﻿ 船体夹层板结构耐冲击性能优化研究
 舰船科学技术  2023, Vol. 45 Issue (7): 18-21    DOI: 10.3404/j.issn.1672-7649.2023.07.004 PDF

Research on impact resistance optimization of hull sandwich plate structure
LIU Wen-ping, DING Yu
College of Applied Technology, Dalian Ocean University, Dalian 116300, China
Abstract: In order to improve the safety performance of ships, the impact resistance optimization method of sandwich plate structure is studied to improve the impact resistance of sandwich plate. Considering the energy absorption, impact depth, ultimate impact velocity and maximum deflection of the sandwich plate structure, the impact resistance optimization model of sandwich plate structure is established. The Pareto solution set of the impact resistance optimization scheme is obtained by using progressive genetic algorithm. Through entropy weight method, in Pareto solution set, the optimal scheme of maximum energy absorption, minimum impact depth, maximum ultimate impact velocity and minimum maximum deflection corresponding to the impact resistance of sandwich plate is obtained. Experimental results show that this method can effectively optimize the impact resistance of sandwich plate structure. The application of this method can improve the energy absorption of sandwich plate, increase the peak impact resistance and prolong the impact resistance time, that is, improve the impact resistance.
Key words: hull sandwich plate     impact resistance     structural energy absorption     ultimate impact velocity     maximum deflection     genetic algorithm
0 引　言

1 夹层板结构耐冲击性能优化 1.1 耐冲击性能优化模型

 ${b_1} = \frac{E}{M} \;。$ (1)

 ${\lambda _2} = \frac{D}{M} ，$ (2)

 $V = \sqrt {\frac{{E'}}{{{m_2}}} + \frac{{E'}}{{{m_2}}} \cdot \frac{{{m_2}}}{{{m_1}}}} \;。$ (3)

 $h = {h_1} + {h_2} 。$ (4)

${\varepsilon _x}$ ${\varepsilon _y}$ 的计算公式如下：

 $\begin{split} & {\varepsilon }_{x}=\frac{{A}_{x}}{2Rk+2Rt}\text{，}\\ &{\varepsilon }_{y}=\frac{{A}_{y}}{2Rk+2Rt} 。\end{split}$ (5)

${A_x}$ ${A_y}$ 的计算公式如下：

 $\begin{split} {A_x} = &{A_{x,all}} - {A_{xf}} = - \beta \frac{\partial }{{\partial x}}{\left( {\frac{\bf{{\partial }}}{{\partial x}} + \frac{\partial }{{\partial y}}} \right)^2}{h_1} +\\ &2{\beta _f}\frac{\partial }{{\partial x}}{\left( {\frac{\partial }{{\partial x}} + \frac{\partial }{{\partial y}}} \right)^2}{h_1} ，\\ {A_y} = &{A_{y,all}} - {A_{yf}} = - \beta \frac{\partial }{{\partial y}}{\left( {\frac{\partial }{{\partial x}} + \frac{\partial }{{\partial y}}} \right)^2}{h_1} +\\ &2{\beta _f}\frac{\partial }{{\partial y}}{\left( {\frac{\partial }{{\partial x}} + \frac{\partial }{{\partial y}}} \right)^2}{h_1} 。\\ \end{split}$ (6)

 $\begin{split} & {h_{2x}} = \int_0^x {{\varepsilon _x}{\rm{d}}x} = - \dfrac{{\beta {{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{{2C}} + \dfrac{{{\beta _d}{{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} ，\\ & {h_{2y}} = \int_0^y {{\varepsilon _y}{\rm{d}}y} = - \dfrac{{\beta {{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{{2C}} + \dfrac{{{\beta _d}{{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} 。\end{split}$ (7)

${h_2}$ 的计算公式如下：

 ${h_2} = {h_{2x}} + {h_{2y}} = - \dfrac{{\beta {{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} - \dfrac{{2{\beta _d}{{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} ，$ (8)

