Research On Meshing, Optimization And Mechanical Properties Of Free-form Grid Structures

With the gradual improvement of people’s pursuit of architectural aesthetics, the increasing level of CAD and the great progress in construction techniques, the modellings of ruled surface in spatial grid structure, such as cylindrical, spherical, ellipsoid, are increasingly unable to meet the growing architectural performance requirements. The free-form grid structure, with its innovative and unique designs and powerful visual expression, is constantly applied to the mall theaters, stadiums, transportation hubs and other landmarks and is increasingly favored by architects of all ages.Since the free-form grid structure is extremely complex and varied in shape, the traditional meshing method used in the design of regular surfaces has stretched. So how to provide high-quality meshing solution quickly and efficiently for architects becomes the primary problem in the free-form structure design. At the same time, optimization based on uniformity and research based on the mechanical properties are also the key issues for the design of free-form grid structure. A preliminary study on the above problems is performed in this paper, and the corresponding results are obtained.Meshing is implemented on the surface created by architects. In the field of free-form surface modelling, NURBS is becoming mainstream design method gradually. As a powerful tool for geometry design, NURBS provides a unified mathematical expression for any surface. Through the control point, the weight factor, the node vector information and the degree, it can easily realize the shape control of surface. Firstly, this paper will introduce the basic principles of parametric design in NURBS and explain its physical meaning of the control parameters.Based on the NURBS, this paper presents an automated meshing method, self-defined element method. It takes node as the object and node in the same generation is taken as a whole to realize the advancing based on method of self-defined element. Firstly, we define grid elements based on the evolutional laws of nodes. Besides, proper elements are selected automatically according to the surface feature to generate the nodes of next generation. In this way, it could be adaptive to changes in surface size and we could assemble element in each step to establish parametric expression of grid topology. We represent the parametric distance by Riemannian metric and parametric coordinates of nodes were determined. Finally, we map the parametric grid back onto surface to form spatial grid. This study compiles meshing and visualization program based on MATLAB and proves the effectiveness and versatility of the method through numerical examples.In the design of free-form grid structure, the initial meshing schemes are often difficult to ensure the uniformity of the grid whether by the artificial way or automatic method. Therefore, further optimization is always required. In this paper, rod length variance is taken as optimization object and the program of uniformity optimization is compiled based on Rhinoceros. The program will convert the spatial grid into parametric grid and adjust the node to optimal coordinate one by one. It can realize the optimization and get uniform grid.In the current research, we tend to focus on aesthetic and visual requirements and the mechanical performance needs further study. The mechanical properties of structure determine its safety, serviceability and durability directly and the mechanical properties of free-form grid structure are also key issues of its design. Based on ANSYS, this study focuses on static performance, vibration characteristics, and stable performance of freeform grid structures. It seeks to provide a useful reference for practical engineering applications.In summary, this paper studies on meshing, optimization and mechanical properties of the freeform grid structure and seeks to provide theoretical guidance and technical support for the design of free-form grid structure.