树状结构稳定性研究

发布时间：2019-02-23 23:06

【摘要】：树状结构是由Frei Otto提出的一个结构形态学概念,同时也是建筑仿生结构中的一种特殊形式。它多级分支、三维开展,造型自然优美;且力流清晰,受力均匀合理,承载力高,支承范围广,因此在大跨空间结构中得到了越来越广泛的应用。目前国内外学者对树状结构的研究主要集中在形态创建方法,节点性能等方面,而对其稳定性研究较少。基于此,本文对树状结构的整体稳定性和构件计算长度系数进行系统研究,分析其参数影响规律,探讨构件计算长度系数的确定方法,并给出主要影响参数的取值范围建议,以及构件计算长度系数的最终取值公式,可为树状结构在工程中的设计应用及后续研究积累经验。本文工作主要包含以下几方面内容:1.树状结构整体稳定性分析。将树状结构分为有侧移和无侧移两种形式,首先在弹性范围内分析结构的失稳形式,发现与传统柱相似,有侧移结构最易发生整体倾覆,无侧移结构最易发生绕树干和一级分枝连接节点的失稳,且一般整体失稳先于构件失稳。进而考虑几何和材料非线性,对树状结构进行全过程分析,得到了有侧移结构和无侧移结构不同的失稳过程和形式,其中,有侧移结构失稳更趋于缓和,失稳位移较大,受非线性影响较小,而无侧移结构失稳较为突然,但一般稳定性较好。之后对初始缺陷、结构跨度、总高度等参数的影响规律进行了分析。2.树状结构构件计算长度确定方法。首先从理论出发,利用解析法推导了平面一级和二级树状结构构件计算长度系数的计算公式,并从而确定了构件计算长度系数的影响参数和影响机理。进而提出了等效刚度法,并以平面有侧移树状结构为例说明了其分析过程。之后分析了获取屈曲荷载系数的常用方法,提出对树状结构应采用一阶整体失稳法,并给出其具体分析流程,说明该方法关键在于获取结构整体的计算长度系数值。最后对三种方法进行对比分析,决定采用一阶整体失稳法进行后续研究。3.树状结构构件计算长度系数参数分析。对树状结构主要构件计算长度系数的影响参数进行分析,给出了各参数的取值范围建议。之后在参数建议范围内,采用一阶整体失稳法,进行了系统的参数分析,统计给出了有侧移和无侧移树状结构树干以及各级分枝计算长度系数的最终计算公式和取值范围。
[Abstract]:Tree structure is a concept of structural morphology put forward by Frei Otto, and it is also a special form of building bionic structure. It has been widely used in large span spatial structures because of its multi-level branches, three-dimensional development, natural beautiful modeling, clear force flow, uniform and reasonable force, high bearing capacity and wide support range. At present, scholars at home and abroad mainly focus on the formation of the tree structure, node performance and other aspects, but less on its stability. Based on this, this paper makes a systematic study on the whole stability of tree structure and the calculated length coefficient of the component, analyzes the influence law of its parameters, discusses the method of determining the calculated length coefficient of the component, and gives some suggestions on the value range of the main influence parameters. The formula of calculating length coefficient of component can accumulate experience for the design and application of tree structure in engineering. This paper mainly includes the following aspects: 1. Analysis of the whole stability of tree structure. The tree structure is divided into two types: lateral displacement and non-lateral displacement. Firstly, the instability of the structure is analyzed in the elastic range. It is found that, similar to the traditional column, the structure with lateral displacement is most prone to overall overturn. The instability of the joints around the trunk and the first branch is most likely to occur in the non-lateral structure, and the instability of the whole structure is prior to the instability of the component in general. Furthermore, considering geometric and material nonlinearity, the whole process analysis of tree structure is carried out, and different instability processes and forms are obtained between the structure with and without lateral displacement. The instability of the structure with lateral displacement tends to be more moderate and the displacement of instability is larger. The influence of nonlinearity is small, but the instability of the structure without lateral displacement is more sudden, but the general stability is better. After that, the influence of initial defect, span, total height and other parameters are analyzed. 2. The method of determining the calculating length of tree structure component. Based on the theory, the formulas for calculating the length coefficients of the first and second order tree structures are derived by using the analytical method, and the influence parameters and mechanism of the calculated length coefficients of the members are determined. Then the equivalent stiffness method is put forward, and the analysis process of the plane tree structure with lateral displacement is illustrated. Then the common methods for obtaining buckling load coefficients are analyzed. The first order global instability method is proposed for the tree structure and its detailed analysis flow is given. It is shown that the key of this method is to obtain the calculated length coefficient of the whole structure. Finally, the three methods are compared and analyzed, and the first order global instability method is adopted for further study. 3. The parameter analysis of the calculated length coefficient of tree structure. The influence parameters of the calculated length coefficient of the main components of tree structure are analyzed and the range of each parameter is suggested. Then, in the range of parameter suggestion, the first order global instability method is used to carry out the systematic parameter analysis, and the final formula and the range of the calculated length coefficients of the tree trunks with and without lateral movement are given.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU391

【参考文献】