SIMULATION OF THE MOTION OF AN ELASTIC HULL IN REGULAR WAVES BASED ON MPS-FEM METHOD
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摘要: 船舶在海洋中航行时经常会受波浪的作用, 在波浪的作用下, 船体可能会发生六自由度的运动. 在船体运动幅度较小时, 可以简单地将船体运动视为刚体运动. 但当波浪环境较为剧烈、船体运动幅度较大时, 船体可能会发生变形, 此时船舶弹性的影响无法忽略. 因此, 研究弹性船体在波浪中的运动对船舶运动性能和航行安全具有重要的意义. 移动粒子半隐式方法MPS方法是一种基于拉格朗日方法表示的无网格粒子类方法, 该方法在模拟具有自由面大变形特征的问题时具有其独特的优势. 有限元方法FEM作为一种传统的并且已被广泛应用的结构求解方法, 具有很好的稳定性、准确性和鲁棒性. 本文将MPS方法与FEM方法二者的优势结合, 基于MPS-FEM耦合方法, 使用自主开发的MPSFEM-SJTU流固耦合求解器, 模拟刚性船体和弹性船体在规则波中的运动, 并分析船体的弹性对船体运动响应的影响. 首先模拟刚性船体在不同波长的规则波中的运动, 研究规则波波长对船体运动响应的影响. 接着分别模拟了刚性和弹性船体在规则波中的运动, 结果表明, 刚性船体的运动幅值大于弹性船体的运动幅值, 而弹性船体船舯附近的压力大于刚性船体.Abstract: A ship always encounters waves and may move with six degrees of freedom in the naval architecture and ocean engineering. The ship can be regarded as a rigid body simply when the motion amplitude is small. However, when the wave gets severe, the ship's motion amplitude get large and the ship hull may deforms a lot. In this situation, ship's elasticity may effects the pressure on the hull and the ship response motion, which cannot be ignored. Therefore, it is of great significance to simulate the motion of an elastic ship in waves and to study the influence of the hull elasticity, which can improve the ship performance and the navigation safety. Moving particle semi-implicit (MPS) method is a mesh free particle method based on Lagrangian representation. This method has its unique advantages in simulating problems with large deformation characteristics of free surfaces. As a traditional structural solution method, finite element method (FEM) has been widely used and has been proved with good stability, accuracy and robustness. In this paper, the advantages of MPS method and FEM method are combined and the in-house fluid-structure interaction solver MPSFEM-SJTU is used to simulate the motions of rigid and elastic hulls in regular waves. The impact of hull elasticity on the hull motion response and the pressure on the hull is analyzed. Firstly, the effect of regular wave length on the motion response of hull is studied by simulating the motion of a rigid hull in regular waves with different wavelengths. Then the motions of rigid and elastic hull in regular waves are simulated respectively. The results show that the motion amplitude of rigid hull, both pitch and heave, are greater than those of the elastic hull. and the pressure near the midship of elastic hull is greater than that of rigid hull. For the pressure distribution on elastic and hull surface, the pressure at the bottom near the midship is greater than that on the rigid hull due to the bending of the elastic ship.
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Key words:
- MPS method /
- regular wave /
- fluid-structure interaction /
- elastic ship hull /
- ship motion
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图 4 四个测点处的波高时历曲线
Figure 4. Time history curves of wave height at four measuring points
图 7 t = t0, t = t0 + T/8, t = t0 + T/4, t = t0 + 3T/8 时刻弹性悬臂梁变形情况
Figure 7. Deformation of elastic beam at t = t0, t = t0 + T/8, t = t0 + T/4, t = t0 + 3T/8
图 8 悬臂梁端点位移的时历曲线
Figure 8. The time history curves of the displacement of the cantilever beam endpoint
图 9 船体粒子与梁模型的等效关系
Figure 9. Equivalent relationship between hull particles and beam model nodes
图 10 非均匀船体梁模型特征参数沿船长的变化
Figure 10. Variation of characteristics along the length of a nonuniform hull beam model
图 14 不同波长下的船体运动响应平均幅值
Figure 14. Motion response average amplitude at different wavelengths
图 17 弹性和刚性船体的运动响应时历曲线
Figure 17. Time history curves of motion response of elastic and rigid hull
图 18 刚性和弹性船体不同截面处的压力时历曲线
Figure 18. Time history curves of pressure at different sections of rigid and elastic hull
表 1 kvlcc2船实船和模型船参数
Table 1. Characteristic parameters of the kvlcc2 ship
Characteristic parameter Real scale Model scale ship length Lpp/m 320.0 3.2 ship breadth B/m 58.0 0.58 ship depth D/m 30.0 0.3 draft d/m 20.8 0.208 displacement $\nabla /m^3$ 312622 0.312 scale ratio 100 − 
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表 2 船舶运动响应参数
Table 2. Ship motion response parameters
Particle spacing Average peak value Average valley value Average amplitude Attenuation heave/m $\Delta {x} = 0.03\mathrm{m}$ −0.010 −0.0962 0.0265 − $\Delta {x} = 0.035\mathrm{m}$ −0.073 −0.0925 0.0197 −25.26% $\Delta {x} = 0.04\mathrm{m}$ −0.078 −0.101 0.0235 −11.12% pitch/(°) $\Delta {x} = 0.03\mathrm{m}$ 0.055 −0.0425 0.0979 − $\Delta {x} = 0.035\mathrm{m}$ 0.050 −0.0389 0.0887 −9.471% $\Delta {x} = 0.04\mathrm{m}$ 0.049 −0.0305 0.0797 −18.59%
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表 3 弹性刚性船体运动响应参数对比
Table 3. Comparison of motion response parameters of elastic and rigid hulls
Average peak value Average valley value Average
amplitudepitch/(°) rigid ship 2.775 −2.9012 5.676 elastic ship 2.091 −2.1619 4.253
(−25.1%)heave/m Rigid ship 0.00764 −0.00714 0.0148 elastic ship 0.00569 −0.00738 0.0131
(−11.5%)
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