Research On Branching Structures Based On Fractal Theory

Branching structures are widely used in space structures because of its reasonable stress characteristics, graceful shape. With more and more branching structures are applied in the practical project, branching structures morphosis research construction method is highly valuble in theory and application.The branching structure method mentioned in this paper is through the application of structures optimization theory to achieve the purpose of options for architectural design. Structures optimization theory is the core content of this method, including the shape optimization, topology optimization and section optimization.For different architecture intents and constraint conditions, this method provides two strategies to build structural form, fixed initial topology form and dynamic changing topology form. For each form, there is an example to test the rationality of this method and determine the morphological characteristics of the construction. For the fixed initial topology form, the topological relation is given at the start, the shape of the structure is adjusted to the stain energy sensitivity of nodes in the optimization procedure, it stops when the stain energy comes down to convergence value, then, adjust the bar section to get the final structure. This method applies to situations that the building appearance is strictly required and the topology shape is specific required. For the dynamic changing topology form, a simple initial topology structure is given, then, adjusting the shape of the structure due to the node strain energy sensitivity theory until the strain is convergent, using unit strain energy sensitivity theory and fractal theory to fractal grow specified bars, so as to change the topology structure. At last, optimizing the bar section to get the final structure. This method applies to situations that the building appearance is not strictly required and the topology shape is not specific required. The structure we get is freer, and because the structural force influence the change of the topology structure, the structure we get is more reansonable in mechanics level, the new topology provides new load path, which makes the strain energy change abruptly, thus, the strain energe can continue to fall down after shape optimization.The construction method of dendritic bionic strcutures introduced in this article considers the strain energy, when the structure is effected by dead load, as objective function. It inspects the characteristic quantity like the strain energy, the average of bending moment, the maximum axial force, the average axial force and the maximum vertical displacement etc. in the development process of the structure. The mechanics characteristic of dendritic bionic strcutures can be concluded at last, used as reference for the design and engineering application of the dendritic bionic strcutures.