基于力密度法的索膜结构与空间钢结构的整体协同分析研究

发布时间：2018-09-19 16:59

【摘要】：张拉膜结构是近几十年逐渐发展起来的一种新型的张拉整体结构,索膜空间结构以其新颖的造型、巧妙的构思、高效的结构得到日益广泛的应用。在静力荷载分析中,索膜结构与支撑结构的相互作用问题是膜结构设计的难点与关键之一,它关系到计算的结果是否准确合理、结构的强度和刚度是否可以满足建筑的安全性要求等。我国的《膜结构技术规程》中规定：“对于可能产生较大位移的支撑点,在计算中应考虑支座位移的影响,或与支撑结构一起进行整体分析”。但迄今为止,对有弹性支撑的索膜空间结构的研究都是将膜结构与弹性支撑体系分离开单独分析,在膜结构与弹性支撑结构的整体协同分析方面还是一个空白。本文从协同分析的思路出发,对索膜结构与弹性支撑结构的整体协同形态分析、静荷载分析进行了系统深入的研究。本文在找形方面,推导了力密度法的平衡方程以及T单元的平衡方程,并在此平衡方程的基础上,推导了由力密度控制的索单元力密度矩阵以及T单元力密度矩阵；通过弹性索杆单元的应力应变关系及几何关系,建立了索杆单元平衡平衡,并推导了整体坐标系下由弹性控制的索与压杆的切线刚度矩阵；建立了索膜结构找形分析的平衡方程。本文在荷载分析方面,介绍了索膜结构等效刚度矩阵以及索元与膜线单元原长的计算；进一步引用弹性T单元的概念,推导出了由弹性控制的T单元的切线刚度矩阵,并建立了引入弹性T单元后索膜结构荷载分析时整体平衡方程；提出一种有效的方法来解决膜结构荷载分析时可能出现的褶皱问题。本文引入矩阵位移法的单元矩阵组装规则,将CSR稀疏矩阵存储技术引入到整体刚度矩阵的存储运算,采用Gauss-Seidel迭代法求解平衡方程,有效的提高了运算效率。在前文理论推导的基础上,建立了索膜结构与空间钢结构的整体协同找形分析以及整体协同荷载分析的平衡方程,编制了索膜结构与空间钢结构的整体协同找形分析以及荷载分析的核心计算程序,通过一些算例分析,得出了一些有意义的结论。
[Abstract]:Tensioned membrane structure is a new type of tensioning structure developed gradually in recent decades. The cable-film space structure has been widely used for its novel shape, ingenious conception and efficient structure. In static load analysis, the interaction between cable-membrane structure and braced structure is one of the difficulties and keys in membrane structure design, which is related to whether the calculation results are accurate and reasonable. Whether the strength and stiffness of the structure can meet the safety requirements of the building, etc. The Technical Specification for membrane structures in our country stipulates that "the influence of support displacement should be taken into account in the calculation of support points which may produce large displacements, or the whole analysis should be carried out together with the bracing structure". Up to now, however, the research on elastic braced cable-membrane space structure is to separate the membrane structure from the elastic bracing system, which is still a blank in the overall cooperative analysis between the membrane structure and the elastic braced structure. Based on the idea of cooperative analysis, this paper makes a systematic and in-depth study on the overall cooperative morphology analysis and static load analysis of cable-membrane structure and elastic braced structure. In this paper, the equilibrium equation of force density method and the equilibrium equation of T element are derived. On the basis of the equation, the force density matrix of cable element and the force density matrix of T element controlled by force density are derived. Through the stress-strain relation and geometric relation of elastic cable bar element, the equilibrium of cable bar element is established, and the tangent stiffness matrix of cable and compression bar controlled by elasticity in the whole coordinate system is deduced. The equilibrium equation for shape finding analysis of cable-membrane structures is established. In the aspect of load analysis, the equivalent stiffness matrix of cable-membrane structure and the calculation of the original length of cable element and membrane element are introduced, and the tangent stiffness matrix of elastic T element is derived by referring to the concept of elastic T element. The integral equilibrium equation of cable-membrane structure load analysis with elastic T element is established, and an effective method to solve the fold problem of membrane structure load analysis is proposed. In this paper, the element matrix assembly rule of matrix displacement method is introduced, the CSR sparse matrix storage technique is introduced into the storage operation of the global stiffness matrix, and the balance equation is solved by the Gauss-Seidel iterative method, which effectively improves the operation efficiency. On the basis of the previous theoretical derivation, the equilibrium equations of the integral cooperative form-finding analysis and the overall cooperative load analysis of cable-membrane structure and spatial steel structure are established. In this paper, the core calculation programs for the integral coordinated form-finding analysis and load analysis of cable-membrane structure and spatial steel structure are developed, and some meaningful conclusions are obtained through some examples.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU399

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