Extension of the Voronoi Diagram Algorithm to Orthotropic Space for Material Structural Design

Abstract

Nowadays, the interaction of additive technologies and methods for designing or optimizing porous structures has yielded good results. Construction with complex microarchitectures can be created using this approach. Varying the microarchitecture leads to changes in weight and mechanical properties. However, there are problems with geometry reconstruction when dealing with complex microarchitecture. One approach is to use Voronoi cells for geometry reconstruction. In this article, an extension of the Voronoi diagram algorithm to orthotropic space for material structural design is presented. The inputs for the method include porosity, ellipticity, and ellipticity direction fields. As an example, a beam with fixed end faces and center kinematic loading was used. To estimate robust results for different numbers of clusters, 50, 75, and 100 clusters are presented. The porosity for smoothed structures ranged from 21.5% up to 22.8%. The stress–strain state was determined for the resulting structures. The stiffness for the initial and smoothed structures was the same. However, in the case of 75 and 100 clusters, local stress factors appeared in the smoothed structure. The maximum von Mises stress decreased by 20% for all smoothed structures in the area of kinematic loading and increased by 20% for all smoothed structures in the area of end faces.