Computational morphogenesis of free-form grid structures with Voronoi diagram

Free-form grid structures have developed increasingly with the development of computer-aided design and advanced construction technology. However, the grid generation is still a difficulty for designing free-form grid structures. The computational morphogenesis of free-form grid structures with the Voronoi diagram is proposed to solve this difficulty. Voronoi diagram is introduced to form the irregular grid of structures. Morphologies of plane and curved surface Voronoi grid structure are formulated to realize parametric modeling of the structural grid. A comprehensive structural index is proposed for evaluating free-form grid structures quantitatively from the aspects of both architectural and structural behaviors. Taking the seeds as optimization variables and the comprehensive structural index as optimization objective, the grid generation problem is transformed into an optimization problem. Numerical examples show that the proposed morphogenesis is feasible and effective for the grid generation of free-form structures. The free-form grid structures generated by the proposed method have not only appealing geometry but also good mechanical behavior. The consideration of the symmetry can accelerate the grid generation process. Different grid distributions can be realized with different supports.

Automated summary

The development of free-form grid structures has been facilitated by computer-aided design and advanced construction technology, however, grid generation remains a challenge. The use of Voronoi diagrams in computational morphogenesis helps form irregular grids for these structures, with the approach proving to be effective in generating visually appealing and structurally sound grids. The consideration of symmetry during the grid generation process can help accelerate it, while different grid distributions can be achieved by varying support conditions.