On the Optimal Design of Steel Shells with Technological Constraints

Round 1

Reviewer 1 Report

The article is clearly laid out. All key elements are clearly presented: abstract, introduction, methodology, results, and conclusions.

The title clearly describes the content of the article.

The authors focus their work on the minimization of the cost variable, which they link directly in this case to the minimization of volume. The simplification made is understandable, although the real cases present a large number of additional variables (stiffeners, etc.) which suggests that this hypothesis can be explained in greater detail in the article.

Ideally, the results obtained should be compared with other available numerical work or, ideally, with experiments.

There are several editing errors in the body of the article.

Author Response

Dear reviewer,

I am grateful to you for giving us very useful suggestions and remarks, which contributed to the improvement of our manuscript. Your suggestion regarding additional variables (stiffeners) is quite appropriate. Plans for our new research include shells with stiffeners (page 16, line 408).

For further clarification, the function C is precisely defined.

By choosing the specific price to be c = e, the function C is reduced to the volume of the shell (see page 5, line 136).

In Example 1, we illustrated the results of the minimum ring thicknesses e₁ and e₂ in units, i.e. mm (page 13, line 284).

In the Introduction (page 2, line 45), the reasons why technological constrains are introduced in certain cases are further explained.

Two more recent journal paper references have been added.

With the best regards,

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper „On the optimal design of steel shells with technological constraints” by Turnić et al. is an article that highlights important issues. The manuscript contains valuable scientific content and should be published after considering the following comments:

• The authors concluded that objective function is cost C, but according to optimization theory, cost is an optimization criterion that will be obtained as a minimization (or maximization) of an objective function, which in my opinion is not precisely defined here. A scientific article should contain all the information clearly and unambiguously in order to be able to repeat the considerations presented in the manuscript. The objective function adopted in the optimization process should be clearly indicated.
• As the authors generally adopt certain values, e.g. "yield stress of steel is s 0 = 235MPa", they should adopt, for example, a specific material and provide its basic properties.
• In the chart - Figure 6, the values on the X-axis have incorrect decimal separators, commas are used instead of dots.
• The paper presents a proposal of an optimization algorithm, but in order to prove that the proposed model is correct, it would be necessary to validate the model with real conditions, at least in a basic way, that is, in my opinion, there is a significant lack of this manuscript.
• Calculation examples should be performed for specific quantities, and therefore the results should contain units.
• In the adopted model, not all technological limitations are fully clear.
• Conclusions are too general. It is necessary to compare results obtained with results from references.
• Conclusions should contain plans for further research.
• Old references should be replaced by more recent journal paper references.
• The formatting does not fully comply with the guidelines imposed by the journal.
• Generally, the language needs revision.

Author Response

Dear reviewer,

Thank you very much once again, for giving us very useful suggestions and remarks which is in order to improve our manuscript.

We have now precisely defined the objective function C. The cost C is a function that contains design variables, shell thicknesses of the rings, e_i. By choosing the specific cost to be c_i= e_i, the function C is reduced to the volume of the shell that needs to be minimised. The numbers of design variables can also be increased, for example, when the shell has the stiffeners etc. (see page 5, line 136).

In this manuscript, our aim was not to fully adopt the properties of the material. The results obtained are presented through the dimensionless quantities. In the numerical example 1, for the yield stress of steel (σ_o= 235 Mpa) and radius (R= 2 m) of the shell, the optimal dimensions of the ring thicknesses in units are shown (page 13, line 284). Our plans for further research are to conduct an experiment of optimal plastic design of shells where the properties will be adopted.

In the chart- Figure 6, the decimal separators of the values on the X- axis are corrected.

The numerical procedure solves a system of seven, that is, three nonlinear equations. In the procedure it is shown how with the knowledge of the mechanical- physical part of the problem, numerical solution can be facilitated. Thus, for example, we use a linear relationship between the plasticity moments of two rings over the variable ξ, knowing that it is in the interval (0<ξ<1).

Also, for the initial values ​​for ring thicknesses in the iterative procedure, we start from a sufficiently small value close to zero because it is the minimum volume.

 In the theoretical part, section 3, technological constrains are given and they are covered in optimum conditions. In the Introduction (page 2, line 45) we have further clarified the reasons why technological constrains are introduced in certain cases. In the examples in section 5, for shells with their boundary conditions, it is sufficient only that the technological conditions are taken i.e. that the shell is composed of rings and the basic assumptions are not violated.

 In the conclusions, a section related to further research plans has been added (page 16, line 408).

Two more recent journal paper references have been added. Due to adequate citations related to basic theoretical parts, it is difficult to replace old references.

Figure 4 has been slightly modified (page 5, line 138).

Text (page 15, line 138) is deleted.

With the best regards,

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors supplemented the manuscript, taking into account my previous comments, therefore I recommend the article for publication in its current form.