Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The author discusses a FEM for sandwich beams with cellular cores. The author discusses the Natural Neighbor Radial Point Interpolation Method (NNRPIM) with high-order simulations in a general form. Numerical results are presented in Section 3 for one circular hole per cell.  The general extended description with developed various modification is applied to a simple problem. The author doesn’t concern the dense packed disk when the numerical problem arises. The results are not compared with the well-known analytical formulas.

Consequently, the manuscript presents a simple application of FEM to the well-known boundary value problem and should be rejected.

Author Response

Dear reviewer #1,

In this numerical paper, the NNRPIM was extended for the first time to the analysis of sandwich beam with PUF foams considering a full multiscale analysis. The novelty and focus here is the NNRPIM, therefore the FEM is applied only as a comparison numerical technique. This work condenses a serious amount of work within the topic of meshless methods, in which the author programmed from scratch all the routines necessary to produce the documented results.

Best regards,

Jorge Belinha

Reviewer 2 Report

Comments and Suggestions for Authors

No experimental validation or correlation. Not even the experimental results from the literature have been compared, as far as I went through the manuscript.

Author Response

Dear reviewer #2,

 

Thank you for your comments.

In this numerical paper, the NNRPIM was extended for the first time to the analysis of sandwich beam with PUF foams considering a full multiscale analysis. The focus here is the NNRPIM and its numerical performance. Therefore, the FEM is applied as a comparison numerical technique and only the numerical issues are addressed and studied. This work condenses a serious amount of work within the topic of meshless methods, in which the author programmed from scratch all the routines necessary to produce the documented results. The experimental validation/correlation is beyond the scope of the present study.

 

Best regards,

Jorge Belinha

Reviewer 3 Report

Comments and Suggestions for Authors

This paper deals with the analysis of the mechanical behaviour of sandwich beams with cellular cores using a multi-scale approach combined with the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The study shows that NNRPIM can approximate high order FEM solutions, albeit with a significant increase in computational cost when seeking comparable smoothness of approximations, an aspect that facilitates these complex calculations. In addition, the author highlights the ability of NNRPIM to accurately reproduce the solutions obtained from FEM analysis, which is a very novel and interesting aspect for the scientific community. 

The paper is very well written, some sections in great detail, but I understand that it is too complex to summarise further, as this would lose the mathematical follow up of the method proposed by the author. For this reason I recommend its publication in this form. I have checked the article thoroughly and found no typing errors, which is a reflection of the author's meticulous work.

Author Response

Dear reviewer #3,

Thank you very much for your kind comments.

Best regards,

Jorge Belinha

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors, thank you very much for this important article about modeling possibilities for sandwich like constructions, there are some comments below about possible improvements.

1.    Introduction section can be concluded with detailed novelty of this research.

2.    Methodology section will be much clearer with added values of investigated sandwiched constructions.

3.    When analyzing obtained results, it is very important to mention all practical issues related to different layers of investigated materials.

4.     All conclusions part can be added with some investigated numerical indicators.

5.    All references are adequate to investigated topics, but some article are really outdated and can be changed with newest research.

Finally, I would like to express my gratitude to this article Authors for the great work.

 

Sincerely, Reviewer. 

 

Author Response

Dear reviewer #4,

 

Thank you very much for your comments, which allowed to improve the manuscript. Next, I will address each comment and within the manuscript, the reviewer can find the modified text in blue and red.

 

Comment 1.    Introduction section can be concluded with detailed novelty of this research.

Answer: Following the reviewer’s suggestion, in the Introduction section it was highlighted a concluding text detailing the novelty of this research and its chief goals (blue text).

 

Comment 2.    Methodology section will be much clearer with added values of investigated sandwiched constructions.

Answer: Since, in this manuscript, the methodology section addresses only the numerical description of the meshless method applied (the NNRPIM), additional research works of other authors related with sandwiched constructions were cited and discussed in the introduction section (red text).

 

Comment 3.    When analysing obtained results, it is very important to mention all practical issues related to different layers of investigated materials.

