自锚式吊拉组合桥非线性计算程序开发
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摘要
大跨度自锚式吊拉组合桥是一种由多种非线性因素耦合的受力复杂的结构体系,所以几何非线性问题相对突出,但是到目前为止,尚缺少一个简单、成熟、精确的结构分析方法来解决自锚式吊拉组合桥设计和施工中遇到的问题,而桥梁工程界迫切需要解决和精确预测结构受力和变形形态,因此有必要针对该桥型的非线性问题展开精确的研究。本文以拟建的大连跨海大桥为工程背景,围绕大跨度自锚式吊拉组合桥成桥及施工过程几何非线性而展开。主要内容如下：
(1)采用解析法计算自锚式吊拉组合桥主缆线形方面。基于分段悬链线理论,提出了一套完整的可精确考虑索鞍影响的自锚式吊拉组合桥主缆线形计算的解析方法。提出了空缆状态IP点的概念,使考虑索鞍影响的空缆线形的计算方法与成桥状态线形计算方法一致,简化了空缆线形的计算方法。推导了成桥状态主跨和边跨索力修正的计算公式；给出了有多个索鞍存在时,各个索鞍预偏量的迭代计算方法；编写了解析法程序CAB,该程序数据输入简单、直观。通过算例验证程序具有很好的收敛性,而且计算精度很高,可用于各种形式的悬索桥和吊拉组合桥主缆线形的精确计算。
(2)自锚式吊拉组合桥几何非线性有限元分析方面。详细介绍了切线刚度矩阵、节点荷载、单元荷载、单元抗力的各种处理方法。给出了用CR列式全量法进行非线性分析的方法,该方法的优点为：①在CR坐标系下能精确扣除单元刚体运动,取消了增量步内为小转动的限制；②基于全量平衡条件而不是增量平衡条件计算单元抗力,避免了误差累积；③使非线性计算结果的精度不再依赖于切线刚度矩阵的精度,省去了推导精确的切线刚度矩阵的庞大的工作量,即节省了计算时间,由保证了收敛速度和计算结果的精度。根据索的基本假定和悬链线平衡方程,推导了两节点悬链线索单元刚度矩阵及节点力的迭代格式。给出了可以完全考虑自锚式吊拉组合桥活载非线性的计算方法。编制了高精度的平面非线性有限元分析程序FBNL。通过大量经典算例验证,证明该方法具有极高的精度和效率,收敛速度较其他方法也要快很多。
(3)自锚式吊拉组合桥理想成桥状态确定方面。提出了以有限元法与解析法相结合确定自锚式吊拉组合桥理想成桥状态的综合算法。详细介绍了使用本文程序FBNL进行理想成桥状态确定的计算流程。
(4)自锚式吊拉组合桥施工过程非线性分析方面。将CR列式全量法引入多阶段、多工况的桥梁结构分析,不但精度和效率高,而且使得单元增减、约束增减、拉索张拉等因素的分析更为简便统一。建立了自锚式吊拉组合桥施工过程计算的非线性无应力状态法；给出了计入几何非线性的结构安装构形和无应力构形的计算方法。采用解析法与有限元法相结合的综合算法,编制了桥梁结构施工过程精细分析的非线性有限元程序BCNL,可用来精确模拟自锚式吊拉组合桥各个施工状态,也可用来优化自锚式吊拉组合桥的施工方案,具有很好的计算精度和计算速度。详细介绍了程序BCNL的主要特点和功能。
(5)基于解析法和非线性有限元分析的CR列式全量法,采用高精度的悬链线索单元,建立精细的几何非线性分析模型,对大连跨海大桥进行成桥状态和施工过程非线性分析。
Self-anchored cable-stayed suspension bridge is a complex structure system with various nonlinear factors coupling, so it's gepmetrically nonlinear problems are relatively outstanding. But up to now, there is no simple, mature and accurate structure analysis method for solving the problems in design and construction of self-anchored cable-stayed suspension bridge, while bridge engineering kingdom urgently need to solve and accurately predict the structure stress and deformation shape. So it is necessary to expand fine study on the nonlinear problems for self-anchored cable-stayed suspension bridge. With the engineering background of Dalian Gulf Bridge to be built, this paper focuses on the geometrically nonlinear analysis in bridge finished state and in bridge construction process of self-anchored cable-stayed suspension bridge. The work mainly covers the following aspects:
(1) About using analytic method to calculate cable lineshape of self-anchored cable-stayed suspension bridge. Based on segmental catenary theory, a set of complete analytic method for cable-shape finding is put forward, which can take saddle influence into accurate construction. IP concept for cable finish state is presented, which make the calculation method considering the saddle influence of cable finish state is uniform to the method of bridge finished state and make the calculation method for cable lineshape of cable finish state simple. The formulas for cable-force correction of main span and side span on bridge finished state are deduced. The iterative calculation method for pre-displacement of each saddle is provided with several saddles exit. Analytical method program has properties of good convergence and high calculation accuracy, which can be used in cable lineshape accureate calculation of various forms of suspension bridge and cable-stayed suspension bridge.