 $h = {h_1} - - \dfrac{{\beta {{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} - \dfrac{{2{\beta _d}{{\left( {\dfrac{\partial }{{\partial x}} + \dfrac{\partial }{{\partial y}}} \right)}^2}{h_1}}}{C} 。$ (9)

 $F = {w_1}f\left( {{\lambda _1}} \right) + {w_2}f\left( {\frac{1}{{{\lambda _2}}}} \right) + {w_3}f\left( V \right) + {w_4}f\left( {\frac{1}{{{h_{\max }}}}} \right) 。$ (10)

1.2 耐冲击性能优化模型求解

1) 生成初始种群。种群内每个个体均代表一个船体夹层板结构耐冲击性能优化方案。令初始种群是 ${Z_0}$ ；令已知可行域中某个内点是 ${S_0}$ ${Z_0}$ 经过选择、交叉、变异迭代操作后，得到较优的船体夹层板结构耐冲击性能优化方案 ${Y_1}$ 。更新 ${S_0}$ ，获取初始种群，经过选择、交叉、变异迭代操作后，得到较优的船体夹层板结构耐冲击性能优化方案 ${Y_2}$ 。以此类推，获取多样性较优的船体夹层板结构耐冲击性能优化方案的可行解集 $\left\{ {{Y_1},{Y_2}, \cdots ,{Y_n}} \right\}$ 。其中，可行解数量是 $n$ 。设置可行解的上限是 ${Y_{\max }} = \max \left\{ {{Y_1},{Y_2}, \cdots ,{Y_n}} \right\} + {c_1}$ ；可行解的下限是 ${Y_{\min }} = \min \left\{ {{Y_1},{Y_2}, \cdots ,{Y_n}} \right\} + {c_2}$ ；其中，学习因子是 ${c_1}$ ${c_2}$ 。获取可行解的上下限 $\left[ {{Y_{\min }},{Y_{\max }}} \right]$ 后，通过二进制编码的方式生成初始个体，组建初始种群。选择、交叉、变异操作初始种群。

2) 分析迭代次数是否达到最大值，若达到最大值，则输出船体夹层板结构耐冲击性能优化方案的Pareto解集。

1) 按照船体夹层板结构耐冲击性能优化问题的实际情况，确定耐冲击性能优化方案的优选指标集，令Pareto解集内，共包含 $m$ 个夹层板耐冲击性能优化方案，优选指标数量是 $\eta$

2) 求解各船体夹层板结构耐冲击性能优化方案内，各指标的权重，计算公式如下：

 ${\omega _j} = \dfrac{{1 - \dfrac{{{U_j}}}{{\ln m}}}}{{\displaystyle\sum\limits_{j = 1}^\eta {\dfrac{{{U_j}}}{{\ln m}}} }} 。$ (11)

${U_j}$ 的计算公式如下：

 ${U_j} = - \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^\eta {\dfrac{{{l_{ij}}}}{{\displaystyle\sum\limits_{i = 1}^m {{l_{ij}}} }}} } \ln \dfrac{{{l_{ij}}}}{{\displaystyle\sum\limits_{i = 1}^m {{l_{ij}}} }} 。$ (12)

3) 综合评价，船体夹层板结构耐冲击性能优化方案的综合评价值越大，说明该优化方案越佳，评价值 ${o_i}$ 公式如下：

 ${o_i} = \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^\eta {{\omega _j}\frac{{{\alpha _{ij}} - \min \left\{ {{\alpha _{ij}}} \right\}}}{{\max \left\{ {{\alpha _{ij}}} \right\} - \min \left\{ {{\alpha _{ij}}} \right\}}}} } 。$ (13)

Pareto解集内，最大 ${o_i}$ 对应的方案，即最大吸能、最小撞深、最大极限冲击速度、最小最大挠度，对应的船体夹层板结构耐冲击性能优化最佳方案。

2 试验结果与分析

 图 1 优化前后船体夹层板的吸能变化情况 Fig. 1 Energy absorption of sandwich plates before and after optimization

 图 2 船体夹层板结构的冲击力变化情况 Fig. 2 Change of impact force of sandwich plate structure of hull
3 结　语

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