刚性单层网壳结构找形与稳定研究
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摘要
世博轴阳光谷结构以其独特的造型及流畅的网格划分成为世博会建筑中的耀眼明星。对于自由曲面网壳结构的网格划分及考虑杆件失稳的稳定性能分析目前国内还没有相关研究。本文以阳光谷结构为出发点,探索刚性单层网壳结构更加合理的几何外形的找形方法,即通过对刚性结构进行找形来寻找具有较高的承载力和建筑美学价值的网壳形体,并达到两者的和谐统一。通过对单层柱面网壳、单层球面网壳、单层自由曲面网壳进行找形研究,分析找形方法的优势；同时对在网壳结构整体稳定中如何考虑杆件失稳影响的稳定分析方法进行研究；最后对考虑弯矩作用的梭形格构柱的稳定性能的进行系统研究。
第一章回顾了网壳结构的发展历史、分类和发展方向,系统阐述了找形分析和稳定分析的基本理论和分析方法的研究现状,介绍了本文的研究背景,明确了本文的研究内容。
第二章对单层柱面网壳进行找形研究,提出了基于力密度法的找形方法。通过在找形过程中引入自重,解决了高斯曲率为零、杆件内力为压力的单层圆柱面网壳的找形问题。将传统柱面网壳和找形网壳的静力性能和稳定承载力进行比较,分析找形的效果。最后提出一种单层抛物面网壳,可供设计人员在实际设计中方便采用。
第三章对单层球面网壳进行找形研究,解决了高斯曲率为正、杆件内力为压力的单层球面网壳的找形问题。找形得到的网壳曲面外形与球面非常接近,但网格划分均匀,建筑外形美观,稳定承载力随矢跨比的增大也有不同程度的提高。针对找形网壳杆件类型复杂的问题,提出了基于作图方法的找形网壳优化方法,在提高网壳承载力的同时减少杆件类型,方便实际生产和安装。
第四章对自由曲面网壳的设计思路进行探索,提出自由曲面网壳设计的思路：首先应用力密度法对自由曲面进行找形分析,寻找既满足建筑美观要求又符合结构受力合理的曲面形式；针对找形得到的曲面由离散点构成的问题,通过逆向建模分析的获取点云、NURBS曲线构建、NURBS曲面构建三个步骤得到连续光滑自由曲面；针对常规的自动网格划分方式既不能达到美观的要求又不能体现力的传递的问题,提出通过先人为控制后区域细化的方式对光滑自由曲面初步划分网格,然后对初步划分网格进行力密度法优化处理,以得到流畅美观的网格。并以世博轴1号阳光谷为例,按照上述设计思路对阳光谷自由曲面的找形及网格划分做了详细的研究。最后对经曲面找形和网格优化的找形阳光谷与实际阳光谷进行静力性能和稳定性能的分析比较。
第五章系统分析了杆件失稳对网壳结构整体稳定性能的影响。在网壳结构稳定分析中,提出将单根杆件划分为多个单元并引入杆件初始缺陷方法来“引导”杆件失稳,并通过比较有限元计算和钢结构设计规范轴压构件的稳定承载力来确定杆件初始缺陷幅值。网壳结构整体失稳前不出现杆件失稳时,目前仅考虑节点缺陷的分析方法是适用的；但对结构整体失稳前存在杆件失稳的网壳,有必要引入杆件初始缺陷考虑杆件失稳对结构整体稳定承载力的影响。针对上述情况,提出了网壳结构稳定分析的合理计算流程。对阳光谷结构的稳定分析过程详细地描述了杆件逐步失稳的过程及其对整体稳定承载力的影响。
第六章应用非线性有限元法研究了考虑弯矩作用时梭形格构柱的稳定承载力,主要考察了初始几何缺陷的作用方向与分布形式对稳定承载力的影响。分析了梭形格构柱抗弯刚度和抗剪刚度的特点,研究如何调整参数使梭形格构柱的抗弯能力和抗剪能力达到合适的比例,从而达到最大稳定承载力的方法。提出了考虑弯矩作用梭形格构柱稳定承载力的实用计算方法,使广大设计人员能较快掌握梭形格构柱的设计和计算。
第七章对本文研究内容进行了总结,并指出单层网壳结构今后的研究方向。
The sun valleys of the Expo Axis are the eye-catcher in the Expo buildings because of their unique styles and gorgeous grid mesh. There is rare research on the grid mesh of free-form surface lattice shells and stability analysis considering member buckling in China. This thesis based on sun valley, looking for a form-finding method that will find a more rational geometry for single-layer lattice shells, in other word, through the form-finding technology a new form of lattice shell with both high load capacity and architectural aesthetics will be found. The advantages of form-finding of rigid structure is confirmed by investigation on form-finding on single-layer cylindrical lattice shells、single-layer spherical lattice shells and single-layer free-form lattice shells; a stability analysis method that considering member buckling is also studied; the stability behavior of shuttle-shape steel lattice column with bending moment is fully investigated at last.
