Implementing the General Theory for Finding the Lightest Manmade Structures Using Voronoi and Delaunay

Abstract

In previous efforts, the foundation of a general theory that searches for finding lightest manmade structures using the Delaunay diagram or its dual the Voronoi diagram was set (Ezzat, 2016). That foundation rests on using a simple and computationally cheap Centroid method. The simple Centroid method is expected to play a crucial role in the more sophisticated general theory. The Centroid method was simply about classifying a cloud of points that represents specific load case/s stresses on any object. That classification keeps changing using mathematical functions until optimal structures are found. The point cloud then is classified into different smaller points' groups; each of these groups was represented by a single positional point that is related to the points' group mean. Those representational points were used to generate the Delaunay or Voronoi diagrams, which are tested structurally to prove or disprove the optimality of the classification. There was not a single optimized classification out of that process but rather a family of them. The point cloud was the input to the centroid structural optimization, and the family of the optimized centroid method is the input to our proposed implementation of the general theory (see Figure 1). The centroid method produced promising optimized structures that performed from five to ten times better than the other tested variations. The centroid method was implemented using the two structural plugins of Millipede and Karmaba, which run under the environment of the Grasshopper plugin. The optimization itself is done using the grasshopper's component of Galapagos.