Grid Mesh And Optimization Of Single-Layer Free-form Rigid Structure And Practical Applications

With the development of science and age, especially our appreciate level of architectural beauty continues to increase, the conventional analytic surface construction already cannot meet our aesthetic needs, but the emergence of free-form surface architecture just changes the situation which satisfies our pursuit of novelty. Among the all kinds of free-form surface structures, the grid structure have been the most widely used, because of its good applicability and maturity of the design and construction techniques. However, grid design is still the key and difficult point for this kind of architectural design. Most of the existing grid mesh and optimization method imitate from the finite element meshing technology, however, the requirement between finite element grid and practical architectural grid is different, resulting the most finite element methods can only apply for a specific project. Most practical projects are still relied on experience of the engineers, which also limits the further application of free-form surface grid structure.To solve this problem, this paper puts forward grid meshing and optimization method of single-layer free-form surface structure, on the basis of the existing methods, and the gird research results are applied to actual free-from architectural design. The main work is as follows:Firstly, the concept of single-layer free-form surface rigid structures is explained, and the existing free-form surface mesh and optimization methods are summarized. It also introduces the research purpose and significance of this thesis, and give the research content.Secondly, it briefly discusses the theory of the conception of NURBS surfaces, and researches the equal-area developing method of free-form surface. In numerous free-form surface description method, NURBS method is selected as a unified description method, besides, its calculation formula are expounded and derived. It explains the equal-area developing method of simple free-form surface, and gives the treatment of complex freeform surface.Then, the flat triangular mesh and optimization method is proposed, which arranges grid points in the plane area, gives a certain quality to every grid point, introduces the repulsion, then gets the points position based on VFIFE, finally achieves the uniform grid point in plane area. Mapping method based on equal-area developing method is proposed, so it can map the plane grid back to space surface. The polygon mesh method and grid optimization method based on force are introduced, which enrich the content of the free-form surface grid design.Fourth, it reviews and summarizes the basic flow of grid mesh and optimization method mentioned in this thesis. According to the theories and algorithms aforementioned above, a grid mesh and optimization program is developed. In addition, several complex free-form surface structures are using to test and verify the grid program, proving that it has good grid design.Finally, the contents of this paper are summarized, pointing out some future research topics of the free surface meshing and optimization.