Chapter 1 reviews the development history, classification and development orientation of lattice shells, the theory status of form-finding and stability analysis are studied systematically. It also introduces the background and research contents of this thesis.
Chapter 2 aimed at investigating the rational form-finding problem of single-layer lattice shell structures, a form-finding method for rigid structures based on force density is proposed. The form-finding of single-layer cylindrical lattice shell with zero Gaussian curvature is realized by accounting for the self-weight of the structure during the form-finding process. Static and stability behavior of traditional cylindrical lattice shell and form-finding lattice shell are compared, and the effect of form-finding is confirmed. A new single-layer paraboloid lattice shell is proposed at last, which could be used in practical design.
Chapter 3 focuses on the rational form-finding of single-layer spherical latticed gird shell structures. The form-finding of single-layer spherical lattice shell with positive Gaussian curvature is realized by accounting for the self-weight of the structure during the form-finding process. The shape of form-finding lattice shell is very close to sphere, but with more uniform grid mesh and better aesthetical shape, the stability behavior of form-finding lattice shell is also improved compared to traditional single-layer spherical lattice shell. Aimed at solving the problem of complicated member types of form-finding lattice shell, a optimizing method based on graphing is presented, which could not only increases the load capacity, but also decreases member types at the same time.
Chapter 4 explores the design ideas of free-form lattice shells. The design process of free-form lattice shells is as follows:at first, form-finding of free-form surface is accomplished by applying force density method, aimed at looking for a surface that could not only fulfill the aesthetic requirement but also transfer loads fluently in structural view; then using the point clouds acquisition, NURBS curve construction and NURBS surface construction technologys that widely used in reverse engineering to construct a continuous surface; the normal automatic mesh method adopted in softwares is not suitable for free-form structures, a new mesh method combined with artificial control and local auto mesh is presented, another optimizing step based on force density method is taken after rough grid mesh, then a fluent and aesthetic grid mesh could be gained through these processes. The number 1 sun valley of Expo Axis is taken as an example to investigate the form-finding and grid mesh of free-form lattice shells according to the design ideas. The static and stability behavior of form-finding sun valley lattice shell and practical sun valley lattice shell will be compared at last.
Chapter 5 investigates the effect of member buckling on overall stability of lattice shells systematically. In stability analysis, a method is presented to introduce initial imperfection in members to lead members to buckling, imperfection amplitude is determined by comparison of FEM results and calculation according to steel structure design code. The analyzing method considering only node imperfection is proper if there is no member buckle before overall buckling; while for lattice shells that members buckle before overall buckling, member imperfection is more detrimental than node imperfection on stability capacity, and stability analysis without member imperfection will overestimate the load capacity of the structure. For the above, a reasonable calculation procedure for stability analysis of lattice shells is proposed. The stability analysis of sun valley describes the buckling process of members and their effect on overall stability.
