# Numerical and Experimental Study on Trimaran Cross-Deck Structure’s Fatigue Characteristics Based on the Spectral Fatigue Method

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## Abstract

**:**

## 1. Introduction

## 2. Theory of Spectral Fatigue Analysis

#### 2.1. Fatigue Damage Equation for a Narrow Band Random Process

#### 2.2. Wide Band Rainflow Correction Factor

## 3. Structural Response Analysis

#### 3.1. FE Models

#### 3.2. Calculation of Wave Load and Stress Transfer Function

## 4. Experiments

#### 4.1. $S-N$ Curve

#### 4.2. Maximum Likelihood Method

#### 4.2.1. Maximum Likelihood Method of Mean $S-N$ Curve

#### 4.2.2. Maximum Likelihood Method of $P-S-N$ Curve

#### 4.3. Full-Scale Model Design

#### 4.4. Fatigue Tests

#### 4.5. Fatigue Test Results

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Armstrong, T. On the performance of a large high-speed trimaran. J. Mech. Eng. Aus.
**2006**, 3, 123–132. [Google Scholar] [CrossRef] - Fang, M.C.; Chen, T.Y. A parametric study of wave loads on trimaran ships traveling in waves. Ocean Eng.
**2008**, 35, 749–762. [Google Scholar] [CrossRef] - Wang, S.M.; Ma, S.; Duan, W.Y. Seakeeping optimization of trimaran outrigger layout based on NSGA-II. Appl. Ocean Res.
**2018**, 78, 110–122. [Google Scholar] [CrossRef] - Lloyd’s Register. Rules for the Classification of Trimarans; Lloyd’s Register: Britain, UK, 2006. [Google Scholar]
- Cui, W. A state of the art review on fatigue life prediction methods for metal structures. J. Mar. Sci. Technol.
**2002**, 7, 43–56. [Google Scholar] [CrossRef] - Fricke, W.; von Lilienfeld-Toal, A.; Paetzold, H. Fatigue strength investigations of welded details of stiffened plate structures in steel ships. Int. J. Fatigue
**2011**, 34, 17–26. [Google Scholar] [CrossRef] - Bai, Y. Marine Structural Design; Elsevier Science: Amsterdam, The Netherlands, 2003; pp. 363–371. [Google Scholar]
- Det Norske Veritas. Fatigue Assessment of Ship Structures; Det Norske Veritas: Oslo, Norway, 2010. [Google Scholar]
- Fricke, W.; Cui, W.; Kierkegaard, H.; Kihl, D.; Koval, M.; Mikkola, T.; Parmentier, G.; Toyosada, M.; Yoon, J.-H. Comparative fatigue strength assessment of a structural detail in a containership using various approaches of classification societies. Mar. Struct.
**2002**, 15, 1–13. [Google Scholar] [CrossRef] - Lotsberg, I. Assessment of fatigue capacity in the new bulk carrier and tanker rules. Mar. Struct.
**2006**, 19, 83–96. [Google Scholar] [CrossRef] - ISSC Committee Report. Fatigue and Fracture. In Proceedings of the 17th International Offshore and Ship Structures Congress, Seoul, Korea, 16–21 August 2009. [Google Scholar]
- Wirsching, P.H.; Light, M.C. Fatigue under wide band random stresses. ASCE J. Struct. Div.
**1980**, 106, 1593–1607. [Google Scholar] - ABS. Guidance Notes on Spectral-Based Fatigue Analysis for Vessels; American Bureau of Shipping: Houston, TX, USA, 2004. [Google Scholar]
- Li, Z. A comparison of direct calculation approaches applied on the fatigue strength assessment of a panamax container ship. In Proceedings of the ASME 31th International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil, 10–15 June 2012. [Google Scholar]
- Wang, Y.G. Spectral fatigue analysis of a ship structural detail—A practical case study. Int. J. Fatigue
**2010**, 32, 310–317. [Google Scholar] [CrossRef] - Nguyen, K.T.; Garbatov, Y.; Guedes Soares, C. Spectral fatigue damage assessment of tanker deck structural detail subjected to time-dependent corrosion. Int. J. Fatigue
**2013**, 48, 147–155. [Google Scholar] [CrossRef] - Kukkanen, T.; Mikkola, T.P.J. Fatigue assessment by spectral approach for the ISSC comparative study of the hatch cover bearing pad. Mar. Struct.
**2004**, 17, 75–90. [Google Scholar] [CrossRef] - Xue, J.; Pittaluga, A.; Cervetto, D. Fatigue damage calculation for oil tanker and container ship structures. Mar. Struct.
**1994**, 7, 499–535. [Google Scholar] [CrossRef] - Peng, Y.H.; Liu, J.H.; Wang, F.H. Fatigue assessment and analysis of trimaran structure. Shipbuild. China
**2011**, 52, 25–35. [Google Scholar] - Lotsberg, I.; Landet, E. Fatigue capacity of side longitudinals in floating structures. Mar. Struct.
**2005**, 18, 25–42. [Google Scholar] [CrossRef] - Fricke, W.; Paetzold, H. Full-scale fatigue tests of ship structures to validate the S–N approaches for fatigue strength assessment. Mar. Struct.
**2010**, 23, 115–130. [Google Scholar] [CrossRef] - Ren, H.L.; Ma, K.K.; Li, C.F.; Zhang, Z.; Xu, W.; Feng, G. Design analysis and fatigue testing of the typical structural details of aluminium ships. In Proceedings of the ASME 37th International Conference on Ocean, Offshore and Arctic Engineering, Madrid, Spain, 17–22 June 2018. [Google Scholar]
- Longuet-Higgins, M.S. On the joint distribution of wave periods and amplitudes in a random wave field. Proc. R. Soc. Lond.
**1983**, 389, 241–258. [Google Scholar] [CrossRef] - Ren, H.L.; Zhen, C.B.; Li, C.F.; Feng, G. Study on structural form design of trimaran cross-deck. In Proceedings of the ASME 31th International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil, 10–15 June 2012. [Google Scholar]
- China Classification Society. Guidelines of Small Waterplane area Twin Hull Craft; China Communication Press: Beijing, China, 2005. [Google Scholar]

