Topology and Parametric Optimization-Based Design Processes for Lightweight Structures

Round 1

Reviewer 1 Report

A quantitative comparison of different topology optimizations is conducted using several examples.

However, the authors misunderstand structural expression, updating scheme and classifications of topology optimizations and there are some mistakes and misunderstandings in the manuscript.

Some problems should be addressed before publication.

1. In line 82, the authors wrote ``These are based on genetic algorithms such as; Artificial Immune Algorithms, Ant Colonies, Particle Swarms, Simulated Annealing, Harmony Search, and Differential Evolution schemes [12]. '', but the above sentence is caused by misunderstanding of authors. Artificial Immune Algorithms, Ant Colonies, Particle Swarms, Simulated Annealing, Harmony Search, and Differential Evolution are the evolution strategies which is different from Genetic algorithms. Moreover, some of them consider the gradient of function and are not NGTO. Please read Ref. 12 carefully and reconstruct the classification of topology optimizations.

2. Related to comment1, I recommend to cite a paper on topology optimization based on CMA-ES [Comp. Meth. Appl. Mech. Engrg. 332, 624 (2018)]. The paper presents GTO based on multipoint search.

3. The authors demonstrate quantitative comparison. However, does the authors consider the trial and error for initial guess needed for GTO based on single point search? How the trial and error are evaluated?

4. In line 134, ``In this paper, the LSM was chosen as a GTO technique due to its effectiveness and simplicity in the post-processing [18].''. But level set method is NOT a GTO technique, it is one of the structural expression technique. Rewrite the sentence correctly.

5. Rightmost in Figure2 must be modified. The figure is too low quality and lead to misunderstanding of reader.

6. Related to the comment 5, does the used level set functions have some properties such as signed distance [Ref. 21] or piece-wise constant [Comp. Meth. Appl. Mech. Engrg. 199, 2876-2891 (2010)] or simply satisfying Lipschitz continuity ?

Comments for author File: Comments.pdf

Author Response

We wish to thank you for your constructive comments in this first round of review. Your comments provided valuable insights to refine its contents and analysis. Herein, we try to address the issues raised as best as possible. All the changes in the revised manuscript are highlighted with yellow color.

A quantitative comparison of different topology optimizations is conducted using several examples.

However, the authors misunderstand structural expression, updating scheme and classifications of topology optimizations and there are some mistakes and misunderstandings in the manuscript.

Some problems should be addressed before publication.

1. In line 82, the authors wrote “These are based on genetic algorithms such as; Artificial Immune Algorithms, Ant Colonies, Particle Swarms, Simulated Annealing, Harmony Search, and Differential Evolution schemes [12]. “, but the above sentence is caused by misunderstanding of authors. Artificial Immune Algorithms, Ant Colonies, Particle Swarms, Simulated Annealing, Harmony Search, and Differential Evolution are the evolution strategies which is different from Genetic algorithms. Moreover, some of them consider the gradient of function and are not NGTO. Please read Ref. 12 carefully and reconstruct the classification of topology optimizations.

The reviewer is correct. The text about the classification of topology optimizations is rewritten/reconstructed.

2. Related to comment1, I recommend to cite a paper on topology optimization based on CMA-ES [Comp. Meth. Appl. Mech. Engrg. 332, 624 (2018)]. The paper presents GTO based on multipoint search.

Interesting paper. The paper is cited. The CMA-ES-based topology optimization seems to be an efficient evolutionary approach. The authors should consider using it in their future publications.

3. The authors demonstrate quantitative comparison. However, does the authors consider the trial and error for initial guess needed for GTO based on single point search? How the trial and error are evaluated?

It is true that GTO is prone to get stuck to local minima of moderate performance. No general remedy has been provided so far, and it seems difficult to overcome this limitation. Thus, the reviewer is perfectly right in saying that starting from another initial guess would probably result in a different result. Herein, we consider the default option of ANSYS level-set topology optimization routine, which consists of starting with a full-domain initialization.

The following text is added to the conclusions: ‘Hence, the above conclusions are case depended in a sense that starting from another initiation, the TO will result in a different local minimum of different performance. In this work, the authors just consider the standard ANSYS implementation, which consists in starting with a full design domain initialization (no other alternative is provided); thus, no trial and error were possible. However, the above conclusions are, in general, expected to apply true for the majority of test cases.’

