PIVOT: A Framework for Minimizing Stress Deviations in Structural Form
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Date
2021-04-23
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Abstract
Design of efficient structural members is certainly an intricate process that requires a sound explanation, an exact fit of art and science perhaps, to harness the ever-increasing range of solutions assisted by computational advancements and manufacturing innovations. Many frameworks have been introduced previously to optimize the structural form, however, obtaining a uniform stress distribution has been neglected in favor of determining the least volume satisfying the objective function. Inadvertently, in the process of changing the volume, there are changes to the underlying geometry as well. Since there have been recent studies documenting the impact of geometry on the mechanical performance, it is crucial to obtain reliable knowledge regarding the impact it can have on strategic redistribution of stresses while keeping the volume constant. This investigation proposed the use of Voronoi tessellation, a bioinspired mathematical approach, to determine the positioning of void spaces. Stress-weighted centroids of Voronoi cells were utilized for selecting Voronoi sites based on two different weights. This technique was tested against the Lloyd’s algorithm that utilizes geometric centroids to select Voronoi sites. The results demonstrate a statistically significant difference between the Lloyd’s algorithm and PIVOT. The proposed approach, with weights inversely proportional to the stresses, showed affirmative signs of convergence while reducing the standard deviation of stress, mean stress and lowering the maximum stress value without making any changes to the volume.
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Structural Optimization, Voronoi Tessellation, Geometry and Mechanics