Calculation of Wave Force and Dynamic Response Analysis of Offshore Platforms based on the radial basis function
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摘要: 对于细长杆件上的受力，工程上大多是通过Morison方程来计算波浪荷载。由于以往求解波浪力的Morison方程大部分都是简化方程，将桩体假设为刚体，没有考虑到桩体的弹性变形。基于径向基函数这一无网格方法，将考虑了桩体弹性变形的Morison方程和动力平衡方程联立求解，得到单桩在波浪荷载作用下的波浪力和动力响应，并将其与规范方法和以往的文献方法作对比，验证了此方法的准确性。将此方法应用于实际工程案例，可得到最不利工况下工作平台的动力响应。径向基函数计算简便，易于掌握，可将其应用于实际工程中，为以后的海上结构物计算提供了一个新的方向。Abstract: In engineering practice, the Morison equation is commonly used to calculate wave loads on slender structures. Traditionally, the Morison equation for wave force calculation is often simplified, assuming the pile as a rigid body and neglecting the elastic deformation of the pile. By employing the Radial Basis Function (RBF), a mesh-free method, this study simultaneously solves the Morison equation, which considers pile elastic deformation, and the dynamic balance equation. This approach obtains the wave force and dynamic response of a single pile under wave load, and compares the results with those from standard methods and previous literature to validate its accuracy. Applying this method to actual engineering cases reveals the dynamic response of the working platform under the most unfavorable conditions. The RBF method is computationally straightforward and easy to master, making it suitable for practical engineering applications and providing a new direction for the calculation of offshore structures in the future.
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图 1 径向基函数方法和规范方法与试验结果的比较
Fig. 1 Comparison of radial basis function methods and normative methods with test results
图 2 桩顶的位移、速度、加速度、急动度
Fig. 2 Displacement, speed, acceleration and emergency motion of the pile bolck
图 3 大波高大周期各时程曲线图
Fig. 3 Plot of each time course of the large wave high and large period
表 1 单桩参数表
Tab. 1 Parameter Table of pile
参数 E (kPa) G(kPa) A(m2) Ix(m4) Iy(m4) p(kg/m3) kxA (m2) kyA (m2) 钢管桩 2.×108 0.79×108 0.0698 2.19×10-3 2.19×10-3 7.85×103 0.0349 0.0349 
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表 2 不同波况的波浪力系数
Tab. 2 Wave force coefficients for different wave conditions
H/L B/L=0.128,d/L=0.246 T=1.6，d=0.9,D=0.47 实验值 规范值 线性波 stokes2阶 stokes3阶 0.01 0.08 0.08 0.07 0.07 0.07 0.02 0.15 0.15 0.14 0.14 0.14 0.03 0.23 0.23 0.22 0.22 0.22 0.04 0.31 0.30 0.28 0.28 0.29 0.05 0.38 0.38 0.35 0.36 0.36 0.60 0.45 0.46 0.42 0.43 0.44 0.70 0.51 0.55 0.49 0.51 0.52 0.08 0.56 0.63 0.56 0.58 0.60 H/L B/L=0.191,d/L=0.302 T=1.6,d=1.151,D=0.73 实验值 规范值 线性波 stokes2阶 stokes3阶 0.02 0.06 0.08 0.07 0.07 0.07 0.04 0.19 0.20 0.17 0.18 0.18 0.05 0.24 0.27 0.23 0.23 0.23 0.06 0.32 0.35 0.30 0.30 0.30 0.08 0.39 0.46 0.38 0.39 0.39
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表 3 工作平台波浪参数
Tab. 3 Wave parameters of the working platform
工况 1 2 3 4 波高 2.0 2.4 2.5 2.6 周期 17 17.3 17.4 17.7
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