(2) About geometrical nonlinear analysis of self-anchored cable-stayed bridges. All kinds of solution method of tangent stiffness matrix, nodal loads, effictive nodal forces and internal forces are introduced. CR total formulation method used in nonlinear analysis is provided, the advantages of which included:①The restriction of small rotations in incremental step is removed by using CR coordinate to eliminate the rigid body motion accurately.②Internal forces are calculated based on the total equilibrium condition but not on incremental equilibrium condition, which avoid accumulative error.③Make the precision of nonlinear calculation do not depend on the precision of tangent stiffness matrix, leave out the huge workload of deducing accurate tangent stiffness matrix, which not only save calculation time but also ensure the convergence rate and the accuracy of calculation result. Based on cable basic assumption and catenary equilibrium equation, the stiffness matrix and interation scheme of nodal force for catenary cable element of two nodes. The calculation method for complete live-load nonlinearity is given. The nonlinear finite element analysis program FBNL with high accuracy is complied. Proved through a lot of classical examples, this method has extremely high accuracy and efficiency, and its convergence rate is faster than the other methods.
(3) About the determination of ideal finished dead state of self-anchored cable-stayed suspension bridge. The synthesis algorithm by combining analytic method with finite element method to determine the ideal finished dead state of self-anchored cable-stayed suspension bridge is put forward. The calculation flow determing the ideal finished dead state by using the program PBNL is described in detail.
(4) About the nonlinear analysis of construction process of self-anchored cable-stayed suspension bridge. By introducing CR total formulation into structural analysis of bridges, high precision and efficiency is achieved and analysis of some case become straightforward such as activating or deactivating element, adding or removing support and pretension or retention cable stay. The nonlinear stress-free staus method for construction calculation of self-anchored cable-stayed suspension bridge is established. The calculation methods of erection configuration and stress-free configuration involving the geometrically nonlinearity are given. Based on the synthesis algorithm combing finite element method with analytic method, the nonlinear element program BCNL for finite analysis of construction process is comiled, which can be used to accurately simulate each construction state of self-anchored cable-stayed suspension bridge and can optimize construction scheme. The program has good calculation accuracy and calculation speed. The main features and functions of program BCNL are described in detail.
(5) Based on CR formulation method and analytic method, adopting catenary cable element, a refined geometrical nonlinear model is established for nonlinear analysis of finished dead state and construction process of Dalian Gulf Bridge.
(1)采用解析法计算自锚式吊拉组合桥主缆线形方面。基于分段悬链线理论,提出了一套完整的可精确考虑索鞍影响的自锚式吊拉组合桥主缆线形计算的解析方法。提出了空缆状态IP点的概念,使考虑索鞍影响的空缆线形的计算方法与成桥状态线形计算方法一致,简化了空缆线形的计算方法。推导了成桥状态主跨和边跨索力修正的计算公式；给出了有多个索鞍存在时,各个索鞍预偏量的迭代计算方法；编写了解析法程序CAB,该程序数据输入简单、直观。通过算例验证程序具有很好的收敛性,而且计算精度很高,可用于各种形式的悬索桥和吊拉组合桥主缆线形的精确计算。
(2)自锚式吊拉组合桥几何非线性有限元分析方面。详细介绍了切线刚度矩阵、节点荷载、单元荷载、单元抗力的各种处理方法。给出了用CR列式全量法进行非线性分析的方法,该方法的优点为：①在CR坐标系下能精确扣除单元刚体运动,取消了增量步内为小转动的限制；②基于全量平衡条件而不是增量平衡条件计算单元抗力,避免了误差累积；③使非线性计算结果的精度不再依赖于切线刚度矩阵的精度,省去了推导精确的切线刚度矩阵的庞大的工作量,即节省了计算时间,由保证了收敛速度和计算结果的精度。根据索的基本假定和悬链线平衡方程,推导了两节点悬链线索单元刚度矩阵及节点力的迭代格式。给出了可以完全考虑自锚式吊拉组合桥活载非线性的计算方法。编制了高精度的平面非线性有限元分析程序FBNL。通过大量经典算例验证,证明该方法具有极高的精度和效率,收敛速度较其他方法也要快很多。
(3)自锚式吊拉组合桥理想成桥状态确定方面。提出了以有限元法与解析法相结合确定自锚式吊拉组合桥理想成桥状态的综合算法。详细介绍了使用本文程序FBNL进行理想成桥状态确定的计算流程。
(4)自锚式吊拉组合桥施工过程非线性分析方面。将CR列式全量法引入多阶段、多工况的桥梁结构分析,不但精度和效率高,而且使得单元增减、约束增减、拉索张拉等因素的分析更为简便统一。建立了自锚式吊拉组合桥施工过程计算的非线性无应力状态法；给出了计入几何非线性的结构安装构形和无应力构形的计算方法。采用解析法与有限元法相结合的综合算法,编制了桥梁结构施工过程精细分析的非线性有限元程序BCNL,可用来精确模拟自锚式吊拉组合桥各个施工状态,也可用来优化自锚式吊拉组合桥的施工方案,具有很好的计算精度和计算速度。详细介绍了程序BCNL的主要特点和功能。
(5)基于解析法和非线性有限元分析的CR列式全量法,采用高精度的悬链线索单元,建立精细的几何非线性分析模型,对大连跨海大桥进行成桥状态和施工过程非线性分析。
