了当前工程界最常用的和最广泛的有限位移计算理论,并从虚功原理出发推导了全量形式下和增量形式下几何非线性有限元的一般公式,在总结众多考虑非线性影响因素的拉索计算方法的基础上,推导了适合在长大跨度桥梁中使用的拉索单元,并在大型有限元程序中ANSYS中进行了二次开发,利用建立的非线性索单元,结合大位移理论,形成了适用于索拱组合体系等长大跨度桥梁的非线性分析理论。
第三章以湘江四大桥为背景,详细介绍了索拱组合桥结构体系的受力特点,在第二章的基础上开发了可用于对索拱组合桥进行几何非线性分析的有限元程序NSGCB程序,并用经典算例验证了其可靠性,使用NSGCB程序对湘江四大桥受力性能进行了详细的分析,着重研究了斜拉索倾角、斜拉索初张力对主拱受力性能的影响,对比分析了在设计荷载作用下索拱组合桥与普通系杆拱桥受力性能的差异,同时分析了极限承载能力状态下两种拱桥体系受力性能的优劣,对几何非线性因素对索拱组合桥受力性能的影响进行了定量分析。
第四章阐述了桥梁结构极限承载能力概念,总结了目前研究桥梁结构极限承载能力问题的主要方法,从理论研究和试验研究两个方面概述了目前我国拱桥特别是钢管混凝土拱桥的极限承载能力的研究现状,给出了对索拱组合桥梁进行材料非线性分析的计算方法和计算公式。结合第三章给出的几何非线性分析的计算方法和计算公式,针对大跨度索拱组合桥梁在失稳、破坏期间表现的几何和材料非线性特征,采用高精度不分层等截面梁单元和钢管混凝土组合材料统一本构关系,通过荷载增量法,采用分级逐步加载的方式,对目前国内第一座索拱组合桥—湘江四大桥进行了在多种静力荷载作用下的极限承载能力分析,追踪整个结构在加载过程中的变形过程,直至失去承载能力。
第五章建立了缆索吊装过程中索拱组合连续体系的非线性参数振动力学分析模型,考虑了由于索的初始垂度、大位移而引起的几何非线性因素的影响,推导了索拱组合结构参数振动的非线性动力学方程,运用多尺度摄动方法,对拉索可能发生的参数共振和亚谐波共振进行了理论研究和数值分析,确定了索-拱组合结构中拉索参数共振和亚谐波共振的影响因素及发生条件。
第六章在利用索拱连接条件的基础上,建立了索拱组合体系的无穷维非线性动力学分析模型。利用多尺度摄动方法对非线性方程进行了求解,讨论了在无外激励作用情形下索拱组合体系的非内共振情况和内共振情况,同时对索拱组合体系在外激励作用下的非线性动力学行为进行了详细的分析,定性研究了索拱在分别发生主共振条件下索拱非内共振情形和索拱之间内共振情形,
第七章以湘江四大桥第一施工阶段结构为研究对象,在索拱分别发生主共振条件下,分非内共振和内共振两种情况对索拱发生内共振的模式、分叉类型及其混沌性质进行了深入的讨论和研究,得到了产生动力不稳定、分叉及混沌的频域区间及相应激励幅值区间,详细讨论了索拱结构参数对索拱非线性动力性能的影响,确定了索拱各结构参数的敏感性,提出了设计吊装系统时应重点考虑的结构动力学参数。
第八章对本文的工作进行了总结,并指出了今后在索拱组合体系研究上需要努力的方向。
Along with the appearance of lightness, flexibility and inherently low damping cables, the cable-stayed arch system are applied widely on civil engineering, the system first was applied in construction structure and so on the stadium, and it mainly is taken the temporary stress structure system in the erection stage of long span arch bridges in bridge engineering, but the application as the permanent stress structure system in the bridge engineering still is at the exploration stage, This paper take the cable-stayed system as the project background, mainly has conducted the research in two aspects: one is that the forth bridge of Xian tan in which the system is taken the temporary stress structure for the first time in china was taken as the research object, based on theory of nonlinear finite element analysis method, Considered the effects of geometric non-linearity as well as material non-linearity, The mechanics performance of the cable-stayed bridge was conducted the thorough research; the other is that the temporary cable-stayed arch system which widely exists in the erection stage of the long-span arch bridges was taken as the research object, using the non-linear dynamics theory, the parametric and sub-harmonic resonances of cables are analyzed, and the internal resonance, bifurcation as well as chaos of the cable and the arch has been thoroughly studied. The studies have more profound theoretical significances and important engineering application values. The main content in this paper is as follows:
Chapter one carries on the summary to the cable-stayed arch in civil engineering application, specially carries on the detailed outline to the cable-stayed arch in bridge engineering. From the temporary cable-stayed arch and the permanent cable-stayed arch, the chapter outlines study methods, research situation and recent advances on the system first, and introduces the aim, contents and innovations of the study in this paper.
