Parametric study on application of Voronoi patterns in design of 2-D beams

Abstract

The trend of engineering has been towards modern innovation in designs by maintaining not only the esthetic point of view but also stability and efficiency. In this regard, in this study, one of the nature-inspired structures, Voronoi tessellation, is introduced and applied as a structural configuration in the design of beams. Thus, various models of beams built with Voronoi diagrams are considered. To this end, first, the rules and regulations which govern the structure of Voronoi tessellation will be presented. Then various stages of generating the geometry of Voronoi beams will be described in detail. Considering the logical architectural requirements, the presented models are prepared as 2D-beams with different degrees of uniformity comprising the minimum and maximum Voronoi cells, which will be designed according to guidelines. In the next step, uniform loading under different boundary conditions will be applied to all Voronoi beams, and the results including structural weight, maximum displacement, and load-bearing capacity will be presented. The results of beams designed with Voronoi structures reveal that increasing the size of minimum cell will result in the rise of the maximum displacements as well as load-to-weight ratios and considerably reduce the weight of Voronoi beams but demonstrate sufficient load-bearing capacity. It also proves that as the non-uniformity of cells increases, displacements will grow. In addition, although the weight of samples will reduce, the load-to-weight ratios of the archetypes remain almost constant. Placing more supports for these structures will lead to an improvement in all aspects of design, especially on the response of beams with large spans.