﻿ 船舶搁浅对船舷外部结构损伤的数值计算研究
 舰船科学技术  2022, Vol. 44 Issue (20): 50-53    DOI: 10.3404/j.issn.1672-7649.2022.20.010 PDF

Numerical study on damage of ship grounding to external structure of ship's side
WU Jing, LIU Ya-qi, SHI Yu-zhou
Jiangsu Shipping College, Nantong 226010, China
Abstract: Ship grounding accident is a kind of maritime accident that occurs frequently in the world. Obstacles such as reefs will have a huge impact on the external structure of the ship hull during the grounding process. Once the external structure of the ship hull fails, it will cause serious accidents such as ship hull fracture. In this paper, the damage of the external structure of the ship's side is calculated and simulated according to the scene of ship grounding, and the basic theory of structural damage calculation is introduced.
Key words: grounding     ship's side     finite element     Ansys-APDL
0 引　言

1 搁浅状态下船舷外部结构强度的力学基础

1）应力-应变公式

 $\left[ P \right]{\text{ = }}\left( {{p_x},{p_y},{p_z}} \right) \text{，}$
 $\left[ Q \right]{\text{ = }}\left( {{q_x},{q_y},{q_z}} \right) \text{，}$

 $\left[ f \right]{\text{ = }}\left( {u,v,w} \right) \text{，}$

 $\left\{ \begin{gathered} \left( {{\sigma _x},{\sigma _y},{\sigma _z}} \right) ，\\ \left( {{\tau _x},{\tau _y},{\tau _z}} \right)。\\ \end{gathered} \right.$

 $\left\{ \begin{gathered} \left( {{\varepsilon _x},{\varepsilon _y},{\varepsilon _z}} \right)，\\ \left( {{\kappa _x},{\kappa _y},{\kappa _z}} \right)。\\ \end{gathered} \right.$

 $\begin{gathered} \frac{{\delta {\sigma _x}}}{{\delta x}} + \frac{{\delta {\tau _x}}}{{\delta y}} + \frac{{\delta {\tau _z}}}{{\delta z}} + {q_x} = 0，\\ \frac{{\delta {\tau _x}}}{{\delta x}} + \frac{{\delta {\sigma _y}}}{{\delta y}} + \frac{{\delta {\tau _y}}}{{\delta z}} + {q_y} = 0，\\ \frac{{\delta {\tau _x}}}{{\delta x}} + \frac{{\delta {\tau _y}}}{{\delta y}} + \frac{{\delta {\sigma _z}}}{{\delta z}} + {q_z} = 0 。\\ \end{gathered}$

2）形变公式

 ${\varepsilon _x} = \frac{{\delta u}}{{\delta x}},{\varepsilon _y} = \frac{{\delta v}}{{\delta y}},{\varepsilon _z} = \frac{{\delta w}}{{\delta z}} \text{，}$

 ${\kappa _x} = \frac{{\delta u}}{{\delta x}} + \frac{{\delta v}}{{\delta y}},{\kappa _y} = \frac{{\delta w}}{{\delta x}} + \frac{{\delta v}}{{\delta y}},{\kappa _z} = \frac{{\delta u}}{{\delta y}} + \frac{{\delta v}}{{\delta z}} 。$

 图 1 船舷结构材料的应力应变曲线 Fig. 1 Stress strain curves of ship side structural materials

3）材料本构方程

 ${\sigma _y} = \left[ {1 + {{\left( {\frac{\varepsilon }{c}} \right)}^{\frac{1}{p}}}} \right]\left( {{\sigma _0} + \beta {E_p}\varepsilon _p^{eff}} \right) \text{，}$

2 船舶搁浅过程船舷外部结构的载荷分解

 图 2 风浪条件下船舵的力学模型 Fig. 2 Mechanical model of rudder under wind and wave conditions

1）波浪载荷

 $f{\text{ = }}{\varphi _0}\cos \left( {kx - {w_0}t} \right) \text{。}$

 $\begin{gathered} u{\text{ = }}\dfrac{\text{π} }{2}{\varphi _0}{\theta ^{kt}}\cos \left( {kx - {w_0}t} \right) ，\\ w = \dfrac{1}{2}{\varphi _0}{\theta ^{kt}}\sin \left( {kx - {w_0}t} \right)。\\ \end{gathered}$

 ${M_w} = \frac{1}{2}{K_g} \cdot h \cdot B \cdot {A_1} \cdot {A_2} \cdot {L^2} \times {10^{ - 2}} \text{。}$

${K_g} = 1.437\alpha \left[ {0.032 + 0.013\left( {{C_b}/\alpha - 0.60} \right)} \right]$ $\alpha$ 为水线长度系数， ${C_b}$ 为船舶宽度系数[2]

${A_1}$ 为速度系数，按下式计算：

 ${A_1} = 1 - \left( {3 + 25{F_{nw}}} \right){M_s}/(D) + 1.5{F_{nw}} \text{。}$

2）冲击载荷

 ${F_X} = \frac{{3.58{\sigma _0}{t_w}{t^{0.61}}_eb_0^{}}}{{{k_0}}} \text{。}$

 图 3 不同风速下冲击作用力与筋板厚度的关系 Fig. 3 The relationship between impact force and rib thickness under different wind speeds
3 基于有限元分析技术的船舶搁浅过程船舷外部结构损伤数值计算 3.1 有限元建模

1）船体动量和能量守恒方程：

 $\begin{gathered} {F_X}t = m{v_1} - m{v_2}，\\ {F_X}s = \frac{1}{2}m{v_1}^2 - \frac{1}{2}m{v_2}^2。\\ \end{gathered}$

2）海水能量守恒方程[3]

 $\left\{ {\begin{array}{*{20}{c}} {\dfrac{{\partial k}}{{\partial t}} + {{\bar u}_i}\dfrac{{\partial k}}{{\partial {x_j}}} = \dfrac{\partial }{{\partial {x_j}}}\left[ {\left( {1 + {\sigma _k}{v_t}} \right)\dfrac{{\partial k}}{{\partial {x_j}}}} \right] + {P_k} - k\omega }，\\ {\dfrac{{\partial \omega }}{{\partial t}} + {{\bar u}_j} = \dfrac{\partial }{{\partial {x_j}}}\left[ {\left( {1 + {\sigma _k}{v_t}} \right)\dfrac{{\partial \omega }}{{\partial {x_j}}}} \right] + 2(1 - {F_i})\delta } 。\end{array}} \right.$

 图 4 船舷局部结构的有限元模型 Fig. 4 Finite element model of ship side local structure
3.2 船舶搁浅时船舷外部结构的损伤有限元仿真

 $\log N = 12.16 - 3.0\log S，\;\;\;\;\;t = 45，$
 $\log N = 12.16 - 0.75\log \left( {\frac{t}{{32}}} \right) - 3.0\log S，\;\;\;\;t \ne 45 \text{。}$

 $S_{r} N_{t}^{m^{m}}=1.09 。$

 图 5 船舷局部结构损伤仿真结果 Fig. 5 Simulation results of local structural damage of ship side
4 结　语

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