Chapter two in detail introduces the finite displacement theory. Using the total Lagrangian formulations and the updated Lagrangian formulations, the non-linear FEM equation are derived from the virtual work principle, Based on the summary to the nonlinear cable element, the spatial catenary cable element which suits in the long-span bridge was derived. A user nonlinear cable element was defined in FEM software ANSYS using User Programmable Features. The stiffness matrix of spatial element was derived, and the shearing deformation of beam was considered. Thus the beam element has the widespread serviceability. With the help of the cable element and the beam element, the nonlinear analysis theory which suitably applies in the long-span cable-stayed arch bridge is formed through the large displacement theory.
In chapter three, based on the forth bridge of XIANGTAN, the mechanics characteristic of the cable-stayed arch bridge are introduced in detail. On the basis of chapter two, the nonlinear analysis program (NSGCB) was developed, by which the analysis can be performed to the cable-stayed arch bridge with geometrical non-linearity. Using the program, the mechanics characteristic of the cable-stayed arch bridge in detail were analyzed, the effects of the initial tension of cables and the tilt angle of cables on the mechanics characteristics of cable-stayed arch bridge are discussed with emphasis, the difference of the two kinds of arch bridges are contrasted with under designing load, and the difference of the two kinds of arch bridges are contrasted with under ultimate load. The effects of the non-linear factors on the cable-stayed arch bridge are analyzed by the quota.
Chapter four describes the concept of the ultimate bearing capacity of bridges, and outlines main study methods by which the ultimate bearing capacity of bridges was studied. The research present situation of the ultimate bearing capacity of CFST arch bridge was summarized from fundamental research and experimental study. The computational method and formula by which the cable-stayed arch bridge was analyzed was given. On the basis of above-mentioned work, considered nonlinear characteristics of concrete filled steel tube arch in both material and geometry in deformation and instability, based on the constitutive relations of combinatorial material of concrete filled steel tube and the finite element method of high accuracy beam, the ultimate bearing capacity of the cable-stayed arch bridge was analyzed under many kinds of static loads, and traced the distortion process during increasing load until losing bearing capacity.
In chapter five, we present the nonlinear mechanical model for parametric vibration problem of cable-stayed arch structure. The nonlinear equations of motion of the cable-stayed arch structure were derived, and the static sag of the cable as well as the geometric nonlinearity is considered. Appling the multi-scale perturbation method, the parametric and sub-harmonic resonances of cables were analyzed. We obtained the influence factor and the condition of the parametric and sub-harmonic resonances of cables in the cable-stayed arch structure.
In chapter six, a nonlinear dynamical modal of cable-stayed the cable-stayed arch structure is built by application of the cable-arch connecting condition. The nonlinear dynamical equation of the cable-arch connecting condition was solved by the multi-scale perturbation method. The internal resonance of the cable-stayed arch system subjected to the external excitation is investigated; the nonlinear dynamical characteristic of the cable-stayed arch system subjected to the external excitation is discussed in detail. The internal resonance and the non-internal resonance of the cable-arch were studied qualitatively with primary resonance of the cable-stayed arch structure.
In chapter seven, taking the first construction stage of the forth bridge of XIANGTAN as research object,, the internal-resonant modal, the bifurcation and chaos of the cable-stayed arch structure were thoroughly and systematically studied with the appearance of primary resonance of the cable-stayed arch structure under internal resonance and non- internal resonance respectively. The region of dynamic instability, the region of bifurcation, the region of chaos and the region of excitation amplitude are obtained, the effects of structural parameter on the nonlinear dynamic performance of the cable-stayed arch structure are analyzed in detail, and then we have determined the sensitivity of structural parameters. Based on the above work, the dynamic parameters of the cable-stayed arch structure are considered with emphasis during designing the temporary structure system in the erection stage of long span arch bridges.
Chapter eight have carried on the summary to main contents of the study in this paper, and have pointed out the diligently direction in the cable-stayed arch system.
