Structural optimization is a methodology used to generate novel structures within a design space by finding a maximum or minimum point within a set of constraints. Topology optimization, as a subset of structural optimization, is often used as a means for light-weighting a structure while maintaining mechanical performance. This article presents the mathematical basis for topology optimization, focused primarily on the Bi-directional Evolutionary Structural Optimization (BESO) and Solid Isotropic Material with Penalization (SIMP) methodologies, then applying the SIMP methodology to a case study of additively manufactured lattice cells. Three lattice designs were used: the Diamond, I-WP, and Primitive cells. These designs are all based on Triply Periodic Minimal Surfaces (TPMS). Individual lattice cells were subjected to a uniaxial compression load, then optimized for these load conditions. The optimized cells were then compared to the base cell designs, noting changes in the stress field response, and the maximum and minimum stress values. Overall, topology optimization proved its utility under this loading condition, with each cell seeing a net gain in performance when considering the volume reduction. The I-WP lattice saw a significant stress reduction in conjunction with the mass and volume reduction, marking a notable increase in cell performance.
Results in Materials
Spear, D. G., Lane, J. S., Palazotto, A. N., & Kemnitz, R. A. (2022). Computational based investigation of lattice cell optimization under uniaxial compression load. Results in Materials, 13, 100242. https://doi.org/10.1016/j.rinma.2021.100242