Pre-determination of prediction of yield-line pattern of slabs using Voronoi diagrams

Abstract

Abstract The article presents a new method of predicting the yield-lines of statically loaded slabs, based on roof geometry (straight skeletons) and Voronoi diagrams for a polygon. A surprising analogy was found between the layout of the plate’s yield-lines and the edge lines of the embankments created as a result of the free falling of loose material onto the plate-shaped polygon. According to the proposed method, the yield-lines have the shape not only of segment lines, but also parabolas (in 3D interpretation also hyperbolas). The method proposed here is purely geometric and can be used to pre-determine the shape of the yield-lines. It allows to predict the shape of the grid of the yield-lines for plates with various support methods, including point support. In addition, the method is relatively simple and can be implemented in the standard CAD software environment. However, the method requires knowledge of descriptive geometry in the field of roof skeletons design (straight skeletons) and roofs with restriction.