Concurrent Topology Optimization of Curved-Plate Structures with Double-Sided Stiffeners
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThroughout the article, avoid personnel words like “we”
Double reference for just naming the methods to be avoided like “density-based methods7, 8” “8, 9”
Check this “Plate shape as shown in 错误!未找到引用源。”
Equation :8 the density of any element x2
H2 is the second Heaviside function … table 1 is misleading Heaviside function x1 and x2… correct it.
Check “K is the global stiffness matrix” equation in the paragraph. Give it separately.
ρpi what? Check the consistency?
Check and change the figure name 8 and 9 like sketch …
Optimized plate and beam dimensions are to be presented to the reader to identify the filling portions of plate and beam.
Any stiffness comparison before and after optimization.
conclusion to be rewritten
Comments on the Quality of English Languagementioned to author, minor revision required
Author Response
Throughout the article, avoid personnel words like “we”
Response: Thanks for pointing out this issue, we have fixed it in the revised paper.
Double reference for just naming the methods to be avoided like “density-based methods7, 8” “8, 9”
Response: We have fixed it in the revised paper.
Check this “Plate shape as shown in 错误!未找到引用源。”
Response: Thanks so much for your comments, we have fixed it in the revised paper.
Equation :8 the density of any element x2
Response: We have fixed it in the revised paper.
H2 is the second Heaviside function … table 1 is misleading Heaviside function x1 and x2… correct it.
Response: We have fixed these confusing statements.
Check “K is the global stiffness matrix” equation in the paragraph. Give it separately.
Response: Thanks for your suggestions, we have revised accordingly.
ρpi what? Check the consistency?
Response: p is a penalization parameter, generally set as 3, which is used to penalize the design variable \ρ_i to be 0 or 1. We have add explanation about this.
Check and change the figure name 8 and 9 like sketch …
Response: We have checked the figure names in the whole paper, and revised some of the inappropriate ones.
Optimized plate and beam dimensions are to be presented to the reader to identify the filling portions of plate and beam.
Response: We have added the dimensions for the optimized result shown in Figure 8.
Any stiffness comparison before and after optimization.
Response: We have added a stiffness comparison before and after optimization for the example shown in Fig. 11 (a). The compliance decrease from initial 1857 to final 36, say the stiffness increases 51.6 times through optimization.
conclusion to be rewritten
Response: Thanks for your suggestion, we have rewritten the conclusion.
Reviewer 2 Report
Comments and Suggestions for AuthorsTitle: Concurrent topology optimization of curved plate structures with double-sided stiffeners
Abstract: Please expand: H-DGTP. 'sensitivity analysis' and 'shaping of plates': Please clarify.
Introduction: 'internal holes are avoided': Please mention about the casting defects. 'design variables': Please elucidate the influence of density and height fields and angles on collaborative optimization design.
Topology optimization model: The symbols are not explained properly. The references can be cited appropriately. Figure 4 caption should be better.
Sensitivity Analysis: Please reveal the effect of temperature.
Numerical implementations: Please write about the choice of the iteration counters.
Numerical examples: Iteration curves of objective function are different at large number of iterations. Please expose the reasons, Figure 7 and Figure 8.
Conclusions: ' structural stiffness and dynamic minimum frequency': Please modify.
Author Response
Abstract: Please expand: H-DGTP. 'sensitivity analysis' and 'shaping of plates': Please clarify.
Response: Thanks for pointing out these confusing statements, we have revised them in the updated manuscript.
Introduction: 'internal holes are avoided': Please mention about the casting defects. 'design variables': Please elucidate the influence of density and height fields and angles on collaborative optimization design.
Response: We have revised these problems in the revised paper.
Topology optimization model: The symbols are not explained properly. The references can be cited appropriately. Figure 4 caption should be better.
Response: We have fixed these problems in the revised paper.
Sensitivity Analysis: Please reveal the effect of temperature.
Response: Because in this article, we only considered the optimization of mechanical stiffness, temperature has no influence on sensitivity. In the future, we plan to extend this method to thermomechanical coupling problems, where temperature will have a significant impact on sensitivity and optimization results. We have added a discussion on this issue in the conclusion section.
Numerical implementations: Please write about the choice of the iteration counters.
Response: We have clarified the choice of the iteration counters in the revised paper, where i_max is set as 400.
Numerical examples: Iteration curves of objective function are different at large number of iterations. Please expose the reasons, Figure 7 and Figure 8.
Response: During the optimization process, we increase the parameter controlling the steepness of the Heaviside function. Throughout the iteration history, these discontinuities arise due to changes in this parameter. We have included relevant discussions on this Phenomenon.
Conclusions: ' structural stiffness and dynamic minimum frequency': Please modify.
Response: we have fixed this in the revised paper.
Reviewer 3 Report
Comments and Suggestions for Authors1. The authors should clarify the scope and novelty of the manuscript at the end of the introduction section.
