Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics

Round 1

Reviewer 1 Report

I think that the topic and research you have conducted is really interesting. However, I asked for major revision for your work due to two main reasons. The first one is what I think it is incorrect Taylor expansion in Eq. (2) which can affect all derivation of other equations. I know that might be a typo, but I had to be so careful about this point.  Second, the issue related to the computational cost as you can see in my review report.

However, asking for major revision does not mean that I underestimate your work. I still appreciate the effort you did, and I think that your results deserve to be published after the modifications I mentioned in my review report.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Title: Review of "Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics"

1.       Could the authors revisit the introduction to provide a more structured overview of the problem statement?

2.       Would the authors please double check the manuscript for any typographical or grammatical errors?

3.       Can the authors review the English structure of the article, including punctuation, semicolons, and other structures?

4.       Could the authors consider improving the alignment of mathematical expressions for better clarity and readability?

5.       How does the novel approach introduced in the article differ from traditional methods in simulating and analyzing elastostatics?

6.       What are the key findings or results of the numerical simulations presented in the article?

7.       Additionally, I strongly recommend the authors to enhance the References section by including articles that utilize advanced simulation methods:

 https://doi.org/10.1016/j.cma.2009.12.001  https://doi.org/10.1016/j.rinp.2023.106938    https://doi.org/10.1016/j.compstruc.2020.106246

These articles will complement the current literature and provide additional insights into advanced simulation methods.

Overall, the paper contributes some insights into numerical simulation methods for elastostatics and provides a promising avenue for addressing complex engineering problems. With revisions and responses to the questions raised, the manuscript has the potential to contribute to the field.

Average. Authors should review the English structure of the article

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you for the time you spent to follow my comments. I hope my comments helped you to increase the quality of your paper. 

Regarding the low computational cost of your numerical experiments, I would recommend you to treat different problems in future in which the execution time last for many hours. In my opinion, this is more plausible way to compare the computational cost of the numerical methods. I am not sure how you can do that in your problems, but for example increasing the number of nodes can be one possibility.

Wish you the best in your future work.

Author Response

Thank you very much for your advice. We increased the number of nodes to better measure the cost of computing.