Chapter 6 investigates the stability bearing capacity of shuttle-shape lattice columns considering the action of bending moment through geometrically and materially nonlinear FE method. The emphasis is on the effects of orientation and distribution pattern of initial geometric imperfections on the stability bearing capacity of shuttle-shape columns. The character of moment stiffness and shear stiffness of shuttle-shape columns is summarized. Attention is paid on how to adjust parameters to get proper proportion of moment stiffness and shear stiffness to maximize stability bearing capacity of shuttle-shape columns. A practical computing method to calculate the stability bearing capacity of shuttle-shape lattice columns considering the action of bending moment is proposed, which could be used quickly by designers.
The last chapter gives the summary and points out some future research topics of single-layer lattice shells.
第一章回顾了网壳结构的发展历史、分类和发展方向,系统阐述了找形分析和稳定分析的基本理论和分析方法的研究现状,介绍了本文的研究背景,明确了本文的研究内容。
第二章对单层柱面网壳进行找形研究,提出了基于力密度法的找形方法。通过在找形过程中引入自重,解决了高斯曲率为零、杆件内力为压力的单层圆柱面网壳的找形问题。将传统柱面网壳和找形网壳的静力性能和稳定承载力进行比较,分析找形的效果。最后提出一种单层抛物面网壳,可供设计人员在实际设计中方便采用。
第三章对单层球面网壳进行找形研究,解决了高斯曲率为正、杆件内力为压力的单层球面网壳的找形问题。找形得到的网壳曲面外形与球面非常接近,但网格划分均匀,建筑外形美观,稳定承载力随矢跨比的增大也有不同程度的提高。针对找形网壳杆件类型复杂的问题,提出了基于作图方法的找形网壳优化方法,在提高网壳承载力的同时减少杆件类型,方便实际生产和安装。
第四章对自由曲面网壳的设计思路进行探索,提出自由曲面网壳设计的思路：首先应用力密度法对自由曲面进行找形分析,寻找既满足建筑美观要求又符合结构受力合理的曲面形式；针对找形得到的曲面由离散点构成的问题,通过逆向建模分析的获取点云、NURBS曲线构建、NURBS曲面构建三个步骤得到连续光滑自由曲面；针对常规的自动网格划分方式既不能达到美观的要求又不能体现力的传递的问题,提出通过先人为控制后区域细化的方式对光滑自由曲面初步划分网格,然后对初步划分网格进行力密度法优化处理,以得到流畅美观的网格。并以世博轴1号阳光谷为例,按照上述设计思路对阳光谷自由曲面的找形及网格划分做了详细的研究。最后对经曲面找形和网格优化的找形阳光谷与实际阳光谷进行静力性能和稳定性能的分析比较。
第五章系统分析了杆件失稳对网壳结构整体稳定性能的影响。在网壳结构稳定分析中,提出将单根杆件划分为多个单元并引入杆件初始缺陷方法来“引导”杆件失稳,并通过比较有限元计算和钢结构设计规范轴压构件的稳定承载力来确定杆件初始缺陷幅值。网壳结构整体失稳前不出现杆件失稳时,目前仅考虑节点缺陷的分析方法是适用的；但对结构整体失稳前存在杆件失稳的网壳,有必要引入杆件初始缺陷考虑杆件失稳对结构整体稳定承载力的影响。针对上述情况,提出了网壳结构稳定分析的合理计算流程。对阳光谷结构的稳定分析过程详细地描述了杆件逐步失稳的过程及其对整体稳定承载力的影响。
第六章应用非线性有限元法研究了考虑弯矩作用时梭形格构柱的稳定承载力,主要考察了初始几何缺陷的作用方向与分布形式对稳定承载力的影响。分析了梭形格构柱抗弯刚度和抗剪刚度的特点,研究如何调整参数使梭形格构柱的抗弯能力和抗剪能力达到合适的比例,从而达到最大稳定承载力的方法。提出了考虑弯矩作用梭形格构柱稳定承载力的实用计算方法,使广大设计人员能较快掌握梭形格构柱的设计和计算。
第七章对本文研究内容进行了总结,并指出单层网壳结构今后的研究方向。
The sun valleys of the Expo Axis are the eye-catcher in the Expo buildings because of their unique styles and gorgeous grid mesh. There is rare research on the grid mesh of free-form surface lattice shells and stability analysis considering member buckling in China. This thesis based on sun valley, looking for a form-finding method that will find a more rational geometry for single-layer lattice shells, in other word, through the form-finding technology a new form of lattice shell with both high load capacity and architectural aesthetics will be found. The advantages of form-finding of rigid structure is confirmed by investigation on form-finding on single-layer cylindrical lattice shells、single-layer spherical lattice shells and single-layer free-form lattice shells; a stability analysis method that considering member buckling is also studied; the stability behavior of shuttle-shape steel lattice column with bending moment is fully investigated at last.