第一章主要对索拱组合结构体系在土木工程中的应用进行了总结,特别对在桥梁工程中的应用进行了详细的阐述,从永久性的索拱组合体系和临时性的索拱组合体系两个方面,对该结构体系的研究方法、研究现状及进展进行了综述,介绍了本文的研究目的及研究内容。
第二章介绍了当前工程界最常用的和最广泛的有限位移计算理论,并从虚功原理出发推导了全量形式下和增量形式下几何非线性有限元的一般公式,在总结众多考虑非线性影响因素的拉索计算方法的基础上,推导了适合在长大跨度桥梁中使用的拉索单元,并在大型有限元程序中ANSYS中进行了二次开发,利用建立的非线性索单元,结合大位移理论,形成了适用于索拱组合体系等长大跨度桥梁的非线性分析理论。
第三章以湘江四大桥为背景,详细介绍了索拱组合桥结构体系的受力特点,在第二章的基础上开发了可用于对索拱组合桥进行几何非线性分析的有限元程序NSGCB程序,并用经典算例验证了其可靠性,使用NSGCB程序对湘江四大桥受力性能进行了详细的分析,着重研究了斜拉索倾角、斜拉索初张力对主拱受力性能的影响,对比分析了在设计荷载作用下索拱组合桥与普通系杆拱桥受力性能的差异,同时分析了极限承载能力状态下两种拱桥体系受力性能的优劣,对几何非线性因素对索拱组合桥受力性能的影响进行了定量分析。
第四章阐述了桥梁结构极限承载能力概念,总结了目前研究桥梁结构极限承载能力问题的主要方法,从理论研究和试验研究两个方面概述了目前我国拱桥特别是钢管混凝土拱桥的极限承载能力的研究现状,给出了对索拱组合桥梁进行材料非线性分析的计算方法和计算公式。结合第三章给出的几何非线性分析的计算方法和计算公式,针对大跨度索拱组合桥梁在失稳、破坏期间表现的几何和材料非线性特征,采用高精度不分层等截面梁单元和钢管混凝土组合材料统一本构关系,通过荷载增量法,采用分级逐步加载的方式,对目前国内第一座索拱组合桥—湘江四大桥进行了在多种静力荷载作用下的极限承载能力分析,追踪整个结构在加载过程中的变形过程,直至失去承载能力。
第五章建立了缆索吊装过程中索拱组合连续体系的非线性参数振动力学分析模型,考虑了由于索的初始垂度、大位移而引起的几何非线性因素的影响,推导了索拱组合结构参数振动的非线性动力学方程,运用多尺度摄动方法,对拉索可能发生的参数共振和亚谐波共振进行了理论研究和数值分析,确定了索-拱组合结构中拉索参数共振和亚谐波共振的影响因素及发生条件。
第六章在利用索拱连接条件的基础上,建立了索拱组合体系的无穷维非线性动力学分析模型。利用多尺度摄动方法对非线性方程进行了求解,讨论了在无外激励作用情形下索拱组合体系的非内共振情况和内共振情况,同时对索拱组合体系在外激励作用下的非线性动力学行为进行了详细的分析,定性研究了索拱在分别发生主共振条件下索拱非内共振情形和索拱之间内共振情形,
第七章以湘江四大桥第一施工阶段结构为研究对象,在索拱分别发生主共振条件下,分非内共振和内共振两种情况对索拱发生内共振的模式、分叉类型及其混沌性质进行了深入的讨论和研究,得到了产生动力不稳定、分叉及混沌的频域区间及相应激励幅值区间,详细讨论了索拱结构参数对索拱非线性动力性能的影响,确定了索拱各结构参数的敏感性,提出了设计吊装系统时应重点考虑的结构动力学参数。
第八章对本文的工作进行了总结,并指出了今后在索拱组合体系研究上需要努力的方向。
Along with the appearance of lightness, flexibility and inherently low damping cables, the cable-stayed arch system are applied widely on civil engineering, the system first was applied in construction structure and so on the stadium, and it mainly is taken the temporary stress structure system in the erection stage of long span arch bridges in bridge engineering, but the application as the permanent stress structure system in the bridge engineering still is at the exploration stage, This paper take the cable-stayed system as the project background, mainly has conducted the research in two aspects: one is that the forth bridge of Xian tan in which the system is taken the temporary stress structure for the first time in china was taken as the research object, based on theory of nonlinear finite element analysis method, Considered the effects of geometric non-linearity as well as material non-linearity, The mechanics performance of the cable-stayed bridge was conducted the thorough research; the other is that the temporary cable-stayed arch system which widely exists in the erection stage of the long-span arch bridges was taken as the research object, using the non-linear dynamics theory, the parametric and sub-harmonic resonances of cables are analyzed, and the internal resonance, bifurcation as well as chaos of the cable and the arch has been thoroughly studied. The studies have more profound theoretical significances and important engineering application values. The main content in this paper is as follows:
Chapter one carries on the summary to the cable-stayed arch in civil engineering application, specially carries on the detailed outline to the cable-stayed arch in bridge engineering. From the temporary cable-stayed arch and the permanent cable-stayed arch, the chapter outlines study methods, research situation and recent advances on the system first, and introduces the aim, contents and innovations of the study in this paper.
