# A CFD-FEA Method for Hydroelastic Analysis of Floating Structures

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## Abstract

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## 1. Introduction

## 2. Problem Statement and Method of Solution

#### 2.1. Problem Statement

#### 2.2. Coupling Approach

#### 2.3. Coordinate Systems

#### 2.4. Backbone Beam

#### 2.5. Section Loads Calculation

## 3. Numerical Modeling and Simulation

#### 3.1. Numerical Modeling

#### 3.2. Mesh Sensitivity Analysis

#### 3.3. The Influence of Shear Force along the Wetted Surface

## 4. Results and Discussion

#### 4.1. Numerical Results

#### 4.1.1. Wave Simulations

#### 4.1.2. Motions and Deformations of the Floating Body in Waves

#### 4.1.3. Wave Loads

#### 4.1.4. Fluid Pressure

#### 4.2. Validation of the Numerical Method

#### 4.2.1. Comparison with WADAM Numerical Results

#### 4.2.2. Comparison with COMPASS-WALCS-NE Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Andersen, I.M.V. Full Scale Measurements of the Hydro-Elastic Response of Large Container Ships for Decision Support. Ph.D. Thesis, Technical University of Denmark, Copenhagen, Denmark, 2014. [Google Scholar]
- Betts, C.V.; Bishop, R.E.D.; Prices, W.G. The symmetric generalized fluid forces applied to a ship in a seaway. Int. Shipbuild. Prog.
**1977**, 119, 265–278. [Google Scholar] - Wu, Y.S. Hydroelasticity of Floating Bodies. Ph.D. Thesis, Brunel University, Uxbridge, UK, 1984. [Google Scholar]
- Xie, H.; Liu, F.; Liu, X.Y.; Tang, H.Y. Numerical prediction of asymmetrical ship slamming loads based on a hybrid two-step method. Ocean Eng.
**2020**, 208, 107331. [Google Scholar] [CrossRef] - Jiao, J.L.; Huang, S.X. CFD simulation of ship seakeeping performance and slamming loads in bi-directional cross wave. J. Mar. Sci. Eng.
**2020**, 8, 312. [Google Scholar] [CrossRef] - Wang, S.; Soares, C.G. Slam induced loads on bow-flared sections with various roll angles. Ocean Eng.
**2013**, 67, 45–57. [Google Scholar] [CrossRef] - Huang, S.X.; Jiao, J.L.; Chen, C.H. CFD prediction of ship seakeeping behavior in bi-directional cross wave compared with in uni-directional regular wave. Appl. Ocean Res.
**2021**, 107, 102426. [Google Scholar] [CrossRef] - Jiao, J.L.; Huang, S.X.; Soares, C.G. Numerical simulation of ship motions in cross waves using CFD. Ocean Eng.
**2021**, 223, 108711. [Google Scholar] [CrossRef] - Moctar, O.E.; Oberhagemann, J.; Schellinf, T.E. Free surface RANS method for hull girder springing and whipping. Trans. Soc. Nav. Archit. Mar. Eng.
**2011**, 119, 48–66. [Google Scholar] - Oberhagemann, J. On Prediction of Wave-Induced Loads and Vibration of Ship Structures with Finite Volume Fluid Dynamic Methods. Ph.D. Thesis, University of Duisburg-Essen, Duisburg and Essen, Germany, 2016. [Google Scholar]
- Wilson, R.V.; Ji, L.; Karman, S.L.; Hyams, D.G.; Sreenivas, K.; Taylor, L.K.; Whitfield, D.L. Simulation of Large Amplitude Ship Motions for Prediction of Fluid-Structure Interaction. In Proceedings of the 27th Symposium on Naval Hydrodynamics, Seoul, Republic of Korea, 5–10 October 2008. [Google Scholar]
- Liu, Y.; Zhu, R.Q.; Cheng, Y.; Xie, T.; Li, R.Z. Numerical simulation of hydroelastic responses of floating structure based on CFD-FEM method. Ocean Eng.
