# Hydrodynamic and Structural Optimization of a Truss-Floating Aquaculture Vessel

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## Abstract

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## 1. Introduction

## 2. Numerical Methods

#### 2.1. Hybrid Hydrodynamic Model

#### 2.1.1. Potential-Flow Approach

#### 2.1.2. Morison Equation

#### 2.2. Multiobjective Optimization Model

#### 2.2.1. Adaptive Simulated Annealing Algorithm

#### 2.2.2. Multi-Island Genetic Algorithm

## 3. Hydrodynamic Loads and Structural Strength Analysis

#### 3.1. Particulars of the Aquaculture Vessel

#### 3.2. Hydrodynamic Load Analysis

#### 3.3. Structural Strength Analysis

## 4. Optimization Study

#### 4.1. Sensitivity Analysis of Structural Parameters

#### 4.2. Structural Optimization

#### 4.2.1. Results of the Adaptive Simulated Annealing Algorithm

#### 4.2.2. Results of the Multi-Island Genetic Algorithm

#### 4.2.3. Comparison of ASA and MIGA Solutions

## 5. Conclusions

- The hydrodynamic calculations accurately assess the bending moments and torques induced by waves, which are notably lower for the truss-floating tank aquaculture vessel due to its light weight and water-permeable nature compared with conventional ships.
- Under the most severe wave conditions, critical stress areas are identified at the joint between the left and right longitudinal trusses and the central beam. The maximum deformation is observed under the highest wave torque. Therefore, particular attention should be given to addressing torsional challenges when navigating oblique waves for this type of vessel.
- Different positions and sizes of beam members in the truss structure undergo a buckling strength check. The outcomes reveal that the 12 mm and 8 mm components at the connection between the left and right longitudinal trusses and the central beam have either exceeded or nearly reached the safe limits, suggesting potential buckling failure. Consequently, the ship’s structure is optimized based on these findings.
- The sensitivity analysis identifies the sensitive and nonsensitive components. Strengthening sensitive components and reducing the nonsensitive ones can enhance structural strength or reduce vessel weight.
- The optimization process reveals that MIGA appears slightly superior to the ASA algorithm, albeit at the cost of increased computational time. As a result, an efficient approach would involve an initial rough optimization using ASA to quickly assess optimal configurations, followed by the application of the more time-consuming MIGA method for fine-tuning.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Finite element structural model of the whole ship (

**left**), along with the Morison model of the central truss and net (

**right**).

**Figure 7.**Vertical bending moments and wave torques corresponding to each section: (

**a**) Bending moment. (

**b**) Torque.

**Figure 8.**Check of the buckling strength of central truss beam members: (

**a**) Tensile stress check. (

**b**) Compressive stress check.

**Figure 9.**Variable positions for the two truss types: (

**a**) left and right stringer, (

**b**) crossbeam, and (

**c**) dimensions of the structural components.

**Figure 10.**Sensitivity analysis of the design variables in terms of (

**a**) max combined beam stress, (

**b**) max deformation, and (

**c**) mass.

**Figure 11.**Iterative process of optimization based on ASA: (

**a**) Iterative process for bending stress. (

**b**) Iterative process for deformation. (

**c**) Iterative process for total weight. (

**d**) Iterative process for design feasibility.

**Figure 12.**Iterative process of optimization based on MIGA: (

**a**) Iterative process for bending stress. (

**b**) Iterative process for deformation. (

**c**) Iterative process for total weight. (

**d**) Iterative process for design feasibility.

Property | ${\mathit{L}}_{\mathit{pp}}$ | ${\mathit{B}}_{\mathit{wl}}$ | ${\mathit{D}}_{\mathit{m}}$ | ${\mathit{T}}_{\mathit{m}}$ |
---|---|---|---|---|

Value | 129.00 m | 40.00 m | 11.20 m | 10.00 m |

Condition | Displacement (t) | Bow Draft (m) | Stern Draft (m) | Wave Height (m) | Wave Direction (°) |
---|---|---|---|---|---|

Towing | 2182.6 | 6.834 | 8.166 | 0.5, 1, 1.5, 2, 2.5 | 0, 30, 60, 90, 120, 150, 180 |

Breeding | 2819.6 | 10.003 | 10.017 | 2.5, 3, 3.5, 4, 4.5 | 0, 30, 60, 90, 120, 150, 180 |

Condition | Serial Number | Main Load Parameters | Station |
---|---|---|---|

Towing | 1-1 | Vertical bending moment | Sect11 |

1-2 | $L/4$ torque | Sect06 | |

1-3 | $3L/4$ torque | Sect16 | |

Breeding | 2-1 | Vertical bending moment | Sect11 |

2-2 | $L/4$ torque | Sect06 | |

2-3 | $3L/4$ torque | Sect16 |

Condition | Load Parameters | Wave Direction (deg) | Angular Frequency (rad/s) | Phase (deg) |
---|---|---|---|---|

