Research On Morphogenesis Of Space Branching Structures Based On Fractal Theory

With the continuous improvement of material conditions and living standards, people’s requirements for the building are no longer stay in the safe, economic and practical level, people began to pay more attention to the aesthetic value of the building. As a kind of bionic architecture, the branching structure has beautiful configurations, and it is coordinated and unified with nature. It can be used to support the large space with smaller pole pieces, and it has a broad applying foreground in modern architecture.This paper established a new efficient research method for the morphogenesis of space branching structures, which is a combination of geometric theory and numerical analysis.The application of geometric theory is the process of creating the initial branching structure by using the fractal theory and B-spline theory. In this paper, considering the characteristics of self similarity and force of branching structure, the fractal theory is used to construct the below tree-like structure which is more close to nature and meet contemporary aesthetic, and the initial branching structure topology can be manipulated by programming.At the same time, this paper takes into account the possible complex internal and external boundary conditions, and it use the odd cycle parametric B-spline curve to generate a series of curves of different times, so that the superstructure will be flexible and changeable. Then superstructure is meshed by the external and internal boundary conditions and the position of the endpoint of tree-like structure’s ultimate branches using Delaunay triangulation principle in order to analyse the whole structure by the finite element method.Then, the numerical analysis of the initial branching structure is carried out, and the mathematical model of the spatial branching structure is presented. The location of the nodes and the distribution of the elements determines the shape of the structure and the topology of the structure respectively, and the shape and topology of the structure determines the mechanical properties of the structure. Therefore, morphogenesis of space branching structure based on the fractal theory was proposed, useing the node position and element topology as the independent variable. We can move the node and increase or decrease the unit to achieve the goal of minimum strain energy function, which can get the effective and reasonable branching structure. Among them, the moving node is divided into two parts: the lower free node and the upper constrained node. On the basis of this, the method is more economical by achieving the efficient use of materials through cross-section optimization.The creation of the initial structure is the first step of the morphogenesis of space branching structure. The initial model is reasonable or not has a profound influence on the evolution process and the final form, and it is a key step in searching for "good structure form”. In this paper, we have studied the geometry creation method of the initial branching structure, which is simple and easy to operate, and the initial structure is full of rhythming beauty with a flexible building boundary.Strain energy is the key indexe to evaluate the structure, which is the potential energy stored in the structure in the form of stress and strain under the action of force. Under the same static load, the larger the structural stiffness, the smaller the displacement, the smaller the structural strain energy, so the strain energy can relatively truly response stiffness of the structure. The rationality of strain energy as the objective function is discussed in this paper, and the mechanical characteristics of the spatial branching structure are obtained by the analysis of different kinds of examples, which provide the basis for the design and engineering application of the branching structure.