张拉索膜结构的理论研究及其在上海世博轴中的应用
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摘要
世博轴是上海2010年世博会园区最大的景观建筑和人流交通的主轴线,其屋盖结构采用了由张拉索膜结构与自由曲面钢网壳结构组合形成的复杂空间结构体系。其中张拉索膜结构总长度约840m,最大跨度约100m,总面积约64,000m2,为世界上的最大规模。世博轴张拉索膜结构屋盖规模巨大、体形复杂,其设计分析具有相当的难度,本文紧密结合其研究分析工作,发展了现有的张拉索膜结构分析理论,并将成果应用于世博轴张拉索膜结构。
第一章总结了膜结构的分类和发展史,系统的分析介绍了张拉索膜结构的基本理论和分析方法研究现状,明确了本文的研究内容。
第二章回顾了力密度法的基本原理,针对张拉索膜结构中的膜线单元,提出一种考虑膜面二维变形的改进非线性力密度法,可获得更准确的找形结果。提出了空间不规则多边形膜面面积的计算方法,以求得膜线的宽度。并用编制的改进非线性力密度法计算程序对世博轴张拉索膜结构进行了找形分析。
第三章提出了多坐标系力密度法,可准确的完成具有斜边界、弹性边界的张拉索膜结构找形。编制了多坐标系力密度法的计算程序,并对具有理论解的4个算例进行了计算,验证了方法的有效性。运用多坐标系力密度法处理了世博轴张拉索膜结构找形过程中阳光谷拉点处的弹性边界问题和计算模型的斜边界问题。
第四章结合世博轴张拉索膜结构的找形分析、风载分析和数据后处理分析的需求对EASY软件进行了二次开发。编制了EASY软件模型拓扑修正程序,可消除模型中重复的节点编号,避免计算模型产生拓扑混乱问题；编制了风载导入程序,能直接依据风洞试验测点数据在EASY软件中划分出风荷载等压面云图,快速、准确的将各风向风荷载施加到计算模型上；开发了EASY软件至AutoCAD软件后处理接口程序,可将EASY软件的计算结果转换为DXF文件,直观显示应力、内力分布云图、位移分布云图和包络值分布云图。
第五章系统总结了向量式有限元的基本原理,用算例验证了向量式有限元在小变形结构、大变形结构、机构问题上的准确性。介绍了向量式有限元三维杆单元的计算公式,用平板网架算例验证了其准确性。
第六章推导了向量式有限元预张力索杆单元和T单元的计算公式,通过算例验证了公式的正确性。编制了向量式有限元的计算程序,并对世博轴张拉索膜结构进行了连续倒塌研究,对结构与机构相耦合的动力倒塌过程进行了全程跟踪,发现其具有较好的抗连续倒塌性能,就倒塌过程中内力的连续变化过程得出了规律性的结论。
第七章对本文的研究内容进行了总结,指出了张拉索膜结构今后的研究方向。
The Expo Axis project is the biggest landscape building and the major walking passage of the Expo Park of the Expo 2010 Shanghai. Its roofing system is composed of tensioned cable-membrane structure and free surface steel structures. As the biggest tensioned cable-membrane structure in the world, it is about 840m long,100m wide and covers about 64,000m2. The analysis of the Expo Axis roof is a great challenge for its large scale and complex shape. This paper makes some improvement on the theory of tensioned cable-membrane structures and applies it to the design of the Expo Axis project.
Chapter 1 briefly summarizes the classifications of membrane structures and the development history of modern membrane structures in China. The theory status of tensioned cable-membrane structures is also studied systematically.
In chapter2, the theory of force density method is reviewed and an improved nonlinear force density method taking into account the effect of 2-dimensional deformation of the membrane surface is presented. The improved method gains more accurate form finding result of tensioned cable-membrane structures. The area algorithm of the irregular space polygon is proposed to calculate the width of the membrane link. The form finding analysis of the Expo Axis project is done with the program of this method.
Chapter3 presents a force density method based on multi-coordinate-system which deals with the form finding analysis of tensile structures with complex oblique boundaries and spring boundaries. The program of this method is written and four numerical examples are given to illustrate the efficiency of this method. In the form finding analysis of the Expo Axis project, this method is used to deal with the spring boundary of the Sun Valley steel structures and the oblique boundaries of sector model.
In chapter4, some secondary development of EASY software is given. The secondary development contains three programs about the form finding analysis, wind load analysis and the post processing of the results. The topology refining program eliminates the repeated node number of EASY model, avoiding the model topology mess. The wind load application program generates the wind pressure contour area for EASY based on the measuring point data of the wind tunnel experiment and makes the application of the wind load fast and accurate. The interface program exports EASY result files to AutoCAD DXF files. It gives the internal force and stress contour plots, nodal displacement contour plots and envelope value contour plots.
In chapter5, the basic theory of the Vector Form Intrinsic Finite Element Method (VFIFE) is summarized systematically. Examples are given to prove the efficiency of this method on the analysis of small deformed structures, large deformed structures and mechanisms. The space truss element of VFIFE is also studied and verified by the plane truss frame example.