2. The authors should include more recent references related to their work. Also, discuss the existing literature compared with the results.
3. The authors should include a detailed methodology in the manuscript.
4. The authors should check the adequacy and relevance of the numerical examples provided in the manuscript.
5. The authors should compare the computational efficiency of the proposed method to existing techniques.
6. In conclusion should be revised and the author should explain the best results of the manuscript to contain the main results of the manuscript.
7. The abstract of the manuscript should be revised and include the main results of the manuscript
8. In the introduction, some sentences need to be revised.
9. The author can review the language of the manuscript once again because there are many grammatical mistakes.
10. The author should review the references of the manuscript and should be in the style of the journal
Comments on the Quality of English LanguageMinor editing of English language required
Author Response
The authors should clarify the scope and novelty of the manuscript at the end of the introduction section.
Response: we have clarified the scope and contribution in the introduction part.
The authors should include more recent references related to their work. Also, discuss the existing literature compared with the results.
Response: we have added several recent references related to this work. They are list as follows:
[23] Sun, Z.; Wang, Y.; Gao, Z.; Luo, Y. Topology optimization of thin-walled structures with directional straight stiffeners. Applied Mathematical Modelling 2023, 113, 640-663. DOI: https://doi.org/10.1016/j.apm.2022.09.027.
[24] Huang, L.; Gao, T.; Sun, Z.; Wang, B.; Tian, K. An integrated topology and shape optimization framework for stiffened curved shells by mesh deformation. Engineering with Computers 2023. DOI: 10.1007/s00366-023-01887-8.
[25] Sun, Y.; Zhou, Y.; Ke, Z.; Tian, K.; Wang, B. Stiffener layout optimization framework by isogeometric analysis-based stiffness spreading method. Computer Methods in Applied Mechanics and Engineering 2022, 390, 114348. DOI: https://doi.org/10.1016/j.cma.2021.114348.
The authors should include a detailed methodology in the manuscript.
Response: Thanks for the suggestions, and we have added more details about the method.
The authors should check the adequacy and relevance of the numerical examples provided in the manuscript.
Response: Thanks for the suggestions, and we have checked the adequacy and relevance for all of the numerical examples.
The authors should compare the computational efficiency of the proposed method to existing techniques.
Response: Thanks for your suggestions, and we have added a comparison for the computational efficiency between the existing and improved methods, for the considered example, the computational time of the existing method is 1452 seconds, while it is 1857 seconds. As can be seen, the computational efficiency of the proposed method is indeed deteriorated, and this is because the new method has much more design variables, and this will increase the computational time of the sensitivity analysis and optimization solver. We have added discussion on this in the revised paper.
In conclusion should be revised and the author should explain the best results of the manuscript to contain the main results of the manuscript.
Response: Thanks for your suggestions,we have discussed the results in the part of conclusion.
The abstract of the manuscript should be revised and include the main results of the manuscript
Response: Thanks for your suggestions,we have discussed the results in the part of abstract.
In the introduction, some sentences need to be revised.
Response: Thanks for your suggestions, we have revised the introduction part.
The author can review the language of the manuscript once again because there are many grammatical mistakes.
Response: Thanks for your suggestions, we have carefully read the entire text and made our best efforts to optimize the language.
The author should review the references of the manuscript and should be in the style of the journal
Response: Thanks for your suggestions, we have modified the reference style.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAppreciably updated the article but check statement "
We have added a stiffness comparison before and
after optimization for the example shown in Fig. 11 (a). The
compliance decrease from initial 1857 to final 36, say the
stiffness increases 51.6 times through optimization."
Figure 11 is not in the updated article . Do either in figure or text based on formula.
reference format to be corrected. why so many reference added ?
Author Response
Response: Thanks so much for your efforts on this manuscript, which has greatly helped us improve the quality of our paper.
1）Regarding the comparison examples of the results before and after optimization, we have decided to discuss them in Example 1, as shown in Table 2. We also added text discussion as follows: Through optimization, the four methods respectively reduce the objective function from the same initial value of 1201 to 328.81, 317.12, 303.89, and 294.76, which corresponds to an increase in structural stiffness by 3.65, 3.79, 3.95, and 4.07 times, respectively. Thus, it can be seen from these results that the optimized result for method 4 is the best, where the reference plate is curved with its shape freely optimized including the location at boundaries. The reason we use this example to discuss this is that, inaddition to show the objective change through optimization, it can simultaneously demonstrate that method 4 is the best.
2) Regarding the added references, it is because another reviewer suggested that we should increase the proportion of recent references, and we agreed with his suggestion and made the necessary revisions.
Reviewer 3 Report
Comments and Suggestions for AuthorsAccept in its present form
Author Response
Comment 1: Accept in its present form
Response 1: Thanks so much for your comments and efforts you made on this work.
