Combining Macro- and Mesoscale Optimization: A Case Study of the General Electric Jet Engine Bracket

Round 1

Reviewer 1 Report

The paper entitled “Combining macro- and mesoscale optimization: A case study of 2 the GE-Bracket” combined macro- and mesoscale topology optimization for the innovative design of jet engine bracket from General Electric. General topology optimization (SIMP-like algorithm) was used to design the main body of the bracket, and then lattice structures were used as infill. In doing so, the light-weighting goal was achieved. The numerical investigations were conducted comprehensively by considering different load cases. This papers some certain value from an engineering point of view. Some comments must be addressed before publication.

1. The title “Combining macro- and mesoscale optimization: A case study of 2
   the GE-Bracket”. GE is General Electric, and it does not seem a long term (only two words). It is strongly recommended to use General Electric instead of GE in the title.
2. There are some citations issues (Error! Reference source not found) across the whole paper. It may be caused by the version of WORD that the authors were using. Please fix this sort of issue when resubmitting your work.
3. In Introduction, when mentioning topology optimization algorithms, it is better to show some well-established element-based algorithms such as SIMP, BESO, SEMDOT, and FPTO, and corresponding papers should be cited to show authors’ broad knowledge in this field.
4. Still in Introduction, the authors are using ANSYS for optimization. What kind of topology optimization algorithm is applied in ANSYS, for example, SIMP-based? This is also the reason why the Reviewer suggested to give the names of current algorithms.
5. Equations 8 and 9 are vectors and hence space should be added between the two notations.
6. Equation 11, please add nth term, that is …… a_n rho_r^n.
7. In Section 5, the authors mentioned additive manufacturing for their designs using FDM. More details on this sort of research can be found in Smooth Topological Design of Continuum Structures for Additive Manufacturing - DRO (deakin.edu.au) .
8. In Conclusions, “The proposed design was firstly topologically optimized,” The Reviewer read some papers working on similar research. For example,

Sustainable Design and Manufacturing 2014 Part 1 - R. Setchi, R.J. Howlett, M. Naim, H. Seinz - Google Books

Open Access proceedings Journal of Physics: Conference series (iop.org)

Optimal grading of TPMS-based lattice structures with transversely isotropic elastic bulk properties (deakin.edu.au)

The authors should make it specific to explain why it is firstly proposed or simply remove this sentence. It is better to say the authors did a comprehensive study or presented things in a different way. The word “first” should not be used lightly.

9. In Future Research, “A commercial software…..”. Please convert this to A commercial optimization package or platform.
10. In addition, the smoothness of topological boundaries shown in this paper can be further improved. Actually, some new element-based algorithms such as SEMDOT and FPTO can obtain better topological boundaries for future applications. Please refer to:

https://www.sciencedirect.com/science/article/abs/pii/S0965997820309674

https://www.sciencedirect.com/science/article/abs/pii/S0965997820309881

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

In this manuscript the authors apply several different versions of two-scale topology optimization to the GE bracket, a well known challenge problem. The resulting designs are interesting, and the results clearly show the benefits of lattices and of TO. But some aspects of the manuscript must be fixed before publication

1) There are numerous "Error! Reference source not found" errors when referencing figures, clearly must be fixed.

2) The homogenization based two-scale TO approach is not new. For example, optimization via  polynomial interpolation of stiffness tensors, just like in this manuscript, is used in [Watts, S., Arrighi, W., Kudo, J., Tortorelli, D. A., & White, D. A. (2019). Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design. Structural and Multidisciplinary Optimization, 60(5), 1887-1920.]. A more advanced multidimensional interpolation of lattice stiffness, allowing the diameter of individual rods to vary in order to achieve high anisotropy, is described in [White, D. A., Arrighi, W. J., Kudo, J., & Watts, S. E. (2019). Multiscale topology optimization using neural network surrogate models. Computer Methods in Applied Mechanics and Engineering, 346, 1118-1135.]

2) There is little value in optimizing the GE bracket for individual loads, it is well known that these individual loads result in very different designs, and in practice only the worst case load matters. The worst case load is not know a-prior, rather the displacement due to random combinations of loads must be computed, and the worst case defined by a p-norm or related soft-max function. This is sometimes referred to as "robust design". If Ansys cannot do this, that is unfortunate, but it must be mentioned that this is the right way to design the bracket.

3) The authors mention "yield", "strength", and "FOS" throughout the manuscript. But these quantities do not appear in the optimization problem statement Eq 1 - Eq 6. I believe "yield", "strength", and "FOS" are local quantities and are not a simple function of the total compliance. Were the designs obtained by minimizing compliance, and then "yield", "strength", and "FOS" are computed afterwards? Or is there really a mathematical constraint on local stress or strain? This needs to be explained better.

4) There is something wrong with the sentence 198-199

5) The authors attempt to investigate the effect of varying cell size. It is not clear that homogenization can be used for this, since homogenization assumes infinitely small cell size. This is the so-called "scale effect", and higher order methods are required, see [M.M. Ameen, R.H.J. Peerlings, M.G.D. Geers, A quantitative assessment of the scale separation limits of classical and higher-order asymptotic homogenization,
European Journal of Mechanics - A/Solids, Volume 71, 2018, Pages 89-100,]. The varying cell size results that the authors obtained are likely just FEA error, and these results should be eliminated from the manuscript.

Author Response

Please see the attachment

Author Response File: Author Response.pdf