4. In line 134, “In this paper, the LSM was chosen as a GTO technique due to its effectiveness and simplicity in the post-processing [19].”. But level set method is NOT a GTO technique, it is one of the structural expression technique. Rewrite the sentence correctly.

The reviewer is correct. LSM should refer to the coupling of the level-set method for the shape description, with the shape derivative for the gradient computation (refer to [19,22]). The sentence is rewritten correctly.

5. Rightmost in Figure2 must be modified. The figure is too low quality and leads to misunderstanding of reader.

The figure is redesigned. In addition, a higher resolution is used.

6. Related to the comment 5, does the used level set functions have some properties such as signed distance [Ref. 21] or piece-wise constant [Comp. Meth. Appl. Mech. Engrg. 199, 2876-2891 (2010)] or simply satisfying Lipschitz continuity?

No detailed description of the method is provided by ANSYS so far. However, the recent integration of several manufacturing (member size) constraints probably indicates that the signed-distance property is used.

Once again, we thank you for the time you put in reviewing our paper and look forward to meeting your expectations. Since your inputs have been precious, in the eventuality of a publication, we would like to acknowledge your contribution explicitly.

Reviewer 2 Report

The work is devoted to the analysis of various methods of structural optimization. Although significant theoretical research has been conducted, I recommend rejecting the article. The main reason is that the selected examples of constructions are not suitable for analysis in accordance with the purposes of the article.  These examples are usually used for testing topological optimization algorithms. Also, the conditions for these tasks are quite regulated. Therefore, when the conditions change drastically, these tasks lose their original meaning. Additional, I recommend using the optimization algorithms developed in the article to solve a specific engineering problem with specified loads and requirements for geometry and allowable stresses and deflections. For example, it may be some kind of bracket with the known technical specifications from the real engineering practice. Three benchmark examples discussed in this article can only be used to test your implementation of the LSM method. Then submit the article with the results of solving this engineering problem again.

Below are recommendations for improving the text.

1. Explain in the text the notation F (u) in equation (3).
2. Explain the notation u and v in formulas (3)-(9).
3. Describe in more detail how the LSM method was implemented in ANSYS? What procedures were used? What programming language was used? Can potential reader review the developed procedures?
4. What does the term robustness mean in the paper? It is necessary to explain.
5. Check line 255. It seems that some term is missing.
6. Specify a specific formula for the values shown in figure 7.
7. Explain how the Simultaneous PO and TO was performed technically.
8. You are using a classic topological optimization problem that uses compliance of the structure as a minimization function. However, in your work, you solve the problem to minimize stress. For this task, special methods have been developed that give better results. A brief overview of these methods can be found in [Sigmund O, Maute K. Topology optimization approaches: A comparative review. Struct Multidiscip Optim 2013;48:1031–55. doi:10.1007/s00158-013-0978-6]. Please explain why you chose the classic method using compliance of the structure.
9. How was the optimization time calculated in table 3?
10. What practical problem is solved by the structures shown in figures 9, 12, 13? Formulate in more detail the technical requirements for the tasks under consideration. What is the optimal design we need to obtain? For example, why do you need a hole in the first task? Is it possible to freely change the location of the place where the load is applied? It seems that the obtained optimal designs have no practical value.
11. For each obtained optimal design, give the stress distribution with the indication of zones with maximum values.
12. Solutions using topological optimization for L-Bracket, and an MBB-Beam problems are confusing. It is necessary to validate the obtained solutions by comparing them with solutions from the literature.
13. Since topological optimization was initially performed by compliance, not by stress, the data on optimization time is unsubstantiated. Also, further discussions on the effectiveness of the combination of methods are not justified.
14. Discussions of mass reduction for problems solved by different methods are not justified because the resulting structures differ significantly in functional characteristics from the original design.

Author Response

We wish to thank you for your constructive comments in this first round of review. Your comments provided valuable insights to refine its contents and analysis. Herein, we try to address the issues raised as best as possible. All the changes in the revised manuscript are highlighted with yellow color.

The work is devoted to the analysis of various methods of structural optimization. Although significant theoretical research has been conducted, I recommend rejecting the article. The main reason is that the selected examples of constructions are not suitable for analysis in accordance with the purposes of the article.  These examples are usually used for testing topological optimization algorithms. Also, the conditions for these tasks are quite regulated. Therefore, when the conditions change drastically, these tasks lose their original meaning. Additionally, I recommend using the optimization algorithms developed in the article to solve a specific engineering problem with specified loads and requirements for geometry and allowable stresses and deflections. For example, it may be some kind of bracket with the known technical specifications from the real engineering practice. Three benchmark examples discussed in this article can only be used to test your implementation of the LSM method. Then submit the article with the results of solving this engineering problem again.

