# Topology Optimization of an Aerospace Bracket: Numerical and Experimental Investigation
## 3 Results and Discussion
### Experimental Validation  
FDM printing was performed for all components to experimentally verify and compare the stiffness of the optimized models (level-set and density-based) to the original one, thus ensuring that they satisfy the objective of material reduction while maintaining approximately the same displacement levels exhibited by the unoptimized model. As mentioned previously, the 3D printing of the bracket was done using the Ultimaker 3D printer, with the Ultimaker PLA as the printing material and the analysis being adapted to the same material. For this experiment, only cases 3 and 4 of the optimized models were considered as they achieved, in the analysis phase, displacement results matching those of the original model. Figure 11 shows the printed unoptimized (original) and optimized parts of the bracket for the two methods in both cases (3 and 4). Five replicates of the original bracket design and ten optimized design replicates were printed and tested (five for the level-set method and five for the density-based method). The initial and optimized specimens were printed under the same printing conditions to ensure comparability and accuracy of the results. We also arranged the placement of printed components in a way that would yield the same printing orientation, as well as printing without overhangs, to eliminate the need for support material and post-processing which could potentially differentiate the properties of the printed specimens. The LG SmartTester compression machine ([[http://www.lgtester.com/English/index.php?](http://www.lgtester.com/English/index.php?)]([http://www.lgtester.com/English/index.php?](http://www.lgtester.com/English/index.php?)) m=content&cc=index&a=lists&catid=16, accessed on 8 September 2023) was used for testing displacements (stiffness) under the same loading conditions (a compressive load of 1.5 kN). Custom testing fixtures were fabricated to ensure the placement and loading conditions for all tested specimens and secure them in place; Figure 12 depicts the setup for the corresponding compressive testing. As can be seen in Figure 12, A corresponds to the 3D-printed bracket; B is the employed fixture, designed to secure the bracket in place and ensure the same testing conditions; while C depicts the bracket-fixture assembly. Finally, Figure 12D shows the component in testing position, with E capturing a snapshot of a bracket specimen undergoing fracture under a compressive force. The results for the five tested replicates are shown in Table 1. Only two specimens (out of five for each design) are shown in Figure 13 for the sake of clarity, and it is easy to see that the LSM-optimized design is more in alignment with the behavior of the initial unoptimized design. Figure 11: 3D-printed components (original, optimized through level-set method, and optimized through density-based method). As mentioned previously, to ensure the accuracy of the results, both the original and optimized models were placed and secured in the exact same positions when applying the compressive loads. From these results (see Table 1), under the same load of 1.5 kN and the exact same printing and testing conditions, the mean displacement values were 1.45, 1.47, and 1.56 mm for the initial, LSM-optimized, and DBM-optimized designs, respectively. The mean values, along with the reported standard deviations, indicate the achievement of the topology optimization objective for both methods, although the level-set method seems to produce more consistent results, with a better match to the displacement of the unoptimized design. Finally, a comparison between the regions of failure and the high stress regions of the initial model and the two optimized models in case 4 are depicted in Figures 14-16. As one may easily observe by following the red arrows on these figures, the