**2020**, 38, 24–32. [Google Scholar] - Lakshmynarayanana, P.A.; Hirdaris, S. Comparison of nonlinear one- and two-way FFSI methods for the prediction of the symmetric response of a containership in waves. Ocean Eng.
**2020**, 203, 107179. [Google Scholar] [CrossRef] - Lakshmynarayanana, P.A.; Temarel, P. Application of a two-way partitioned method for predicting the wave-induced loads of a flexible containership. Appl. Ocean Res.
**2020**, 96, 102052. [Google Scholar] [CrossRef] - Jiao, J.L.; Huang, S.X.; Soares, C.G. Viscous fluid-flexible structure interaction analysis on ship springing and whipping responses in regular waves. J. Fluids Struct.
**2021**, 106, 103354. [Google Scholar] [CrossRef] - STAR-CCM+ Version 2020.1 Manual. 2020. Available online: https://support.sw.siemens.com/en-US/ (accessed on 1 October 2020).
- Abaqus 6.14-4 Manual. 2014. Available online: https://www.4realsim.com/abaqus/ (accessed on 1 November 2014).
- Park, J.C.L.; Kim, M.H.; Miyata, H. Three-dimensional numerical wave tank simulations on fully nonlinear wave-current-body interactions. J. Mar. Sci. Technol.
**2001**, 6, 70–82. [Google Scholar] [CrossRef][Green Version] - Li, H. 3-D hydroelasticity Analysis Method for Wave Load of Ship. Ph.D. Thesis, Harbin Engineering University, Harbin, China, 2009. (In Chinese). [Google Scholar]
- Dai, Y.S.; Shen, J.W.; Song, J.Z. Ship Wave Loads, 1st ed.; National Defense Industry Press: Beijing, China, 2007; pp. 154–196. (In Chinese) [Google Scholar]
- Sun, Z.; Liu, G.J.; Zou, L.; Zheng, H.; Djiddjeli, K. Investigation of Non-Linear Ship Hydroelasticity by CFD-FEM Coupling Method. J. Mar. Sci. Eng.
**2021**, 9, 511. [Google Scholar] [CrossRef] - Hirt, C.W.; Nichols, B.D. Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries. J. Comput. Phys.
**1981**, 39, 201–225. [Google Scholar] [CrossRef] - ITTC Procedures and Guidelines, 2011. Practical Guidelines for Ship CFD Applications. 7.5-03-02-03. Available online: https://ittc.info/media/1357/75-03-02-03.pdf (accessed on 1 August 2021).
- Ferziger, J.H.; Peric, M. Computational Methods for Fluid Dynamics, 3rd ed.; Springer: Berlin/Heidelberg, Germany, 2002; pp. 135–152. [Google Scholar]
- Lakshmynarayanana, P.A.; Temarel, P. Application of CFD and FEA coupling to predict dynamic behaviour of a flexible barge in regular head waves. Mar. Struct.
**2019**, 65, 308–325. [Google Scholar] [CrossRef][Green Version] - SESAM User Manual WADAM. 2017. Available online: https://www.dnv.com/services/frequency-domain-hydrodynamic-analysis-of-stationary-vessels-wadam-2412 (accessed on 10 November 2021).
- COMPASS-WALCS-N. 2015. Available online: https://www.ccs.org.cn/ccswz/articleDetail?id=201900001000007558&columnId=201900002000000599 (accessed on 12 December 2021).
- Zhang, K.H.; Ren, H.L.; Li, H.; Yan, L. Nonlinear Hydroelasticity of Large Container Ship. In Proceedings of the 26th International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–2 July 2016. [Google Scholar]
- Jiao, J.L.; Ren, H.L.; Adenya, C.A. Experimental and Numerical Analysis of Hull Girder Vibrations and Bow Impact of a Large Ship Sailing in Waves. Shock Vib.
**2015**, 2015, 10. [Google Scholar] [CrossRef][Green Version] - Xiao, W.; Wang, H.Y. Wave loads prediction of large scale new type ship. Ship Boat
**2017**, 167, 39–46. (In Chinese) [Google Scholar]

