## 6 Conclusions  
This paper focuses on minimum compliance as the objective function while using volume as the constraint. It employs the SIMP interpolation model of the variable density  
Figure 12: Boundary conditions and load settings of aircraft bracket.  
Figure 13: The mesh generation and TO structural configurations of the aircraft bracket developed under the recommended criteria: (**a**) hexahedral mesh generation (mesh size = 2 mm). (**b**) TO structural configuration with the hexahedral mesh (\(\overline{v}\) = 30%, \(E\) = 110.3 GPa, \(\mu\) = 0.33, \(x_{\text{initial}}\) = 0.5, \(r\) = 4.8, and \(p\) = 3.5). (**c**) Tetrahedral mesh generation (mesh size = 3 mm). (**d**) TO structural configuration with the tetrahedral mesh (\(\overline{v}\) = 30%, \(E\) = 110.3 GPa, \(\mu\) = 0.33, \(x_{\text{initial}}\) = 0.5, \(r\) = 4.2, and \(p\) = 3).  
method, along with density filtering and MMA, to analyze the factors influencing topology optimization (TO) for a metallic secondary load-bearing gooseneck chain utilized in civil aviation. Key factors examined include mesh type, mesh size, material properties, initial density, filter radius, and penalty factor, with recommended standards proposed for each. In addressing challenges associated with TO, such as isolated bodies and disconnected branches, which can impair structural performance as well as limit additive manufacturing (AM), this paper introduces geometric reconstruction criteria and a reconstruction approach based on the marching cubes algorithm, PolyNURBS modeling, and SolidWorks modeling. This research not only advances the integration of TO and AM technologies in practical engineering applications but also lays a substantial theoretical foundation and provides guidance for future engineering design.  
Nevertheless, certain limitations are acknowledged in this study. First, some features such as isolated bodies, disconnected branches, and thin bars in TO results may compromise structural performance, and their elimination through optimization procedures (rather than post-processing geometric reconstruction) warrants further investigation. Second, while compliance was adopted as the objective function with volume constraints, practical engineering applications necessitate incorporating additional multi-physics constraints such as fatigue stress. Furthermore, although parametric analysis via single-factor methods identified dominant influences of the mesh size, filter radius, and penalty factor, their synergistic interaction mechanisms remain insufficiently resolved, requiring systematic exploration through sensitivity analysis to elucidate coupling relationships. Additionally, the proposed penalty factor recommendations derive from conventional SIMP frameworks prove inapplicable to non-penalization algorithms (e.g., FPTO and SEMDOT). Finally, while fixed high-resolution meshes ensured computational accuracy, they substantially increased computational costs; future studies may implement adaptive meshing or anisotropic mesh refinement strategies to enhance their efficiency (potentially reducing computational load by 30-50%).  
Conceptualization, L.C. and D.Z.; methodology, L.C.; software, L.C.; validation, L.C.; formal analysis, L.C.; writing--original draft preparation, L.C.; writing--review and editing, all the authors; visualization, L.C.; supervision, D.Z.; project administration, D.Z.; funding acquisition, D.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the 2022 Stable Support Plan Program for Shenzhen-based Universities under Grant 20220815150554001.  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.