In chapter6, the tensioned truss element, cable element and T element of VFIFE is proposed and verified. The progressive collapse of the tensioned cable-membrane structure of the Expo Axis project is analyzed by the self-written VFIFE program. The coupled dynamic structural and mechanical behavior is tracked. It is figured out that the structure has good performance against progressive collapse and some conclusions of the internal force time-history are also given.
The last chapter gives the summary and some future research topics.
第一章总结了膜结构的分类和发展史,系统的分析介绍了张拉索膜结构的基本理论和分析方法研究现状,明确了本文的研究内容。
第二章回顾了力密度法的基本原理,针对张拉索膜结构中的膜线单元,提出一种考虑膜面二维变形的改进非线性力密度法,可获得更准确的找形结果。提出了空间不规则多边形膜面面积的计算方法,以求得膜线的宽度。并用编制的改进非线性力密度法计算程序对世博轴张拉索膜结构进行了找形分析。
第三章提出了多坐标系力密度法,可准确的完成具有斜边界、弹性边界的张拉索膜结构找形。编制了多坐标系力密度法的计算程序,并对具有理论解的4个算例进行了计算,验证了方法的有效性。运用多坐标系力密度法处理了世博轴张拉索膜结构找形过程中阳光谷拉点处的弹性边界问题和计算模型的斜边界问题。
第四章结合世博轴张拉索膜结构的找形分析、风载分析和数据后处理分析的需求对EASY软件进行了二次开发。编制了EASY软件模型拓扑修正程序,可消除模型中重复的节点编号,避免计算模型产生拓扑混乱问题；编制了风载导入程序,能直接依据风洞试验测点数据在EASY软件中划分出风荷载等压面云图,快速、准确的将各风向风荷载施加到计算模型上；开发了EASY软件至AutoCAD软件后处理接口程序,可将EASY软件的计算结果转换为DXF文件,直观显示应力、内力分布云图、位移分布云图和包络值分布云图。
第五章系统总结了向量式有限元的基本原理,用算例验证了向量式有限元在小变形结构、大变形结构、机构问题上的准确性。介绍了向量式有限元三维杆单元的计算公式,用平板网架算例验证了其准确性。
第六章推导了向量式有限元预张力索杆单元和T单元的计算公式,通过算例验证了公式的正确性。编制了向量式有限元的计算程序,并对世博轴张拉索膜结构进行了连续倒塌研究,对结构与机构相耦合的动力倒塌过程进行了全程跟踪,发现其具有较好的抗连续倒塌性能,就倒塌过程中内力的连续变化过程得出了规律性的结论。
第七章对本文的研究内容进行了总结,指出了张拉索膜结构今后的研究方向。
The Expo Axis project is the biggest landscape building and the major walking passage of the Expo Park of the Expo 2010 Shanghai. Its roofing system is composed of tensioned cable-membrane structure and free surface steel structures. As the biggest tensioned cable-membrane structure in the world, it is about 840m long,100m wide and covers about 64,000m2. The analysis of the Expo Axis roof is a great challenge for its large scale and complex shape. This paper makes some improvement on the theory of tensioned cable-membrane structures and applies it to the design of the Expo Axis project.
Chapter 1 briefly summarizes the classifications of membrane structures and the development history of modern membrane structures in China. The theory status of tensioned cable-membrane structures is also studied systematically.
In chapter2, the theory of force density method is reviewed and an improved nonlinear force density method taking into account the effect of 2-dimensional deformation of the membrane surface is presented. The improved method gains more accurate form finding result of tensioned cable-membrane structures. The area algorithm of the irregular space polygon is proposed to calculate the width of the membrane link. The form finding analysis of the Expo Axis project is done with the program of this method.
Chapter3 presents a force density method based on multi-coordinate-system which deals with the form finding analysis of tensile structures with complex oblique boundaries and spring boundaries. The program of this method is written and four numerical examples are given to illustrate the efficiency of this method. In the form finding analysis of the Expo Axis project, this method is used to deal with the spring boundary of the Sun Valley steel structures and the oblique boundaries of sector model.
In chapter4, some secondary development of EASY software is given. The secondary development contains three programs about the form finding analysis, wind load analysis and the post processing of the results. The topology refining program eliminates the repeated node number of EASY model, avoiding the model topology mess. The wind load application program generates the wind pressure contour area for EASY based on the measuring point data of the wind tunnel experiment and makes the application of the wind load fast and accurate. The interface program exports EASY result files to AutoCAD DXF files. It gives the internal force and stress contour plots, nodal displacement contour plots and envelope value contour plots.
In chapter5, the basic theory of the Vector Form Intrinsic Finite Element Method (VFIFE) is summarized systematically. Examples are given to prove the efficiency of this method on the analysis of small deformed structures, large deformed structures and mechanisms. The space truss element of VFIFE is also studied and verified by the plane truss frame example.
In chapter6, the tensioned truss element, cable element and T element of VFIFE is proposed and verified. The progressive collapse of the tensioned cable-membrane structure of the Expo Axis project is analyzed by the self-written VFIFE program. The coupled dynamic structural and mechanical behavior is tracked. It is figured out that the structure has good performance against progressive collapse and some conclusions of the internal force time-history are also given.
The last chapter gives the summary and some future research topics.
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