Τopology Optimization under a Single Displacement Constraint Using a Strain Energy Criterion
Round 1
Reviewer 1 Report
See the attached file for the improvement of this article.
Comments for author File: 
Comments.pdf
Author Response
- The flowchart given in the figure 1 is very blur, I recommend to add a clearer version so that a reader can understand.
ANSWER: Figure 1 has been redrawn from scratch and is now at high quality.
- Figure 3 is very blur, I recommend to add a clearer version so that a reader can understand.
ANSWER: This if the maximum quality I can take from my software even if I increase the number of elements.
- Figure 10 is very blur, I recommend to add a clearer version so that a reader can understand.
ANSWER: It is blur in purpose to show what happens until the final structure is eventually produced. Especially in the case (b), I have run the MATLAB code by Sigmund (Re. [52]) and the blur situation is true.
- Figure 11 is very blur, I recommend to add a clearer version so that a reader can understand.
ANSWER: The plot on the left (a) using 100×50 elements is clearer than the right one (b) taken with 60×30 elements (see, page 17, lines 412-415). In other words, according to the proposed method the finer meshes are less blur.
- Towards the word “Τopology” in the title, I can see any relevant thing of topology. Is this a different topology than mathematics?
ANSWER: Actually, the word “topology” has nothing to do with the mathematics and also nothing common with chemical topology. It stands as “Topology Optimization” related to elastic and plastic Structures, which is widely accepted as the procedure to remove material from the interior of a domain so as to undertake the applied loads (forces and moments) using the minimum possible material. In other words, the key problem is where to make the openings (holes).
- Equations are written in quite informal way. I recommend to revisit your equations. See the equations 5 and 6. It looks very informal.
ANSWER: Done!
- Why you use ½ instead of real fraction format?
ANSWER: I have left the exponent () only in Eq.(2), otherwise it does not look nice. Moreover, I have replaced the fractions in the form everywhere else.
- Topological have been extensively studied. Some key works are missing here. Topological properties of reverse-degree-based indices for sodalite materials network, Arabian Journal of Chemistry. DOI: 10.1016/j.arabjc.2022.104160. Verification of some topological indices of Y-junction based nanostructures by M-polynomials. Journal of Mathematics. DOI: 10.1155/2022/8238651. Topology Optimization of Elastoplastic Behavior Conditions by Selectively Suppressing Plastic Work. doi.org/10.3390/math8112062. Topology Optimization for Energy Dissipation Design of Lattice Structures through Snap-through Behavior. Metric based resolvability of polycyclic aromatic hydrocarbons. European Physical Journal Plus. DOI:10.1140/epjp/s13360-021-01399-8.
ANSWER: Two of these papers (the highlighted ones) have been included, mentioned as [20] and [21] (see page 2 and the revised References-[20], [21] on page 19). The rest papers refer to Chemistry, so I believe that cannot be included because the paper refers to Structural Optimization, not to Chemistry bonds.
- Moreover, literature review is too short, this section can be improved.
ANSWER: In addition to the abovementioned [20,21] I have also added six more papers ([17], [18], [19], [47], [48], [49], [50] and [52]).
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper is well written and well organized. The introduction provides a large number of citations, and this is convenient to understand the state of the art.
Although the method is described in detail, there is one issue that, from the point of view of the reviewer, it is easy to overcome. The final designs show gray areas. This means that microstructure is appearing, and this is not possible to manufacture these structures. With the use of a projection (erode, dilate or hyperbolic tangent), these intermediate densities tend to disappear.
Why a projection method is not implemented?
Another question is, which is the difference between the proposed method and the classical SIMP when we consider the computation time. It seems that the mesh used is quite coarse, is the computation time a problem with this method?
Author Response
- Although the method is described in detail, there is one issue that, from the point of view of the reviewer, it is easy to overcome. The final designs show gray areas. This means that microstructure is appearing, and this is not possible to manufacture these structures. With the use of a projection(erode, dilate or hyperbolic tangent), these intermediate densities tend to disappear.
ANSWER: For the sake of transparency, we have implemented the competitive original SIMP method following the MATLAB code cited in Ref. [52]. Comparing the SIMP, this paper shows that our concept previously used in truss optimization is also applicable to topology optimization as well.
Two of these papers (the highlighted ones) have been included, mentioned as [20] and [21] (see page 2 and the revised References-[20], [21] on page 19). The rest papers refer to Chemistry, so I believe that cannot be included because the paper refers to Structural Optimization, not to Chemistry bonds.
- Why a projection method is not implemented?
ANSWER: The implementation of an additional projection method is very reasonable, however I have not the capacity to fiilize it within 10 days.
- Another question is, which is the difference between the proposed method and the classical SIMP when we consider the computation time. It seems that the mesh used is quite coarse, is the computation time a problem with this method?
ANSWER: Regarding the computer time, Figure 9 clearly shows that the proposed method requires much less iterations thus significantly less computer effort. Nevertheless, if we highly increase the mesh density, this should be happen to both, i.e. the proposed and SIMP. In this case the SIMP would require many-many iterations!
Reviewer 3 Report
The manuscript “Τopology optimization under a single displacement constraint using a strain energy criterion” extended and improved the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. The work is well-written and logically structured. However, some improvements are required before further consideration. The comments are:
1. The address of the author is not complete. Please also add the country information (Greece).
2. In Introduction, some new algorithms such as ETO, SEMDOT, and FPTO should be mentioned.
The method proposed in this work can also be used for SEMDOT, and the smooth boundaries can be obtained.
3. Figure 1 seems like a screen shot, and the background can be clearly seen. Please improve it.
4. Figures 4-9 must be further improved. They are not very professional. As the readers will go through the figures first, the Reviewer really hope the author can make more efforts to improve the quality of these figures.
5. The formatting should be further improved. The space should not be used be the “where” after equations.
6. The statement “This papers aims at closing this gap by…” in Introduction is not recommended. The author can directly say what you are going to do. For example, this work aim to implement….
7. In terms of the last case (L-bracket) in Figure 3, the proposed method does not seem very good in solving this case. The topological design does not seem reasonable.
Author Response
The comments are:
- The address of the author is not complete. Please also addthe country information (Greece).
ANSWER: Done!
- In Introduction, some new algorithms such as ETO, SEMDOT, and FPTO should be mentioned. The method proposed in this work can also be used for SEMDOT, and the smooth boundaries can be obtained.
ANSWER: Done! See page 2, lines 50-52; Refs. [17,18,19].
- Figure 1 seems like a screen shot, and the background can be clearly seen. Please improve it.
ANSWER: Done!
- Figures 4-9 must be further improved. They are not very professional. As the readers will go through the figures first, the Reviewer really hope the author can make more efforts to improve the quality of these figures.
ANSWER: Done!
- The formatting should be further improved. The space should not be used be the “where” after equations.
ANSWER: Done!
- The statement “This papers aims at closing this gap by…” inIntroduction is not recommended. The author can directly saywhat you are going to do. For example, this work aim toimplement….
ANSWER: Done!
- In terms of the last case (L-bracket) in Figure 3, the proposedmethod does not seem very good in solving this case. The topological design does not seem reasonable.
ANSWER: Done!
Round 2
Reviewer 3 Report
The revised manuscript can be accepted.