Chapter 1 reviews the development history, classification and development orientation of lattice shells, the theory status of form-finding and stability analysis are studied systematically. It also introduces the background and research contents of this thesis.
Chapter 2 aimed at investigating the rational form-finding problem of single-layer lattice shell structures, a form-finding method for rigid structures based on force density is proposed. The form-finding of single-layer cylindrical lattice shell with zero Gaussian curvature is realized by accounting for the self-weight of the structure during the form-finding process. Static and stability behavior of traditional cylindrical lattice shell and form-finding lattice shell are compared, and the effect of form-finding is confirmed. A new single-layer paraboloid lattice shell is proposed at last, which could be used in practical design.
Chapter 3 focuses on the rational form-finding of single-layer spherical latticed gird shell structures. The form-finding of single-layer spherical lattice shell with positive Gaussian curvature is realized by accounting for the self-weight of the structure during the form-finding process. The shape of form-finding lattice shell is very close to sphere, but with more uniform grid mesh and better aesthetical shape, the stability behavior of form-finding lattice shell is also improved compared to traditional single-layer spherical lattice shell. Aimed at solving the problem of complicated member types of form-finding lattice shell, a optimizing method based on graphing is presented, which could not only increases the load capacity, but also decreases member types at the same time.
Chapter 4 explores the design ideas of free-form lattice shells. The design process of free-form lattice shells is as follows:at first, form-finding of free-form surface is accomplished by applying force density method, aimed at looking for a surface that could not only fulfill the aesthetic requirement but also transfer loads fluently in structural view; then using the point clouds acquisition, NURBS curve construction and NURBS surface construction technologys that widely used in reverse engineering to construct a continuous surface; the normal automatic mesh method adopted in softwares is not suitable for free-form structures, a new mesh method combined with artificial control and local auto mesh is presented, another optimizing step based on force density method is taken after rough grid mesh, then a fluent and aesthetic grid mesh could be gained through these processes. The number 1 sun valley of Expo Axis is taken as an example to investigate the form-finding and grid mesh of free-form lattice shells according to the design ideas. The static and stability behavior of form-finding sun valley lattice shell and practical sun valley lattice shell will be compared at last.
Chapter 5 investigates the effect of member buckling on overall stability of lattice shells systematically. In stability analysis, a method is presented to introduce initial imperfection in members to lead members to buckling, imperfection amplitude is determined by comparison of FEM results and calculation according to steel structure design code. The analyzing method considering only node imperfection is proper if there is no member buckle before overall buckling; while for lattice shells that members buckle before overall buckling, member imperfection is more detrimental than node imperfection on stability capacity, and stability analysis without member imperfection will overestimate the load capacity of the structure. For the above, a reasonable calculation procedure for stability analysis of lattice shells is proposed. The stability analysis of sun valley describes the buckling process of members and their effect on overall stability.
Chapter 6 investigates the stability bearing capacity of shuttle-shape lattice columns considering the action of bending moment through geometrically and materially nonlinear FE method. The emphasis is on the effects of orientation and distribution pattern of initial geometric imperfections on the stability bearing capacity of shuttle-shape columns. The character of moment stiffness and shear stiffness of shuttle-shape columns is summarized. Attention is paid on how to adjust parameters to get proper proportion of moment stiffness and shear stiffness to maximize stability bearing capacity of shuttle-shape columns. A practical computing method to calculate the stability bearing capacity of shuttle-shape lattice columns considering the action of bending moment is proposed, which could be used quickly by designers.
The last chapter gives the summary and points out some future research topics of single-layer lattice shells.
引文
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