Chapter two in detail introduces the finite displacement theory. Using the total Lagrangian formulations and the updated Lagrangian formulations, the non-linear FEM equation are derived from the virtual work principle, Based on the summary to the nonlinear cable element, the spatial catenary cable element which suits in the long-span bridge was derived. A user nonlinear cable element was defined in FEM software ANSYS using User Programmable Features. The stiffness matrix of spatial element was derived, and the shearing deformation of beam was considered. Thus the beam element has the widespread serviceability. With the help of the cable element and the beam element, the nonlinear analysis theory which suitably applies in the long-span cable-stayed arch bridge is formed through the large displacement theory.
In chapter three, based on the forth bridge of XIANGTAN, the mechanics characteristic of the cable-stayed arch bridge are introduced in detail. On the basis of chapter two, the nonlinear analysis program (NSGCB) was developed, by which the analysis can be performed to the cable-stayed arch bridge with geometrical non-linearity. Using the program, the mechanics characteristic of the cable-stayed arch bridge in detail were analyzed, the effects of the initial tension of cables and the tilt angle of cables on the mechanics characteristics of cable-stayed arch bridge are discussed with emphasis, the difference of the two kinds of arch bridges are contrasted with under designing load, and the difference of the two kinds of arch bridges are contrasted with under ultimate load. The effects of the non-linear factors on the cable-stayed arch bridge are analyzed by the quota.
Chapter four describes the concept of the ultimate bearing capacity of bridges, and outlines main study methods by which the ultimate bearing capacity of bridges was studied. The research present situation of the ultimate bearing capacity of CFST arch bridge was summarized from fundamental research and experimental study. The computational method and formula by which the cable-stayed arch bridge was analyzed was given. On the basis of above-mentioned work, considered nonlinear characteristics of concrete filled steel tube arch in both material and geometry in deformation and instability, based on the constitutive relations of combinatorial material of concrete filled steel tube and the finite element method of high accuracy beam, the ultimate bearing capacity of the cable-stayed arch bridge was analyzed under many kinds of static loads, and traced the distortion process during increasing load until losing bearing capacity.
In chapter five, we present the nonlinear mechanical model for parametric vibration problem of cable-stayed arch structure. The nonlinear equations of motion of the cable-stayed arch structure were derived, and the static sag of the cable as well as the geometric nonlinearity is considered. Appling the multi-scale perturbation method, the parametric and sub-harmonic resonances of cables were analyzed. We obtained the influence factor and the condition of the parametric and sub-harmonic resonances of cables in the cable-stayed arch structure.
In chapter six, a nonlinear dynamical modal of cable-stayed the cable-stayed arch structure is built by application of the cable-arch connecting condition. The nonlinear dynamical equation of the cable-arch connecting condition was solved by the multi-scale perturbation method. The internal resonance of the cable-stayed arch system subjected to the external excitation is investigated; the nonlinear dynamical characteristic of the cable-stayed arch system subjected to the external excitation is discussed in detail. The internal resonance and the non-internal resonance of the cable-arch were studied qualitatively with primary resonance of the cable-stayed arch structure.
In chapter seven, taking the first construction stage of the forth bridge of XIANGTAN as research object,, the internal-resonant modal, the bifurcation and chaos of the cable-stayed arch structure were thoroughly and systematically studied with the appearance of primary resonance of the cable-stayed arch structure under internal resonance and non- internal resonance respectively. The region of dynamic instability, the region of bifurcation, the region of chaos and the region of excitation amplitude are obtained, the effects of structural parameter on the nonlinear dynamic performance of the cable-stayed arch structure are analyzed in detail, and then we have determined the sensitivity of structural parameters. Based on the above work, the dynamic parameters of the cable-stayed arch structure are considered with emphasis during designing the temporary structure system in the erection stage of long span arch bridges.
Chapter eight have carried on the summary to main contents of the study in this paper, and have pointed out the diligently direction in the cable-stayed arch system.
引文
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