A novel progressive grid generation method for free-form grid structure design and case studies

Due to its high structural efficiency and aesthetics, free-form grid structures have been widely used in various public structures. However, it is neither a convenient nor an obvious task for engineers to create a discrete grid on a free-form surface that manifests the architect's intent. This paper presents an efficient design approach based on Coulomb's law to generate well-shaped and fluent grids for free-form grid structural design. In the method, nodes of the grid structure are considered to be interacting particles in an electric field and are added to the surface in a progressive way. The nodal position is determined by Monte Carlo simulation and the grid is generated by connecting the particles that are already in equilibrium. According to the different ways of adding particles, two variations of the method are introduced in this paper: point-based progressive method (PBPM), and curve-based progressive method (CBPM). Case studies are provided to demonstrate the effective execution of the proposed method. The results show that the proposed method can effectively avoid mapping distortion and generate grids with regular shape and fluent lines to meet the aesthetic requirements. Furthermore, the proposed method provides flexible control over the direction and size of the grid, which gives architects a more flexible choice.