Structural Optimisation of a Suspension Control Arm Using a Bi-Evolutionary Bone Remodelling Inspired Algorithm and the Radial Point Interpolation Method
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article is well-written, and I really appreciated the introductory section where the algorithms used are explained in detail. The article proceeds in a clear manner, and I believe it is worthy of publication. However, I suggest a major review. In my opinion, important information regarding the setup of the proposed optimization is missing. From Equation (20), I gathered that the goal is to minimize compliance, while the mass reduction is a design constraint. What is the amount of this mass reduction? If all the structures shown in Tables 1, 2, 3, and 4 have the same mass, I would like a clearer explanation of where the FEM and RPIM solutions differ.
There are also less significant points that, in my opinion, deserve modifications.
Speaking further about Tables 1, 2, 3, and 4, it would be better to explain what the numbers and percentages in the tables refer to. I believe they refer to the number of iterations and the percentage of mass relative to the initial mass, but it would be worth specifying this more clearly.
Finally, on line 206, I notice a typo regarding the citation of the source.
Author Response
Answers in attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe research structure of the article is reasonable and the research content is comprehensive. Before it can be accepted, some improvements need to made.
Why is the Bi-evolutionary Bone Remodeling Algorithm and the Radial Point Interpolation Method? Are there some other methods can do the same work or better?
Can the structures obtained through different optimization methods be verified through experiments?
Author Response
Answers in attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors
The findings of the study serve to corroborate the efficacy of alternative numerical methods (such as the "Bi-Evolutionary Bone Remodelling Inspired Algorithm" and the "Radial Point Interpolation Method") in optimisation contexts.
The logical inconsistency can be summarized as follows: It can be reasonably assumed that, in the event that a structural element is correctly parametrically designed, the results will be calculated with the desired quality by the aforementioned computation method and that the optimisation algorithm will function as intended within the given precision. Consequently, at the conclusion of the process, an optimised structure will be produced. This process is analogous to that observed in the assembly of LEGO blocks. It is the responsibility of the computational specialist to define the interaction vectors and to set out the standard optimisation aims, restrictions and final precision.
The authors provided a functioning exemplar. The example is illustrative and has significant industrial implications. The MacPherson suspension system has been employed in approximately one hundred million vehicles over the past four decades, beginning with the Volkswagen Golf (1974). A number of hundred optimisation studies of the lower link were conducted using a variety of formulations. A further intriguing study can be observed in the actual manuscript. However, as the reviewer correctly perceives, the specific optimisation problem was not the central focus of the discussion. The authors will demonstrate the efficacy of the alternative computational algorithm for optimisation problems of a broad nature.
The crucial task is to ascertain the number of mathematical operations (MOPS) required to achieve the desired level of optimisation precision. As previously stated, the structural element is representative of a typical component found in the automotive industry. The presented example may be used as a benchmark for the algorithms in question. The standard procedure is as follows: The structural algorithm S(i) is computed, and the optimisation algorithm O(j) is then applied. For example, S(i), where i=1,2,3,..N, are:
The finite element and alternative structural analysis formulations are designated as follows:
i=1 "Finite Element Formulation with Element Type 1"
i=2 "Finite Element Formulation with Element Type 2"
i=3 "Finite Element Formulation with Element Type 3"
i=4 Radial Point Interpolation Method (RPIM) type1
i=5 Radial Point Interpolation Method (RPIM) type 2
an so on.
For the optimisation selection, the same vectorisation is employed. For example, O(j), with j=1,2,3,..M representing some common optimisation routines:
n the optimisation selection, the same vectorisation is employed. For example, O(j), i=1,2,3,..M are some common optimisation routines:
j=1 a common commercial genetic algorithm
j=2 a common commercial non-linear gradient algorithm
j=3 a bi-evolutionary bone remodelling inspired algorithm
and so on.
The final set of matrices (NxM) provides insight into the efficiency and effort associated with the optimisation process. The first NxM matrix illustrates the reduction in weight, while the second NxM matrix depicts the MOPS, which is a measure of the optimisation effort. The third NxM matrix demonstrates the fulfilment of the restrictions.
These matrices serve as a roadmap for the computational engineer, guiding the selection of an efficient combination of analysis and optimisation codes.
Author Response
Answers in attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThis work presents a comparison between the RPIM and the FEM. The paper is very well organised, including an introducion with a number of references big enough to understand the scope of the article. The next points should be clarified/fixed:
1.- The first paragraph in Section 2 should clarify the difference between both methods. This is specified in next paragraphs, but the description of the RPIM is very similar to FEM.
2.- In some equations( (1), line 163, (13), (19), (20) ...), the symbol comma should be included into the equation environment.
3.- In equation 20, the sum limits seem to be backwards.
4.- In section 4, the sentence "in order to avoid reducing the density of the material in the areas with applied boundary conditios" must be clarified. Do we really need a passive area (solid in this case) near the BC's?
5.- How do you obtain a clear distributions between solid and void? This is due only to the PR?
6.- The connectivity is not ensured at all in this problem, and it can lead to undesirable designs. There are some techniques developed with this objective, but I understand that this is out of the scope of the paper.
7.- Table 1 shows the first numerical examples. Please, include a description of the colormap. I understand that red and blue stand for solid and void, respectively, and green/yellow represent "gray" areas, but it is necessary for the rest of the readers.
8.- In Table 1, please explain the numbers of the solutions (86.06%, 77.00%, 8, 15...). The results are quite strange, in the sense that lot of intermediate density appears and some parts of the structure are not well defined. Why this happen? Regularization techniques such as filtering and projection of the design variable, ensure the minimum length scale. This also happens in Table 2, 3 and 4.
9.- The colormap changes in Table 3 and 4. Consider use the same color than in Table 1 and 2, and then, change the color of the passive areas.
9.- In line 336, the intermediate densities can be easily avoided with projection techniques.
10.- The Figure 6 shows a non-manufacturable design, since the structure is not well defined. Of course, the solution is completely "correct" from a mathematical point of view, but it is well kwown that this kind of problemas sometimes are bad possed, and a post-process is needed.
11.- In Subsection 4.2, some points need to be clarified. The model 4 shows the so called "coating". It can be included in the optimization problem. Model 1 is better from a mathematical point of view, but is worse from a mechanical one, is the reason the thickness of the bars?
12.- In Table 8, the second number of the volume fraction is confusing, the complementary of 70.06 is already 29.94, I think you do not need this second value.
12.- In Table 8, how do you measure K? You have a stiffness matrix and this is a scalar.
13.- In Table 8, the value of the compliance should be included.
Author Response
Answers in attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper has been improved following my suggestions.
