# Topology Optimization Considering Porosity Defects in Metal Additive Manufacturing
## 7 Conclusions  
Porosity is one of the main defects of the manufactured parts by AM. The appearance of porosity will significantly reduce the mechanical and fatigue properties of fabricated parts and accelerate the failure of parts. To reduce the influence of porosity, the pores are  
Figure 11: Convergence history of C-shaped bracket considering porosity constraint.  
Figure 12: Optimization results and porosity constraint distribution clouds of C-shaped bracket, (**a**) optimized shape without considering porosity constraint; (**b**) optimized shape considering porosity constraint; (**c**) porosity constraint distribution clouds without considering porosity constraint; (**d**) porosity constraint distribution clouds considering porosity constraint.  
considered in topology optimization for AM so as to obtain a robust optimization result. In this paper, the concept of topological sensitivity is used to establish the global porosity constraint function, and the shape sensitivity of the porosity constraint is analyzed. Considering the robustness of the algorithm, the topology optimization considering the porosity constraint is performed by two steps. In the preliminary optimization of the structure, a hole nucleation method combining BESO and topological sensitivity is proposed to solve the problem that the level set topology optimization method cannot automatically nucleate holes. Next, the preliminary optimization results are subjected to topology optimization considering porosity constraint, obtaining the results that can reduce the effects of porosity on structural performance. In the L-shaped beam, the porosity constraint value of the optimization results is reduced by 30%. In the C-shaped bracket, the value is reduced by 15%, but the compliance of the structural performance is only slightly increased. Compared with the decrease of porosity constraint value, the change of compliance is very small and within the admissible range. The step-by-step optimization method proposed in this paper will not increase the extra workload for engineers to guess the initial structure and improve the convergence efficiency of the optimization algorithm. This method provides a potential solution for multi-constraint topology optimization problems. In future work, the idea of using topological sensitivity to construct porosity constraints can also be used to consider additive manufacturing defects such as cracks and spheroidization in topology optimization, which further broadens the research field of topology optimization for additive manufacturing defects.  
Conceptualization, S.C., H.W. and Z.S.; methodology, S.C.; software, J.T.; validation, S.C., H.W. and J.T.; formal analysis, S.C. and X.L.; investigation, J.T.; data curation, H.W. and X.L.; writing--original draft preparation, S.C.; writing--review and editing, H.W.; supervision, S.C., Z.S. and J.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data available on request. The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.