## 6 Conclusions  
This article approaches four different TO methods based on compliance minimization procedures applied to 3D elastostatic problems. The SESO, SERA and ESO methods were implemented in Matlab code, and the results obtained are compared with the deterministic SIMP method. A free code, presented in [6], was used to introduce the methods mentioned above, in which a hexahedral finite element is used to discretize the design domain, and an elastic analysis is used to calculate the objective function in each method.  
It is possible to conclude that the implemented models can generate optimal topologies that can support the loads applied under defined boundary conditions. Additionally, with the results presented, it is clear that the SESO and ESO methods, whose design variables are the domain elements, have very close optimal settings with a low computational cost. It is highlighted that these methods' compliance is much lower than those presented with the SIMP method. It was observed that the four methods presented chessboard settings when the filter was disabled, implying an increase in compliance. Nevertheless, SERA and SIMP showed denser chessboard regions. It was also verified that the increase in the number of mesh elements provides an increase in the computational cost since the number of variables increases with the cube of the proportionality ratio of the mesh. In addition, the result presented for the synthesis of flexible mechanisms with the approaches proposed in this article showed good accuracy with the examples in the literature. Moreover, these models can be extended to incorporate constraints of stress, displacements, and natural frequency.  
The authors have been working together for over 9 years, and the tasks in this article were developed as follows: (1) H.L.S.--Implemented SERA-3D and SESO-3D programs in Matlab code. Responsible for writing and structuring the article. (2) V.S.A.--Implemented SERA and SESO codes. Responsible for reviewing the article. Participated in the data analysis of the numerical examples in the article. (3) F.d.A.d.N.--Contributions to the preparation of the article: reading, review and suggestions for examples. (4) V.D.D.A.--Implemented ESO-3D and participated in the data analysis of the numerical examples in the article. (5) M.D.S.C.--Suggested and wrote the discussion section and participated in the review of the article. All authors have read and agreed to the published version of the manuscript.  
CNPq (National Council of Scientific and Technological Development) under Grant Number 30503/2018-5. FAPEMIG (Foundation for Research Support of Minas Gerais State) under Grant number TEC-PPM-00692-18 and Sao Paulo State Research Foundation (FAPESP) under Grant Number 2016/02327-5. Instituto Federal de Educacao Ciencia e Tecnologia de Minas Gerais (IFMG) under Grant Number.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
Figure 17: Topology optimal—(a) YYP ENG 2018 and (b) SESO.  
**Acknowledgments:** The authors are grateful to the Instituto Federal de Educacao Ciencia e Tecnologia de Minas Gerais-IFMG, CNPq (National Council of Scientific and Technological Development) under Grant Number 30503/2018-5 and Number 315632/2020-8, CAPES (the Coordination for Improvement of Higher-Education Personnel), FAPEMIG (Foundation for Research Support of Minas Gerais State)and Grand number TEC-PPM-00692-18 and Sao Paulo State Research Foundation (FAPESP) under Grant Number 2016/02327-5 for their financial support.  
**Conflicts of Interest:** The authors declare no conflict of interest.