The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy
Abstract
:1. Introduction
2. Theoretical Backgrounds of the Proposed Method
2.1. Moored Floating Structure Architecture
2.2. Mechanical Energy Induced by Quasi-Static Forces
2.3. Minimization of Mechanical Energy
3. Validation and Case Studies
3.1. The Suspended Mooring Line
3.2. The WindFloat 2 Floating Platform
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Value |
---|---|
Size of the population | 60 |
Number of generations | 200 |
Crossover type | Multi-point |
Crossover probability | 0.5 |
Mutation probability | 0.5 |
Elite count | 2 |
Tolerance | 1 × 10−6 |
Items | Unit | Value |
---|---|---|
Unstretched length | m | 473.30 |
Line diameter | m | 0.0809 |
Line density | kg/m | 130.40 |
Cross-sectional area (A) | m2 | 0.0051 |
Young’s modulus (E) | Pa | 1.15 × 1011 |
Line stiffness (EA) | N/m | 1.25 × 106 |
Drag tangent coefficient | -/- | 1.00 |
Drag normal coefficient | -/- | 0.03 |
Items | Quasi-Static Forces | Mechanical Energy |
---|---|---|
Case I | and | |
Case II | , and | |
Case III | , and (1.7 m/s) | |
Case IV | , , and (1.7 m/s) |
Items | Unit | Value | Items | Unit | Value |
---|---|---|---|---|---|
Mass | kg | 6.927 × 106 | Drag tangent coefficient | -/- | 1.000 |
Displacement | m3 | 6951.8 | Drag normal coefficient | -/- | 0.025 |
Coord. for COM | m | (0.0, 0.0, −9.0) | Coord. for fairlead point #1 | m | (30.43, 0.0, −18.0) |
Roll inertia for COM | kg-m2 | 4.747 × 109 | Coord. for fairlead point #2 | m | (−15.21, 26.35, −18.0) |
Pitch inertia for COM | kg-m2 | 4.747 × 109 | Coord. for fairlead point #3 | m | (−15.21, −26.35, −18.0) |
Yaw inertia for COM | kg-m2 | 6.722 × 109 | Coord. for anchor point #1 | m | (680.43, 0.0, 0.0) |
Unstretched length | m | 650.0 | Coord. for anchor point #2 | m | (−340.21, 589.27, 0.0) |
Line diameter | m | 0.14142 | Coord. for anchor point #3 | m | (−340.21, −589.27, 0.0) |
Line density | kg/m | 199.0 | |||
Axial stiffness | N | 8.54 × 108 |
Items | Current Direction (°) | |||
---|---|---|---|---|
Case I | 55 | 1025 | None | None |
Case II | 1.7 | 0.0 | ||
Case III | 45.0 | |||
Case IV | 90.0 | |||
Case V | 180.0 |
Translation along Axial () | Translation along Axial () | Translation along Axial () | |||||||
AQWA | Proposed | Error (%) | AQWA | Proposed | Error (%) | AQWA | Proposed | Error (%) | |
Case I | 0.000 | 0.000 | 0.00 | 0.000 | 0.000 | 0.00 | −9.580 | −9.601 | 0.22 |
Case II | 0.320 | 0.342 | 6.88 | 0.000 | 0.000 | 0.00 | −9.590 | −9.594 | 0.04 |
Case III | 0.230 | 0.211 | −8.26 | 0.250 | 0.232 | −7.20 | −9.590 | −9.584 | 0.10 |
Case IV | 0.030 | 0.034 | 6.67 | 0.330 | 0.345 | 4.55 | −9.590 | −9.600 | −0.06 |
Case V | −0.340 | −0.352 | 3.53 | 0.000 | 0.000 | 0.00 | −9.590 | −9.599 | −0.01 |
Rotation about Axial (o) | Rotation about Axial (o) | Rotation about Axial (o) | |||||||
AQWA | Proposed | Error (%) | AQWA | Proposed | Error (%) | AQWA | Proposed | Error (%) | |
Case I | 0.000 | 0.000 | 0.00 | 0.000 | 0.000 | 0.00 | 0.000 | 0.000 | 0.00 |
Case II | 0.000 | 0.000 | 0.00 | 0.050 | 0.053 | 6.00 | 0.000 | 0.000 | 0.00 |
Case III | −0.030 | −0.021 | −30.00 | 0.030 | 0.026 | −13.33 | −0.150 | −0.132 | −12.00 |
Case IV | −0.050 | −0.058 | 16.00 | 0.000 | 0.000 | 0.00 | 0.210 | 0.254 | 11.43 |
Case V | 0.000 | 0.000 | 0.00 | −0.050 | −0.054 | 8.00 | 0.000 | 0.000 | 0.00 |
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Li, C.B.; Chen, M.; Choung, J. The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy. J. Mar. Sci. Eng. 2021, 9, 960. https://doi.org/10.3390/jmse9090960
Li CB, Chen M, Choung J. The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy. Journal of Marine Science and Engineering. 2021; 9(9):960. https://doi.org/10.3390/jmse9090960
Chicago/Turabian StyleLi, Chun Bao, Mingsheng Chen, and Joonmo Choung. 2021. "The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy" Journal of Marine Science and Engineering 9, no. 9: 960. https://doi.org/10.3390/jmse9090960
APA StyleLi, C. B., Chen, M., & Choung, J. (2021). The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy. Journal of Marine Science and Engineering, 9(9), 960. https://doi.org/10.3390/jmse9090960