The remark of the reviewer holds true independently of the chosen test case (real engineering problem or not). For sure, the conclusions of the article do not hold true for all possible cases. However, we believe that the qualitative conclusions concerning the different workflows presented herein can be applied in a great majority of cases and thus can be used as helpful guidelines for engineers who have little to moderate experience in Topology Optimization.

Below are recommendations for improving the text.

1. Explain in the text the notation F (u) in equation (3).

The notation of the F(u) is explained in the text.

2. Explain the notation u and v in formulas (3)-(9).

The notations u and v are explained in the text.

3. Describe in more detail how the LSM method was implemented in ANSYS? What procedures were used? What programming language was used? Can a potential reader review the developed procedures?

ANSYS has not released details of the method. However, one may suspect from the members of the Topology Optimization team (e.g., Michailidis Georgios) that the classical implementation has been devised [19].

4. What does the term robustness mean in the paper? It is necessary to explain.

The term robustness is deleted. The sentence is rewritten as: ‘The goal of these optimizations was the mass reduction of the structures with respect to their yield strength.’

5. Check line 255. It seems that some term is missing.

No term is missing. However, the sentence is reconstructed.

6. Specify a specific formula for the values shown in figure 7.

The intention of the authors with this figure was to present how a sensitivity analysis diagram looks like and not go in detail. However, the following sentence is added: This diagram presents the norm of the partial derivatives of the chosen objective, in this case, the mass, with respect to the selected variables, herein: length, radius, height, and thickness.

7. Explain how the Simultaneous PO and TO was performed technically.

The simultaneous PO and TO were performed as it is described in the paper: ‘an automatic loop was created where a simultaneous PO and TO of the Hollow Plate was executed. The taken design space from each iteration was further used, at the same optimization level, as the topology region of the TO. The results were evaluated according to the structure’s compliance, mass, and maximum stress and always with respect to the aforementioned stress rule’.

Two modules, a PO and a TO, were developed and ‘linked’ inside the ANSYS Workbench. Hence, the shape/size taken by the PO was used as input for the TO. The software evaluates the results based on the optimization criteria: compliance, stress, and mass and then optimizes again until the goals are achieved.

8. You are using a classic topological optimization problem that uses compliance of the structure as a minimization function. However, in your work, you solve the problem to minimize stress. For this task, special methods have been developed that give better results. A brief overview of these methods can be found in [Sigmund O, Maute K. Topology optimization approaches: A comparative review. Struct Multidiscip Optim 2013;48:1031–55. doi:10.1007/s00158-013-0978-6]. Please explain why you chose the classic method using compliance of the structure.

The reviewer is perfectly right in saying that the comparison is not legitimate since structures have not been optimized for stress. Although, as the reviewer mentions, specific approaches have been implemented in literature for stress minimization, until recently, no industrial software seems to manage stress minimization efficiently. Instead, since compliance minimization leads, in vague terms and in the absence of geometric constraints) to iso-stressed boundaries, it is expected that compliance will also work well for minimizing the stress concentration. An explanation is added to the discussion.

9. How was the optimization time calculated in table 3?

As it is mentioned in the paper, the optimization time is calculated by adding the individual times for TO (program output), PO (program output), Validation (V) (program output), and Redesign (R) (measured) in each case study and design process. An additional description is added to the paper.

10. What practical problem is solved by the structures shown in figures 9, 12, 13? Formulate in more detail the technical requirements for the tasks under consideration. What is the optimal design we need to obtain? For example, why do you need a hole in the first task? Is it possible to freely change the location of the place where the load is applied? It seems that the obtained optimal designs have no practical value.

The practical problem is to reduce the mass of the three case studies as much as possible. The reader going from left to right in these figures can follow the mass reduction and the size/shape changes of the models. The optimal design herein is the lightest one with a FOS ≥ 2. The first case study is the optimization of a hollow plate; thus, it contains a hole. This hole could freely change position. On the other hand, the loads were constant, but their applied area could change. A completely free change of the place where the loads can be applied could dramatically increase the number of the optimization parameters and, thus, the optimization time, and that was out of the scope of this paper.

