﻿ 船体结构疲劳可靠性分析的直接计算方法
«上一篇
 文章快速检索 高级检索

 哈尔滨工程大学学报  2018, Vol. 39 Issue (4): 664-667  DOI: 10.11990/jheu.201612092 0

### 引用本文

ZHEN Chunbo, WANG Tianlin, YU Pengyao. Direct calculation approach for fatigue reliability analysis of ship structures[J]. Journal of Harbin Engineering University, 2018, 39(4), 664-667. DOI: 10.11990/jheu.201612092.

### 文章历史

Direct calculation approach for fatigue reliability analysis of ship structures
ZHEN Chunbo, WANG Tianlin, YU Pengyao
College of Traffic Equipment and Ocean Engineering, Dalian Maritime University, Dalian 116026, China
Abstract: To accurately predict the fatigue life of a ship structure, 3D linear potential flow theory and a direct calculation method based on the spectral analysis used for the finite element analysis of an entire ship were adopted. The stress parameters of short-term and long-term sea states were obtained, and the cumulative fatigue damage of the ship during its entire life period was given. The uncertainties involved in fatigue analysis were considered; the reliability index of the hull structure was obtained, and the fatigue reliability analysis of the ship structure was presented based on direct calculation. In this study, the fatigue reliability of a high-performance trimaran was analyzed. The results of this analysis reveal that the fatigue life reliability increases with an increase in the fatigue life, and it is low in areas with serious fatigue.
Key words: direct calculation    fatigue reliability    spectral analysis method    ship structure    3D linear potential flow theory    finite element analysis of an entire ship    stress parameters

Muhammed等[5]总结了基于S-N曲线简化分析方法的船舶与海洋工程疲劳可靠性分析方法，并分析了各不确定性因素对船舶与海洋工程结构物可靠性指标的影响关系。Garbatov等[6]对船舶与海洋工程疲劳可靠性分析中涉及的船舶主尺度、船型、波浪散布图、波浪谱及浪向角、焊接点形状、名义应力的不完整性等因素做了全面地分析对比，并给出了详尽的对比结果。国内方面，何文涛[7]采用Kriging代理模型和裂纹扩展方法研究了船体典型节点的疲劳寿命可靠性问题。徐帅[8]针对LNG船典型热点采用JC法计算疲劳可靠性指标, 并研究极限疲劳损伤值、S-N曲线和疲劳载荷等变量对可靠性指标的敏感性。胡毓仁等[1, 9], 在这方面也做了相当多的工作。

1 船体疲劳强度计算方法 1.1 应力范围的概率密度函数

 ${f_S}\left( S \right) = \frac{S}{{4{m_0}}}\exp \left( { - \frac{{{S^2}}}{{8{m_0}}}} \right)\;\;\;\;0 \le S < + \infty$ (1)

 ${G_{XX}}\left( {{\omega _e}} \right) = {\left| {{H_\sigma }\left( {{\omega _e}} \right)} \right|^2} \cdot {G_{\eta \eta }}\left( {{\omega _e}} \right)$ (2)

1.2 应力参数的定义

 ${\mathit{\Omega }_i} = {f_{{L_i}}}{\rm{E}}{\left( {{S^m}} \right)_i} = {f_{{L_i}}}\int\limits_0^{ + \infty } {{S^m}{f_{{S_i}}}\left( S \right){\rm{d}}S}$ (3)

 $\begin{array}{*{20}{c}} {\mathit{\Omega } = \sum\limits_{i = 1}^k {{\gamma _i}{\mathit{\Omega }_i}} = \sum\limits_{i = 1}^k {{\gamma _i}{f_{{L_i}}}{\rm{E}}{{\left( {{S^m}} \right)}_i}} = }\\ {\sum\limits_{i = 1}^k {{\gamma _i}{f_{{L_i}}}\int\limits_0^{ + \infty } {{S^m}{f_{{S_i}}}\left( S \right){\rm{d}}S} } } \end{array}$ (4)

 $\begin{array}{*{20}{c}} {\mathit{\Omega } = \sum\limits_{i = 1}^k {{\gamma _i}{\mathit{\Omega }_i}} = \sum\limits_{i = 1}^k {{\gamma _i}{f_{{L_i}}}{{\left( {2\sqrt 2 {\sigma _{{X_i}}}} \right)}^m}\mathit{\Gamma }\left( {\frac{m}{2} + 1} \right)} = }\\ {{{\left( {2\sqrt 2 } \right)}^m}\mathit{\Gamma }\left( {\frac{m}{2} + 1} \right)\sum\limits_{i = 1}^k {{\gamma _i}f_{{L_i}{\sigma _{{X_i}}}}^m} } \end{array}$ (5)
1.3 损伤计算

 ${D_{ij}} = \frac{{{T_{ij}}{f_{0ij}}}}{A}\int\limits_0^{ + \infty } {{S^m}{f_{Sij}}\left( S \right){\rm{d}}S}$ (6)

