Stress-weighted centroidal Voronoi tessellation for structural design

The design of efficient structural members is a well-established field with a wide range of methods and techniques available to optimize the structural form. As a result, there are many versions of the problem formulation depending on the optimization objective. However, the minimization of the standard deviation of stress across the design domain has seen limited research when compared to prevalent approaches such as maximizing stiffness. The proposed technique employed the Voronoi tessellation to reposition the material volume and voids on the basis of the structural analysis output. The stress-weighted centroids of the Voronoi cells were utilized to make such iterative changes to the structure. The performance was compared against the centroidal Voronoi tessellation (CVT), also known as Lloyd's algorithm, through computational simulations on homogeneous and statically-loaded 2.5D and 3D full Mersserschimstt-Bo center dot lkow-Blohm (MBB) beams. The findings imply a statistically significant difference between the two algorithms. Additionally, there is evidence to suggest that, with weights inversely proportional to the stresses, reductions can be made to the standard deviation of stress, mean stress, and the maximum stress value without altering the volume. The results are contingent upon the shortlisted scheme, the Extrusion Scaffold, for creating a volumetric entity from the Voronoi tessellation.

Automated summary

This article introduces a method using Voronoi tessellation to optimize the structural form, which reduces the standard deviation of stress, as well as the mean and maximum stress values. The findings suggest that this method has the potential to be applied in structural optimization.