## 3 Results and Discussion
### MBB Beam  
For the MBB beam, design areas measuring 30 \(\times\) 20 and 90 \(\times\) 60 were employed, as illustrated in Figure 5. Across all evaluated scenarios, the iteration count was limited to a maximum of 300. The results clearly demonstrated that different build directions led  
Figure 5: MBB symmetric beam and boundary conditions. to the emergence of distinct topologies. Most significantly, all the resulting designs were in full compliance with the Additive Manufacturing constraint, a factor that takes into consideration the specific direction of construction. In this study, a thorough comparison was made by initially presenting deterministic Topology Optimization (TO) solutions, as shown in Figure 6. The subsequent analyses included both sensitivity (ft = 1) and density filter (ft = 2). The deterministic solutions were then compared with those in Figure 6, involving the Optimality Criterion (OC), Method of Moving Asymptotes (MMA), and interior-point methods. It was observed that the design updated via the interior-point method converged more rapidly than those employing MMA and OC when the sensitivity filter was used. Despite these differences in convergence, both approaches led to topologically similar results. Figure 7 illustrates the deterministic Topology Optimization (DTO) outcomes, achieved in four unique manufacturing directions (W, E, N, S), for the MBB beam with the Additive Manufacturing (AM) filter applied in this research. Consequently, a distribution was achieved that eliminates the necessity for a support structure in the manufacturing direction. Owing to the stability of the results when using the sensitivity filter (ft = 1) in conjunction with the interior-point algorithm, compared to the density filter, subsequent solutions were conducted with the sensitivity filter. Figure 6: Deterministic topology optimization designs for the 30 \(\times\) 20 MBB beam, utilizing the Optimality Criterion (OC), Method of Moving Asymptotes (MMA), and interior-point methods. Figure 7: Deterministic topology optimization designs of 30 \(\times\) 20 MBB beams employing the interior-point approach and AM filter in four different build directions, with the use of a sensitivity filter. The west direction is preferable, achieving the required compliance without hindering performance. The north and south orientations require additional material to maintain the structure, thereby improving fit. Slight modifications in the east and west designs lead to minor increases in compliance. Without the utilization of an AM filter, the reference design (as shown in Figure 6) cannot be printed in any of the considered directions without the aid of a support structure. Figure 8 reveals the results of both RBTO and RBTO with the AM filter. Highlighted by blue lines on the optimal figures, the additive manufacturing table represents the AM filter, which was assessed for the 'W' direction for minimal compliance, in line with prior findings. Additionally, the optimal topologies that were identified were fabricated using a 3D printer (Creality Ender-6, Shenzhen, China). The regions where the overhang angle exceeds the 45\({}^{\circ}\) threshold are marked with red lines, indicating areas that would require support structures if printed without applying the AM constraint. Based on the results presented, the AM-RBTO/W algorithm consistently excels in structural design by achieving lower values for the objective function. Specifically, in the case of a 30 \(\times\) 20 structure size, the AM-RBTO/W algorithm not only yields a lower objective function value but also provides a solution more rapidly compared to the RBTO algorithm. Even for the 90 \(\times\) 60 structure size, where the objective function values were identical, the AM-RBTO/W algorithm retained a benefit by reaching the solution in less time. In a comparison of 3D printing durations, the algorithm incorporating the AM filter finished 13 min quicker.