﻿ 破冰船结构冰致疲劳计算方法
 舰船科学技术  2021, Vol. 43 Issue (12): 25-31    DOI: 10.3404/j.issn.1672-7649.2021.12.005 PDF

1. 哈尔滨工程大学 船舶工程学院，黑龙江 哈尔滨 150001;
2. 北京强度环境研究所，北京 100076

Research on calculation method of ice induced fatigue for icebreaker structures
LIU Wen-chao1, LI Zhe2, CUI Gao-wei2, FENG Guo-qing1
1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2. Beijing Institute of Structure and Environment Engineering, Beijing 100076, China
Abstract: Aiming at the assessment of the ice induced fatigue strength of icebreaker, the ship ice collision simulation method based on the long time history calculation is proposed. Through the finite element simulation of ship ice collision, the fatigue hot spots are identified. The rain flow counting method is used to count the stress time history of each fatigue hot spot, and the mean stress and stress range under the stress cycles are obtained. The influence of the mean stress on the stress amplitude is considered. Combined with Miner linear cumulative damage model, the total damage is given in the design life cycle. This results show that the stress time history of the icebreaker is stable and obeys the Weibull distribution when it is simulated to 600s by using the periodic medium analysis method. The high stress structure caused by ship ice collision mostly occurs in the outer plate area of the ship. As checking the fatigue strength of icebreaker, more attention should be paid to the outer plate area where the ship structure collides with sea ice.
Key words: icebreaker     ice induced fatigue     periodic medium analysis method     cumulative damage
0 引　言

1 低温疲劳强度评估理论

1.1 雨流计数法

1.2 平均应力修正

 $\frac{{{S_a}}}{{{S_{ - 1}}}} + \frac{{{S_m}}}{{{S_u}}} = 1。$ (1)

1.3 低温疲劳S-N曲线

 $\lg N = \lg A - m\lg S \text{。}$ (2)

 $\lg N = {\text{12}}{\text{.883}} - {\text{3}}\lg S，$ (3)
 $\lg N = {\text{13}}{\text{.057}} - {\text{3}}\lg S。$ (4)
1.4 低温疲劳累计损伤度计算

 ${D_{{t_1}ij}} = \frac{{{n_{ij}}}}{{{N_{ij}}}} ，$ (5)

 ${D_t}_{_1} = \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{D_{{t_1}ij}}} } = \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} }，$ (6)

 ${D_t}_{_{\text{0}}}{\text{ = }}\frac{{{D_t}_{_1}}}{{{t_1}{v_1}}} = \frac{1}{{{t_1}{v_1}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{D_{{t_1}ij}}} } = \frac{1}{{{t_1}{v_1}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} } ，$ (7)

 ${D_1} = {S_1}{D_{{t_0}}} = \frac{{{S_1}}}{{{t_1}{v_1}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} }，$ (8)

 $\begin{split} D =& {D_1} + {D_2} + \cdots{D_x} + \cdots + {D_c} = \frac{{{S_1}}}{{{t_1}{v_1}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} } + \\ & \frac{{{S_2}}}{{{t_2}{v_2}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} } + \cdots + \frac{{{S_x}}}{{{t_x}{v_x}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}} + \cdots} } + \\ & \frac{{{S_c}}}{{{t_c}{v_c}}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\frac{{{n_{ij}}}}{{{N_{ij}}}}} } 。\end{split}$ (9)
2 破冰船有限元计算

2.1 破冰船有限元计算工况

2.2 破冰船长时历连续式破冰计算方法

 ${\sigma _y}\left( {{\varepsilon _{eff}}^P,{{\dot \varepsilon }_{eff}}^P} \right) = {\sigma _y}({\varepsilon _{eff}}^P)\left[ {1 + {{\left( {\frac{{{{\dot \varepsilon }_{eff}}^P}}{C}} \right)}^{\frac{1}{P}}}} \right]$ (10)

 图 1 周期性介质分析方法实例说明 Fig. 1 Illustration of periodic media analysis method

 图 2 连续式破冰有限元模拟情况 Fig. 2 Finite element simulation of continuous ice-breaking
2.3 破冰船有限元模拟结果

 图 3 船首与海冰初始碰撞点 Fig. 3 Initial collision point between bow and sea ice

 图 4 横舱壁与纵骨交界处 Fig. 4 Junction of transverse bulkhead and longitudinal

 图 5 船首外板碰撞点1 Fig. 5 Collision point 1 of bow outer shell plate

 图 6 船首外板碰撞点2 Fig. 6 Collision point 2 of bow outer shell plate

 $f=\frac{\sigma_{{h}}}{\sigma_{{n}}} 。$ (11)

3 破冰船冰致疲劳计算结果

 图 7 破冰工况1各疲劳热点应力时历曲线 Fig. 7 Time-history curves of stress in each fatigue hot spot in ice-breaking condition 1

 ${f_s}(S) = \frac{h}{q}{(\frac{S}{q})^{h - 1}}\exp \left[ { - {{\left( {\frac{S}{q}} \right)}^h}} \right] ，$ (12)
 ${F_s}(S) = 1 - \exp \left[ { - {{\left( {\frac{S}{q}} \right)}^h}} \right]。$ (13)

 图 8 各热点不同时间段下Weibull分布参数值 Fig. 8 Weibull distribution parameters of hot spots in different time periods

 图 9 各热点应力范围概率分布 Fig. 9 Probability distribution of stress range for each hot spot

4 结　语

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