## 6 Conclusions  
This study aims at the lightweight design problem of automotive subframes and proposes a multi-stage optimization method based on the Abaqus-Matlab co-simulation platform. Through a closed-loop optimization process of topology optimization-size optimization-experimental verification, the performance of the subframe structure has been significantly improved and the lightweight goal has been efficiently achieved. The main research conclusions are as follows:  
1. Platform innovation: The Abaqus-Matlab integrated optimization platform utilized, through the SIMP method and two-way data interaction mechanism, offers greater flexibility. After building this optimization platform, you can customize optimization algorithms on it according to specific needs.
2. Lightweighting achievements: The optimal force flow transmission path of the subframe was clarified through topological optimization, and the thickness parameters of key components (such as 3.3 mm for side beams, 1.3 mm for front crossbeams, etc.) were determined in combination with parametric size optimization. The final mass was reduced by 47.1% (33.73 kg \(\rightarrow\) 17.84 kg), significantly reducing material redundancy while ensuring structural integrity.
3. Performance verification results: Static analysis shows that the maximum von Mises stress of the optimized subframe is 262 MPa, which is lower than the yield strength of the material (306 MPa). The maximum displacement is 0.92 mm, meeting the design threshold (<1 mm). The maximum relative error between the modal experiment and the simulation results was controlled within 2.7%, verifying the reliability of the optimization scheme.  
The multi-stage optimization method proposed in this research has established a standardized technical process for the lightweight design of vehicle chassis structures. Its platform integration strategy is universal and can be extended to the optimization design field of various mechanical structures. Subsequent research will focus on the coupling optimization of multiple physical fields (structure-acoustic-thermodynamics) to enhance the performance robustness of structures under complex dynamic working conditions.  
Figure 19: Displacement cloud maps of the ten working conditions after the secondary optimization.  
**Author Contributions:** Conceptualization, J.Z. and F.Z.; methodology, J.Z.; software, F.Z.; validation, J.Z. and F.Z.; formal analysis, F.Z.; data curation, F.Z.; writing--original draft preparation, J.Z. and F.Z.; writing--review and editing, J.Z. and F.Z.; visualization, J.Z. and F.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was conducted without any funding support.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors want to thank the editor and anonymous reviewers for their valuable suggestions for improving this paper.  
**Conflicts of Interest:** The authors declare no conflicts of interest.