**Figure 5.**Micro-segment of backbone beam: (

**a**) vertical motion; (

**b**) horizontal motion; (

**c**) torsional motion.

**Figure 12.**Comparison of the results of three sets of meshes: (

**a**) heave of the single floating body; (

**b**) pitch of the single floating body.

**Figure 14.**Comparison of vertical bending moment time history of cross-section x = −75 m at wave height 16 m: (

**a**) comparison diagram; (

**b**) local enlarged diagram.

**Figure 15.**Comparison of vertical bending moment time history of cross-section x = 0 m at wave height 16 m: (

**a**) comparison diagram; (

**b**) zoom-in of the diagram.

**Figure 16.**(

**a**) Wave surface elevation of flow field; (

**b**) a close-up of the flow about the structure.

**Figure 17.**Wave surface elevation at different locations: (

**a**) 250 m in front of the bow of the floating body; (

**b**) 150 m in front of the bow of the floating body; (

**c**) 50 m in front of the bow of the floating body; (

**d**) 200 m to the left of the midship section of the floating body.

**Figure 18.**Rigid body displacements and elastic deformations: (

**a**) rigid body displacements and elastic deformations in the vertical direction; (

**b**) elastic deformations in the vertical direction.

**Figure 20.**Calculation results of vertical velocity and vertical bending moment: (

**a**) vertical velocity at the center of gravity of each section of the floating body; (

**b**) vertical bending moment at cross-section x = −75 m of the floating body; (

**c**) vertical bending moment at cross-section x = 0 m of the floating body; (

**d**) vertical bending moment at cross-section x = 75 m of the floating body.

**Figure 25.**Model of a single floating body: (

**a**) model for WADAM simulation; (

**b**) model for COMPASS-WALCS-NE simulation.

**Figure 26.**Numerical results of vertical bending moment: (

**a**) Comparison of numerical results of the amplitude of vertical bending moment at cross-section x = −75 m; (

**b**) comparison of numerical results of the amplitude of vertical bending moment at cross-section x = 0 m; (

**c**) comparison of numerical results of the amplitude of vertical bending moment at cross-section x = 75 m; (

**d**) nondimensionalized amplitude of vertical bending moment of each cross-section.

**Figure 27.**Comparison of vertical bending moment time history of the cross-section at wave height 12.5 m: (

**a**) cross-section x = −75 m; (

**b**) cross-section x = 0 m.

**Figure 28.**Comparison of vertical bending moment time history of cross-section at wave height 16 m: (

**a**) cross-section x = −75 m; (

**b**) cross-section x = 0 m.

Symbols | Units | Actual Value | Backbone Beam | Deviation | |
---|---|---|---|---|---|

Moment of inertia | ${I}_{y}$ | ${\mathrm{m}}^{4}$ | 2.61 | 2.60 | −0.30% |

Torsional moment of inertia | ${I}_{n}$ | ${\mathrm{m}}^{4}$ | 3.74 | 3.74 | 0.10% |

Vertical bending stiffness | $E{I}_{y}$ | $\mathrm{N}\cdot {\mathrm{m}}^{2}$ | 5.37 × 10^{11} | 5.35 × 10^{11} | −0.30% |

Longitudinal torsional stiffness | $G{I}_{n}$ | $\mathrm{N}\cdot {\mathrm{m}}^{2}$ | 2.96 × 10^{11} | 2.97 × 10^{11} | 0.10% |

Mesh | Minimum Size of Fluid Domain | Base Size of Structure Domain | Number of Meshes | ||
---|---|---|---|---|---|

x | y | z | |||

Mesh A | 1.56 m | 6.00 m | 6.00 m | 1.50 m | 0.8 million |

Mesh B | 0.78 m | 6.00 m | 6.00 m | 0.75 m | 1.5 million |

Mesh C | 0.24 m | 0.24 m | 0.24 m | 0.50 m | 5.2 million |

Wave Direction | Wave Length | Wave Period | Wave Height |
---|---|---|---|

Heading angle 180° | 300 m | 13.862 s | 2.5 m |

5.0 m | |||

7.5 m | |||

10.0 m | |||

12.5 m | |||

16.0 m |

No. of Fluid Pressure Monitoring Point | Location | Coordinates | ||
---|---|---|---|---|

