Research On Integrated Morphogenesis Of Free-form Surface Supported By Branching Structure

Nowadays,when the function of building use is achieved,people pay more attention to architectural aesthetics.The free-form surface supported by branching structure is combined with free-form surface and branching structure.Free-form surface has many shapes and makes people feel dynamic beauty.The bars of branching structure are regular and rhythmic.This essay will take strain energy as objective function and decrease the strain energy of the structure by moving nodes.The main contents of this paper are as follows:1.Initial structure buildInitial structure is the basis of structural optimization.The shape of initial structure determines the direction of structural optimization and also has a profound impact on the optimization results.How to create initial structure is the key of this paper.The free-form surface supported by branching structure is combined with free-form surface and branching structure.B-spline theory is used to build free-form surface and shapes of the surface are diverse.Fractal theory is used to build branching structure and the structure is self-similar.Delaunay triangulation principle is also userd to divided free-form surface.2.Optimization model establishmentOptimization model can reflect optimization algorithm.In this paper,the strain energy is taken as the optimization goal,and the z coordinate of the surface control points,the free node coordinate of the tree-like structure and the intersection coordinate of the shell and the bars are taken as the optimization variables.The controlling points of curved surface’s movement not only reduces the bending stress,membrane stress and-direction displacement of the curved surface itself,but also reduces the average bending moment of the lower tree structure.The movement of the free node of the tree structure mainly affects its mechanical properties.The movement of the free node of the tree structure can reduce the average bending moment of the lower member and the average axial force of the member slightly,but the improvement of the mechanical properties of the upper surface is limited.The movement of the intersection of shell and rod has little effect on the mechanical properties of the whole structure.3.Nodes moving strategyThere are three types of nodes in the structure: surface control points,shell bar intersection points and tree-like structure free nodes.Surface control points only move in z direction and we can adjust the shape of free-form surface by moving surface control points.The free nodes of the tree-like structure can be moved in three dimensions.The mechanical properties of the tree structure can be improved by adjusting the free nodes.The nodes which intersection of shell and bars are special,its movement is actually the sliding on the shell.In this paper,the influence of each movement of these three kinds of nodes on the mechanical properties of the whole structure is analyzed in details.Firstly,the surface control point is moved,then the free node of the tree structure is moved,and finally the intersection of shell and rod is moved.Based on the analysis,the strategy of nodes moving is put forward considering the structural shape change and mechanical properties.The mechanical properties of the structure are further optimized by combining three kinds of node movement.