# Material Cost Minimization Method of the Ship Structure Considering Material Selection

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optimization Algorithm

#### 2.1. Material Selection Strategy

_{1}) based on the original material thickness (t

_{0}) and the ratio of material prices (c

_{1}/c

_{0}) between the original and substitute materials. The equation implies that the thickness of the substitute material can be adjusted to maintain the same total material cost, even if the cost per unit thickness of the substitute material is different from that of the original material.

#### 2.2. Size Optimization

#### 2.3. Optimization Process

#### 2.4. Genetic Algorithm

## 3. Case Study

#### 3.1. Model

#### 3.2. Design Variables

_{i}) and the plate thickness (t

_{i}). Three material types were chosen from a pool of commonly used configurations in the shipyard industry, as shown in Table 4.

#### 3.3. Constraints

^{2}for MS, 315 N/mm

^{2}for HT32, and 355 N/mm

^{2}for HT36. Finally, in Equation (9), ${\sigma}_{sh}$ refers to the shear stress on the structure.

- ${F}_{p}$: factor for combined membrane and bending response (1.50 in general);
- s: stiffener spacing (mm);
- p: pressure (N/mm
^{2}); - ${\sigma}_{a}$: allowable stress (N/mm
^{2}).

#### 3.4. Objective Function

- L
_{x}= width or length in x-direction (mm); - L
_{y}= width or length in y-direction (mm); - ρ = material density (kg/mm
^{3}); - t
_{i}= plate thickness (mm); - C
_{i}= material price (¥/kg).

## 4. Result and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Parameter | Previous Method | Proposed Method |
---|---|---|

Plate Material | Genetic Algorithm | Upgrade Method |

Plate Thickness | Size Optimization |

Price No. | Yield Strength [N/mm^{2}] | Material Cost [\/kg] | Cost Effectiveness Score | Cost Effectiveness Rank | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

HT36 | HT32 | MS | HT36 | HT32 | MS | HT36 | HT32 | MS | High | Medium | Low | |

1 | 355 | 315 | 235 | 90 | 80 | 60 | 3.944 | 3.938 | 3.917 | HT36 | HT32 | MS |

2 | 90 | 85 | 80 | 3.944 | 3.706 | 2.938 | HT36 | HT32 | MS | |||

3 | 90 | 75 | 60 | 3.944 | 4.200 | 3.917 | HT32 | HT36 | MS | |||

4 | 90 | 75 | 50 | 3.944 | 4.200 | 4.700 | MS | HT32 | HT36 | |||

5 | 90 | 90 | 90 | 3.944 | 3.500 | 2.611 | HT36 | HT32 | MS |

Item | Unit | 1st Model | 2nd Model | 3rd Model |
---|---|---|---|---|

L (length) | Mm | 18,030 | 9462 | 9462 |

W (width) | Mm | 7475 | 4970 | 5705 |

H (height) | Mm | 800 | 815 | 815 |

Load | N/mm^{2} | 0.0343 | 0.0343 | 0.0343 |

Initial material type | - | MS, HT32, HT36 | MS, HT32 | MS, HT32 |

Density | kg/m^{3} | 7800 | 7800 | 7800 |

Plate number | 16 | 20 | 18 |

Material Type | Young Modulus (N/mm^{2}) | Density (kg/m^{3}) | Poisson Ratio | Yield Strength (N/mm^{2}) |
---|---|---|---|---|

MS | 200,000 | 7800 | 0.3 | 235 |

HT32 | 200,000 | 7800 | 0.3 | 315 |

HT36 | 200,000 | 7800 | 0.3 | 355 |

Parameter | |
---|---|

Max. Generation | 50 |

Population size | 200 |

Mutation rate | 0.1 |

Random seed | 0 |

Proposed Method (Hour) | GA (Hour) | |
---|---|---|

1st model | 0.06 | >3.0 |

2nd model | 0.22 | >13.0 |

3rd model | 0.12 | >7.0 |

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**MDPI and ACS Style**

Putra, G.L.; Kitamura, M.
Material Cost Minimization Method of the Ship Structure Considering Material Selection. *J. Mar. Sci. Eng.* **2023**, *11*, 640.
https://doi.org/10.3390/jmse11030640

**AMA Style**

Putra GL, Kitamura M.
Material Cost Minimization Method of the Ship Structure Considering Material Selection. *Journal of Marine Science and Engineering*. 2023; 11(3):640.
https://doi.org/10.3390/jmse11030640

**Chicago/Turabian Style**

Putra, Gerry Liston, and Mitsuru Kitamura.
2023. "Material Cost Minimization Method of the Ship Structure Considering Material Selection" *Journal of Marine Science and Engineering* 11, no. 3: 640.
https://doi.org/10.3390/jmse11030640