11. For each obtained optimal design, give the stress distribution with the indication of zones with maximum values.

The stress distribution plots could help the reader interested in the identification of critical zones and maximum stress values to the structures. However, it was not the authors’ intention to highlight these regions but to identify the highest mass savings by comparing the different design processes. In addition, it could not be identified any pattern of the stress results, and the design solutions had max stress at deferent regions. The integration of 30 stress plots inside the paper will dramatically increase its size while it will not offer any interesting insight.

12. Solutions using topological optimization for L-Bracket and MBB-Beam problems are confusing. It is necessary to validate the obtained solutions by comparing them with solutions from the literature.

Neither the geometry nor the loading is similar to benchmark examples, which makes it difficult to compare. Furthermore, non-optimizable regions are considered, which is not usually the case in benchmark results.

13. Since topological optimization was initially performed by compliance, not by stress, the data on optimization time is unsubstantiated. Also, further discussions on the effectiveness of the combination of methods are not justified.

As it has already been mentioned in comment 8, it is expected that compliance will also work well for minimizing the stress concentration, and thus, its results are justified.

14. Discussions of mass reduction for problems solved by different methods are not justified because the resulting structures differ significantly in functional characteristics from the original design.

The authors compared methods and designs. The absolute values of mass has no practical use but only the related ones.

Once again, we thank you for the time you put in reviewing our paper and look forward to meeting your expectations. Since your inputs have been precious, in the eventuality of a publication, we would like to acknowledge your contribution explicitly.

Reviewer 3 Report

1. Line 39: CMP is written as convectional manufacturing process, but it seems conventional manufacturing process

 

2. The explanation of the steps in Tables 2, 4, and 6 seems insufficient.

 

3. The explanation of PO+TO is not sufficient in Fig 13, 15, and 17. It is difficult to know how the shape before the process (8) (left of (8)) was formed. Was it formed before the PO+TO process, or was it optimized by the PO process within the PO+TO process?

 

4. Fig. 18 and 19(a) need to be rivesed. 

 a. The font size is too small.

 b. 3 points are in each design process except Fig. 18(d). it seems the results of 3 types of structure(hollow plate, L-bracket, MBB beam), but it is not mentioned. It needs to be marked in the graph or mentioned separately.

 c. The error bars in the Fig. 18(d) are too blurry

Author Response

We wish to thank you for your constructive comments in this first round of review. Your comments provided valuable insights to refine its contents and analysis. Herein, we try to address the issues raised as best as possible. All the changes in the revised manuscript are highlighted with yellow color.

1. Line 39: CMP is written as convectional manufacturing process, but it seems conventional manufacturing process.

The typographical error is corrected.

2. The explanation of the steps in Tables 2, 4, and 6 seems insufficient.

The word ‘step’ is changed to ‘value increment’ both in the text and in the tables’ caption text.

3. The explanation of PO+TO is not sufficient in Fig 13, 15, and 17. It is difficult to know how the shape before the process (8) (left of (8)) was formed. Was it formed before the PO+TO process, or was it optimized by the PO process within the PO+TO process?

A new description of both of the figures and the PO+TO workflow is added. The shape before the process (8) (left of (8)) was optimized by the PO process within the PO+TO process.

4. Fig. 18 and 19(a) need to be revised.

          a. The font size is too small.

The font size and the resolution of the figures are increased.

         b. 3 points are in each design process except Fig. 18(d). it seems the results of 3 types of structure(hollow plate, L-bracket, MBB beam), but it is not mentioned. It needs to be marked in the graph or mentioned separately.

The following description is added in the text: The interval plot, depicted in Figure 18 (d), shows the means and the confidence intervals (CI) of the mass reduction in each design workflow for all case studies together. The caption of the Fig.18 is changed, respectively.

       c.The error bars in the Fig. 18(d) are too blurry

The resolution of the figure is increased.

Once again, we thank you for the time you put in reviewing our paper and look forward to meeting your expectations. Since your inputs have been precious, in the eventuality of a publication, we would like to acknowledge your contribution explicitly.

Round 2

Reviewer 2 Report

The revised version of the article certainly deserves to be published. My comments on the first version of the article are recommended to be used by the authors in further research.

Reviewer 3 Report

Line 492: Typographical error

    (c) Interval plot for the three case studies => (d) Interval plot for the three case studies