基于分形理论的空间树状结构形态创构研究

发布时间：2019-01-05 03:34

【摘要】：随着物质条件的不断丰富和生活水平的不断提高,人们对建筑的要求不再仅仅停留在安全、经济和实用层面,人们开始更多的关注建筑的美学价值。树状结构作为仿生建筑的一种,其造型优美,与自然协调统一,受力高效合理,能用较小的杆件支撑起较大的空间,在现代建筑领域有着广阔的应用前景。本文所建立的空间树状结构形态创构方法是一种综合了几何理论和数值分析的高效研究方法。几何理论的应用是指利用分形理论和B样条曲线理论进行初始树状结构的几何创建过程。本文综合考虑树状结构的自相似性和力的传递特性,应用分形理论创构出更贴近自然、符合审美的下部树状支撑,并通过编程实现对初始树状结构拓扑的操控。同时,本文考虑到实际工程中可能存在的复杂内外边界条件,利用拓展的参数化(2m-1)次周期B样条曲线函数,生成多种次数、多条曲线共同围成的闭合光滑平面边界,使上部荷载面造型丰富、灵活多变。然后,根据内外边界条件和树状支撑末级分枝的端点位置,利用Delaunay三角剖分原理对上部荷载面进行网格划分,以方便对整体结构进行有限元计算和分析。其次,对已有的初始树状结构进行数值分析,提出了空间树状结构形态创构问题的数学模型。节点位置和单元布置分别决定了结构的形状和拓扑,而结构的形状和拓扑又决定了结构的力学性能。故本文树状结构优化模型是以节点位置和单元拓扑为自变量,通过节点移动和单元增减,最终实现应变能最小的目标函数,得到受力高效合理的树状结构。其中,节点移动又分为下部自由节点移动和上部约束节点移动两方面。在此基础上,通过截面优化达到材料高效利用的目的,使该方法更具工程经济性。初始结构的几何创建是结构形态创构的第一步,初始模型的合理与否对进化过程和最终形态有着深远影响,是寻求“良好建筑结构形态”的关键步骤。本文提出的初始树状结构的几何创建方法操作简单,便于根据建筑条件进行修改,生成的建筑边界灵活多变,树状支撑造型美观,传力高效合理。应变能是结构的状态量,它是指结构在外力作用下以应力和应变的形式储存在结构内部的势能。在相同的静力荷载作用下,结构刚度越大,所产生位移越小,结构应变能也越小,此时结构内力主要以轴力为主,因此应变能这一标量能很好的体现出结构的整体刚度和荷载传递效率。本文通过多个算例论述了以应变能为目标函数的合理性,并对各个算例进行分析得到空间树状结构的形态特征和力学特征,为树状结构的设计及工程应用提供依据。
[Abstract]:With the constant enrichment of material conditions and the improvement of living standards, people's demands on architecture are no longer confined to the level of safety, economy and practice, and people begin to pay more attention to the aesthetic value of architecture. As a kind of bionic architecture, tree structure has beautiful shape, harmony with nature, high efficiency and reasonable force, and can support large space with smaller members. It has a broad application prospect in the field of modern architecture. In this paper, the spatial tree structure is an efficient method which combines geometric theory and numerical analysis. The application of geometric theory refers to the geometric creation process of initial tree structure using fractal theory and B-spline curve theory. In this paper, considering the self-similarity of tree structure and the transfer characteristic of force, the author applies fractal theory to construct the lower tree support, which is closer to nature and aesthetic, and controls the topology of initial tree structure by programming. At the same time, taking into account the complex internal and external boundary conditions that may exist in practical engineering, using the extended parameterized (2m-1) subperiodic B-spline curve function, a closed smooth plane boundary is generated, which is surrounded by multiple times and multiple curves. The upper load surface is rich in shape and flexible. Then, according to the internal and external boundary conditions and the end point position of the last branch of tree bracing, the upper load surface is meshed by using the Delaunay triangulation principle, so as to facilitate the finite element calculation and analysis of the whole structure. Secondly, the existing initial tree structure is numerically analyzed, and the mathematical model of spatial tree structure is proposed. The position of nodes and the layout of elements determine the shape and topology of the structure, and the shape and topology of the structure determine the mechanical properties of the structure. Therefore, the tree structure optimization model in this paper takes node position and unit topology as independent variables, through node movement and element increase and subtraction, the objective function of minimum strain energy is finally realized, and a tree structure with high efficiency and reasonable force is obtained. Among them, node movement is divided into two aspects: lower free node movement and upper constrained node movement. On the basis of this, the material can be used efficiently by cross-section optimization, which makes the method more economical. The geometric creation of initial structure is the first step of structural form creation. Whether the initial model is reasonable or not has a profound influence on the evolution process and the final form. It is the key step to seek "good architectural structure form". The geometric creation method of the initial tree structure presented in this paper is simple to operate and easy to modify according to the building conditions. The generated building boundary is flexible and changeable, the tree shape is beautiful, and the transfer of force is efficient and reasonable. Strain energy is the state quantity of structure. It refers to the potential energy of structure stored in the form of stress and strain under the action of external force. Under the same static load, the greater the stiffness of the structure, the smaller the displacement and the smaller the strain energy of the structure. At this time, the main internal force of the structure is axial force. Therefore, the strain energy as a scalar can well reflect the overall stiffness of the structure and load transfer efficiency. In this paper, the rationality of taking strain energy as the objective function is discussed through several examples, and the morphological and mechanical characteristics of the spatial tree structure are obtained through the analysis of each example, which provides the basis for the design and engineering application of the tree structure.
【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】：TU318

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