**Figure 1.**(

**a**) The whole finite element (FE) model and details (

**b**) Detail 1, (

**c**) Detail 2, and (

**d**) Detail 3.

**Figure 3.**Stress transfer function as follows: (

**a**) Hot spot 1, (

**b**) hot spot 2, (

**c**) hot spot 3, (

**d**) hot spot 4, (

**e**) hot spot 5, (

**f**) hot spot 6, and (

**g**) hot spot 7.

**Figure 4.**Scope of full-scale models as follows: (

**a**) Detail 2, (

**b**) Model 1, (

**c**) Detail 1, and (

**d**) Model 2.

**Figure 7.**The damage graphs of fatigue test models as follows: (

**a**) Damaged position of model 1; (

**b**) Damaged position of model 2; (

**c**) Damaged detail of model 1; and (

**d**) Damaged detail of model 2.

**Figure 9.**Wave scatter diagrams as follows: (

**a**) World Wide Trade, (

**b**) Northwest Pacific, and (

**c**) China Coast.

**Figure 10.**Results of fatigue damage calculation as follows: (

**a**) Hot spot 1, (

**b**) hot spot 2, (

**c**) hot spot 3, (

**d**) hot spot 4, (

**e**) hot spot 5, (

**f**) hot spot 6, and (

**g**) hot spot 7.

**Figure 11.**Compared results of fatigue damage as follows: (

**a**) Hot spot 1 of model 2 and (

**b**) hot spot 4 of model 1.

Item | Unit | Value |
---|---|---|

Length overall | m | 75.0 |

Breadth | m | 15.0 |

Depth | m | 6.0 |

Displacement | t | 650.0 |

Block coefficient of main hull | 0.550 | |

Block coefficient of side hull | 0.420 |

Model | S (MPa) | N (10^{4}) | $\mathbf{lg}\mathit{S}$ | $\mathbf{lg}\mathit{N}$ |
---|---|---|---|---|

Model 1-1 | 243.40 | 14.25 | 2.39 | 5.15 |

Model 1-2 | 232.67 | 15.22 | 2.37 | 5.18 |

Model 1-3 | 170.72 | 40.51 | 2.23 | 5.61 |

Model 1-4 | 167.25 | 28.50 | 2.22 | 5.45 |

Model 1-5 | 164.28 | 27.59 | 2.22 | 5.44 |

Model 1-6 | 138.12 | 144.51 | 2.14 | 6.16 |

Model 2-1 | 209.83 | 18.10 | 2.32 | 5.26 |

Model 2-2 | 178.85 | 33.55 | 2.25 | 5.53 |

Model 2-3 | 150.05 | 80.25 | 2.18 | 5.90 |

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**MDPI and ACS Style**

Zhen, C.; Feng, G.; Wang, T.; Yu, P.
Numerical and Experimental Study on Trimaran Cross-Deck Structure’s Fatigue Characteristics Based on the Spectral Fatigue Method. *J. Mar. Sci. Eng.* **2019**, *7*, 62.
https://doi.org/10.3390/jmse7030062

**AMA Style**

Zhen C, Feng G, Wang T, Yu P.
Numerical and Experimental Study on Trimaran Cross-Deck Structure’s Fatigue Characteristics Based on the Spectral Fatigue Method. *Journal of Marine Science and Engineering*. 2019; 7(3):62.
https://doi.org/10.3390/jmse7030062

**Chicago/Turabian Style**

Zhen, Chunbo, Guoqing Feng, Tianlin Wang, and Pengyao Yu.
2019. "Numerical and Experimental Study on Trimaran Cross-Deck Structure’s Fatigue Characteristics Based on the Spectral Fatigue Method" *Journal of Marine Science and Engineering* 7, no. 3: 62.
https://doi.org/10.3390/jmse7030062