L1-1 | Vertical bending moment | 180 | 1.309 | 55.058 |

L1-2 | $1/4L$ torque | 150 | 1.282 | −19.969 |

L1-3 | $3/4L$ torque | 150 | 1.296 | −42.001 |

L2-1 | Vertical bending moment | 180 | 1.093 | 37.087 |

L2-2 | $1/4L$ torque | 150 | 1.122 | −6.054 |

L2-3 | $3/4L$ torque | 120 | 0.974 | −63.825 |

Condition | Max. Wave | Axial Stress (MPa) | Bending Stress (MPa) | Shear Stress | Deformation | ||
---|---|---|---|---|---|---|---|

Load (N.m) | Tensile | Compressive | Tensile | Compressive | (MPa) | (mm) | |

Max. vertical bending moment | $3.48\times {10}^{7}$ | 191 | 167 | 147 | 147 | 74.3 | 67.8 |

Max. torque | $1.89\times {10}^{7}$ | 180 | 230 | 180 | 163 | 98.1 | 88.9 |

Truss Type and Location | Stringer | Crossbeam | Diameter (m) | Thickness (mm) |
---|---|---|---|---|

Top main beam | Sect200 | Sect212 | 0.38 | 12 |

Middle main beam | Sect201 | Sect213 | 0.38 | 12 |

Bottom main beam | Sect202 | Sect214 | 0.38 | 12 |

Top-middle truss connecting diagonal brace | Sect203 | Sect215 | 0.27 | 10 |

Bottom-middle truss connecting diagonal brace | Sect204 | Sect216 | 0.27 | 10 |

Top-middle truss connecting vertical brace | Sect205 | Sect217 | 0.27 | 10 |

Bottom-middle truss connecting vertical brace | Sect206 | Sect218 | 0.27 | 10 |

Top main beam connecting crossbar | Sect207 | Sect219 | 0.22 | 8 |

Top main beam connecting diagonal bar | Sect208 | Sect220 | 0.22 | 8 |

Middle main beam connecting crossbar | Sect209 | Sect221 | 0.22 | 8 |

Bottom main beam connecting crossbar | Sect210 | Sect222 | 0.22 | 8 |

Bottom main beam connecting diagonal bar | Sect211 | Sect223 | 0.22 | 8 |

Original (mm) | Attribute | ASA opt. (mm) | MIGA opt. (mm) | Attribute | ASA opt. (mm) | MIGA opt. (mm) |
---|---|---|---|---|---|---|

12 | Sect200 | 14 | 13 | Sect212 | 14 | 14 |

12 | Sect201 | 10 | 10 | Sect213 | 10 | 10 |

12 | Sect202 | 12 | 11 | Sect214 | 6 | 8 |

8 | Sect208 | 9 | 9 | Sect220 | 9 | 9 |

8 | Sect209 | 6 | 7 | Sect221 | 7 | 6 |

8 | Sect210 | 6 | 6 | Sect222 | 6 | 6 |

8 | Sect211 | 6 | 7 | Sect223 | 9 | 7 |

Property | Original | ASA opt. | Reduction Ratio | MIGA opt. | Reduction Ratio |
---|---|---|---|---|---|

Bending stress (MPa) | 179.92 | 171.70 | −4.5% | 168.26 | −6.4% |

Deformation (mm) | 88.89 | 86.31 | −2.9% | 85.04 | −4.3% |

Total weight (t) | 1227.80 | 1213.70 | −1.15% | 1207.33 | −1.67% |

Parameters | Original | ASA opt. | MIGA opt. |
---|---|---|---|

Buckling utilization factor for tension bending | 1.13 | 0.95 | 0.92 |

Buckling utilization factor for compression bending | 1.04 | 0.91 | 0.87 |

Yield utilization factor | 0.84 | 0.82 | 0.79 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Zhang, J.; Jiang, C.; Zhang, Z.; Xu, P.; Zhang, Y.
Hydrodynamic and Structural Optimization of a Truss-Floating Aquaculture Vessel. *J. Mar. Sci. Eng.* **2023**, *11*, 2385.
https://doi.org/10.3390/jmse11122385

**AMA Style**

Zhang Y, Zhang J, Jiang C, Zhang Z, Xu P, Zhang Y.
Hydrodynamic and Structural Optimization of a Truss-Floating Aquaculture Vessel. *Journal of Marine Science and Engineering*. 2023; 11(12):2385.
https://doi.org/10.3390/jmse11122385

**Chicago/Turabian Style**

Zhang, Yuchen, Ji Zhang, Changqing Jiang, Zhaode Zhang, Peng Xu, and Yuan Zhang.
2023. "Hydrodynamic and Structural Optimization of a Truss-Floating Aquaculture Vessel" *Journal of Marine Science and Engineering* 11, no. 12: 2385.
https://doi.org/10.3390/jmse11122385