x/m | y/m | z/m | ||

1a | Stern | −147.500 | 0.000 | 2.500 |

1b | −147.500 | 2.498 | 0.000 | |

1c | −147.500 | 2.155 | −2.500 | |

1d | −147.500 | 0.000 | −5.000 | |

2a | Midship | 0.000 | 0.000 | 2.500 |

2b | 0.000 | 2.498 | 0.000 | |

2c | 0.000 | 2.155 | −2.500 | |

2d | 0.000 | 0.000 | −5.000 | |

3a | Bow | 147.500 | 0.000 | 2.500 |

3b | 147.500 | 2.498 | 0.000 | |

3c | 147.500 | 2.155 | −2.500 | |

3d | 147.500 | 0.000 | −5.000 |

Wave Height/m | Method | Amplitude of Vertical Bending Moment ${\mathit{M}}_{\mathit{y}}$$/\mathbf{N}\xb7\mathbf{m}$ | ||
---|---|---|---|---|

x = −75 m | x = 0 m | x = 75 m | ||

2.5 | CFD-FEA | 1.052 × 10^{8} | 2.087 × 10^{8} | 1.096 × 10^{8} |

WADAM | 1.219 × 10^{8} | 2.286 × 10^{8} | 1.261 × 10^{8} | |

Deviation | −13.70% | −8.71% | −13.08% | |

5.0 | CFD-FEA | 1.741 × 10^{8} | 3.430 × 10^{8} | 1.663 × 10^{8} |

WADAM | 2.438 × 10^{8} | 4.573 × 10^{8} | 2.523 × 10^{8} | |

Deviation | −28.59% | −24.99% | −34.09% | |

7.5 | CFD-FEA | 2.355 × 10^{8} | 5.018 × 10^{8} | 2.381 × 10^{8} |

WADAM | 3.657 × 10^{8} | 6.859 × 10^{8} | 3.784 × 10^{8} | |

Deviation | −35.60% | −26.84% | −37.08% | |

10.0 | CFD-FEA | 2.373 × 10^{8} | 5.212 × 10^{8} | 2.622 × 10^{8} |

WADAM | 4.877 × 10^{8} | 9.145 × 10^{8} | 5.045 × 10^{8} | |

Deviation | −51.34% | −43.01% | −48.03% | |

12.5 | CFD-FEA | 3.326 × 10^{8} | 6.756 × 10^{8} | 3.307 × 10^{8} |

WADAM | 6.096 × 10^{8} | 1.143 × 10^{9} | 6.306 × 10^{8} | |

Deviation | −45.44% | −40.89% | −47.56% | |

16.0 | CFD-FEA | 4.742 × 10^{8} | 7.928 × 10^{8} | 3.315 × 10^{8} |

WADAM | 7.802 × 10^{8} | 1.463 × 10^{9} | 8.072 × 10^{8} | |

Deviation | −39.22% | −45.81% | −58.93% |

**Table 6.**Nondimensionalized amplitude of vertical bending moment of cross-section by CFD-FEA method.

Wave Height/m | ${\mathit{M}}_{\mathit{y}}/\left(\mathit{\rho}\mathit{g}\mathit{L}2\mathit{B}\mathit{h}\right)$ | ||
---|---|---|---|

Cross-Section x = −75 m | Cross-Section x = 0 m | Cross-Section x = 75 m | |

2.5 | 0.0093 | 0.0185 | 0.0097 |

5.0 | 0.0077 | 0.0152 | 0.0074 |

7.5 | 0.0069 | 0.0148 | 0.0070 |

10.0 | 0.0052 | 0.0115 | 0.0058 |

12.5 | 0.0059 | 0.0120 | 0.0059 |

16.0 | 0.0066 | 0.0110 | 0.0046 |

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## Share and Cite

**MDPI and ACS Style**

Gu, N.; Liang, D.; Zhou, X.; Ren, H. A CFD-FEA Method for Hydroelastic Analysis of Floating Structures. *J. Mar. Sci. Eng.* **2023**, *11*, 737.
https://doi.org/10.3390/jmse11040737

**AMA Style**

Gu N, Liang D, Zhou X, Ren H. A CFD-FEA Method for Hydroelastic Analysis of Floating Structures. *Journal of Marine Science and Engineering*. 2023; 11(4):737.
https://doi.org/10.3390/jmse11040737

**Chicago/Turabian Style**

Gu, Nan, Deli Liang, Xueqian Zhou, and Huilong Ren. 2023. "A CFD-FEA Method for Hydroelastic Analysis of Floating Structures" *Journal of Marine Science and Engineering* 11, no. 4: 737.
https://doi.org/10.3390/jmse11040737