Self-anchored cable-stayed suspension bridge is a complex structure system with various nonlinear factors coupling, so it's gepmetrically nonlinear problems are relatively outstanding. But up to now, there is no simple, mature and accurate structure analysis method for solving the problems in design and construction of self-anchored cable-stayed suspension bridge, while bridge engineering kingdom urgently need to solve and accurately predict the structure stress and deformation shape. So it is necessary to expand fine study on the nonlinear problems for self-anchored cable-stayed suspension bridge. With the engineering background of Dalian Gulf Bridge to be built, this paper focuses on the geometrically nonlinear analysis in bridge finished state and in bridge construction process of self-anchored cable-stayed suspension bridge. The work mainly covers the following aspects:
(1) About using analytic method to calculate cable lineshape of self-anchored cable-stayed suspension bridge. Based on segmental catenary theory, a set of complete analytic method for cable-shape finding is put forward, which can take saddle influence into accurate construction. IP concept for cable finish state is presented, which make the calculation method considering the saddle influence of cable finish state is uniform to the method of bridge finished state and make the calculation method for cable lineshape of cable finish state simple. The formulas for cable-force correction of main span and side span on bridge finished state are deduced. The iterative calculation method for pre-displacement of each saddle is provided with several saddles exit. Analytical method program has properties of good convergence and high calculation accuracy, which can be used in cable lineshape accureate calculation of various forms of suspension bridge and cable-stayed suspension bridge.
(2) About geometrical nonlinear analysis of self-anchored cable-stayed bridges. All kinds of solution method of tangent stiffness matrix, nodal loads, effictive nodal forces and internal forces are introduced. CR total formulation method used in nonlinear analysis is provided, the advantages of which included:①The restriction of small rotations in incremental step is removed by using CR coordinate to eliminate the rigid body motion accurately.②Internal forces are calculated based on the total equilibrium condition but not on incremental equilibrium condition, which avoid accumulative error.③Make the precision of nonlinear calculation do not depend on the precision of tangent stiffness matrix, leave out the huge workload of deducing accurate tangent stiffness matrix, which not only save calculation time but also ensure the convergence rate and the accuracy of calculation result. Based on cable basic assumption and catenary equilibrium equation, the stiffness matrix and interation scheme of nodal force for catenary cable element of two nodes. The calculation method for complete live-load nonlinearity is given. The nonlinear finite element analysis program FBNL with high accuracy is complied. Proved through a lot of classical examples, this method has extremely high accuracy and efficiency, and its convergence rate is faster than the other methods.
(3) About the determination of ideal finished dead state of self-anchored cable-stayed suspension bridge. The synthesis algorithm by combining analytic method with finite element method to determine the ideal finished dead state of self-anchored cable-stayed suspension bridge is put forward. The calculation flow determing the ideal finished dead state by using the program PBNL is described in detail.
(4) About the nonlinear analysis of construction process of self-anchored cable-stayed suspension bridge. By introducing CR total formulation into structural analysis of bridges, high precision and efficiency is achieved and analysis of some case become straightforward such as activating or deactivating element, adding or removing support and pretension or retention cable stay. The nonlinear stress-free staus method for construction calculation of self-anchored cable-stayed suspension bridge is established. The calculation methods of erection configuration and stress-free configuration involving the geometrically nonlinearity are given. Based on the synthesis algorithm combing finite element method with analytic method, the nonlinear element program BCNL for finite analysis of construction process is comiled, which can be used to accurately simulate each construction state of self-anchored cable-stayed suspension bridge and can optimize construction scheme. The program has good calculation accuracy and calculation speed. The main features and functions of program BCNL are described in detail.
(5) Based on CR formulation method and analytic method, adopting catenary cable element, a refined geometrical nonlinear model is established for nonlinear analysis of finished dead state and construction process of Dalian Gulf Bridge.
引文
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