Answer: Following the reviewer’s suggestion, in the opening paragraphs of section 3.2, a list of highly relevant practical issues no studied in this paper were included (blue text).

 

Comment 4.     All conclusions part can be added with some investigated numerical indicators.

Answer: As suggested by the reviewer, it was included in the conclusion section some investigated numerical indicators (blue text).

 

Comment 5.    All references are adequate to investigated topics, but some article are really outdated and can be changed with newest research.

Answer: Following the reviewer’s suggestion, new research manuscripts are now cited and discussed in the introduction section (red text). The answer to this comment partially overlaps the answer to comment 2, in which more recent works on sandwich structures were included.

 

 

Best regards,

Jorge Belinha

Reviewer 5 Report

Comments and Suggestions for Authors

The research and the results presented in the paper are important for meshless methods. They are original as well.

 

Author Response

Dear reviewer #5,

Thank you very much for your kind comments.

Best regards,

Jorge Belinha

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author claims to propose a "novel approach" and describes, in general terms, the potential applications of this approach to complex problems. However, the presented numerical result is underwhelming. The square array of circular voids is a standard exercise for FEM. 

Therefore, the manuscript should be rejected. 

 

Author Response

Dear reviewer #1,

 

The topic addressed in this paper is actually novel, representing a novel approach in the meshless methods field. I challenge the reviewer to find in the literature a paper dealing with a natural neighbour meshless method (such as the NNRPIM) combined with a full multiscale framework (capable of predicting the microscale homogenized mechanical properties of a PUF foam and then perform a macroscale structural analysis).

I must stress that this paper is not about FEM, is about the NNRPIM. FEM is only used for comparison proposes. The NNRPIM formulation (and programing) is much more demanding than FEM, therefore this kind of research poses a truly research challenge.

Regarding the size of the manuscript, in my opinion it possesses the right size. In this paper, the homogenization technique is presented and validated, the homogenized mechanical properties are calculated, and then, using such homogenized mechanical properties, a benchmark macroscale example is analysed. The results presented (and how they are presented) will allow other authors to make direct comparisons with their own formations (validating their approaches). This work condenses a serious amount of work within the topic of meshless methods, in which the author programmed from scratch all the routines necessary to produce the documented results.

 

Best regards,

Jorge Belinha

Reviewer 2 Report

Comments and Suggestions for Authors

The author did not include the reviewer comment in the revised version.
The journal is called applied sciences not theoratical sciences. I would still recommend the experimental validation either from the literature or by the author himself.
Therefore, I can not accept it for publication

Author Response

Dear reviewer #2,

 

Thank you for your comments.

 

In your previous comments, the reviewer demanded an experimental test, arguing that this is an “Applied Sciences” journal.

I must counterpoint. This is a numerical paper. Programing mathematical formulations and developing new numerical methods for engineering is also “Applied Sciences”.

 

I do not have the means (funding) to perform experimental tests. Therefore, I will re-cap all the work presented here: In this numerical paper, the NNRPIM was extended for the first time to the analysis of sandwich beam with PUF foams considering a full multiscale analysis. The focus here is the NNRPIM and its numerical performance. Therefore, the FEM is applied as a comparison numerical technique and only the numerical issues are addressed and studied.

For comparison purposes it was used the FEM, with the same material properties, essential and natural boundary conditions and with the exact same geometric model (there is not a better comparison model). FEM is a well-known and trusted numerical method, if the results of a new numerical model are close to FEM, it is because the results are solid.

 

In this paper, for the first time, a natural neighbour meshless method (such as the NNRPIM) was combined with a full multiscale framework (capable of predicting the microscale homogenized mechanical properties of a PUF foam and then perform a macroscale structural analysis). This represents a novelty the meshless methods field (which is the main focus of this paper).

 

I must stress that this paper is not about FEM, is about the NNRPIM. FEM is only used for comparison proposes, and any experimental study is beyond the scope of the present work.

 

This work condenses a serious amount of work within the topic of meshless methods, in which the author programmed from scratch all the routines necessary to produce the documented results. The experimental validation/correlation is beyond the scope of the present study.

 

Best regards,

Jorge Belinha