 $D = \sum\limits_{i = 1}^k {\sum\limits_{j = 1}^p {{D_{ij}}} } = \sum\limits_{i = 1}^k {\sum\limits_{j = 1}^p {\frac{{{T_{ij}}{f_{0ij}}}}{A}\int\limits_0^{ + \infty } {{S^m}{f_{Sij}}\left( S \right){\rm{d}}S} } }$ (7)

 $D = \sum\limits_{i = 1}^k {\sum\limits_{j = 1}^p {{D_{ij}}} } = \frac{T}{A}\sum\limits_{i = 1}^k {\sum\limits_{j = 1}^p {{\gamma _i}{\mathit{\Omega }_{ij}}} } = \frac{T}{A}\mathit{\Omega }$ (8)
2 疲劳寿命的可靠性分析方法 2.1 疲劳寿命的随机性质因素组成

 ${S_a} = BS$ (10)

 ${\mathit{\Omega }_a} = {B^m}\mathit{\Omega }$ (11)

 $D = \Delta$ (12)

 ${T_f} = \frac{{\Delta A}}{{{B^m}\mathit{\Omega }}}$ (13)
2.2 疲劳可靠性分析

 $Z = {T_f} - {T_D} = \frac{{\Delta A}}{{{B^m}\mathit{\Omega }}} - {T_D}$ (14)

 $\begin{array}{*{20}{c}} {Z = \ln {T_f} - \ln {T_D} = \ln \left( {\frac{{\Delta A}}{{{B^m}\mathit{\Omega }}}} \right) - \ln {T_D} = }\\ {\ln \Delta + \ln A - m\ln B - \ln \mathit{\Omega } - \ln {T_D}} \end{array}$ (15)

 ${{\tilde T}_f} = \frac{{\tilde \Delta \tilde A}}{{{{\tilde B}^m}\mathit{\Omega }}}$ (16)
 ${C_{{T_f}}} = {\left[ {\left( {1 + C_\Delta ^2} \right)\left( {1 + C_A^2} \right){{\left( {1 + C_B^2} \right)}^{{m^2}}} - 1} \right]^{1/2}}$ (17)

 ${\mu _{\ln {T_f}}} = \ln {{\tilde T}_f} = \ln \left( {\frac{{\tilde \Delta \tilde A}}{{{{\tilde B}^m}\mathit{\Omega }}}} \right)$ (18)
 $\begin{array}{*{20}{c}} {{\sigma _{\ln {T_f}}} = {{\left[ {\ln \left( {1 + C_{{T_f}}^2} \right)} \right]}^{1/2}} = }\\ {{{\left\{ {\ln \left[ {\left( {1 + C_\Delta ^2} \right)\left( {1 + C_A^2} \right){{\left( {1 + C_B^2} \right)}^{{m^2}}}} \right]} \right\}}^{1/2}}} \end{array}$ (19)

 $\beta = \frac{{{\mu _{\ln {T_f}}} - \ln {T_D}}}{{{\sigma _{\ln {T_f}}}}} = \frac{{\ln {{\tilde T}_f} - \ln {T_D}}}{{{\sigma _{\ln {T_f}}}}} = \frac{{\ln \left( {\frac{{{{\tilde T}_f}}}{{{T_D}}}} \right)}}{{{{\left[ {\ln \left( {1 + C_{\ln {T_f}}^2} \right)} \right]}^{1/2}}}}$ (20)
 ${p_r} = \mathit{\Phi }\left( \beta \right)$ (21)
3 疲劳可靠性算例分析

3.1 有限元模型及分析部位

1) 连接桥及湿甲板首端与主船体间断处；

2) 连接桥中部湿甲板与主船体相交处；

3) 连接桥中部主体部位纵骨穿越强框架处；

4) 连接桥中部湿甲板与片体相交处。

3.2 波浪载荷计算及传递函数的计算

 Download: 图 1 全船有限元分析模型 Fig. 1 The whole FE model of trimaran

 Download: 图 3 热点3应力响应传递函数 Fig. 3 The stress transfer function of hotspot 3
3.3 疲劳寿命可靠性结果

4 结论

1) 疲劳寿命可靠度计算算例表明，疲劳寿命的可靠度问题在疲劳损伤较为严重的区域较为严重，疲劳寿命可靠度大小与疲劳载荷不确定性因素的变异系数取值较为敏感。

2) 疲劳载荷以及其他影响疲劳寿命的不确定性因素的概率统计参数的准确确定，对疲劳寿命可靠性的精准计算是相当重要的。

 [1] 胡毓仁, 陈伯真. 船舶与海洋工程结构疲劳可靠性分析[M]. 北京: 人民交通出版社, 1996: 110-114. HU Yuren, CHEN Bozhen. Fatigue reliability analysis of the ship and ocean engineering structures[M]. Beijing: China Communications Press, 1996: 110-114. (0) [2] DOSHI K, ROY T, PARIHAR Y S. Reliability based inspection planning using fracture mechanics based fatigue evaluations for ship structural details[J]. Marine structures, 2017, 54: 1-22. DOI:10.1016/j.marstruc.2017.03.003 (0) [3] MAHMOUD H, RIVEROS G. Fatigue reliability of a single stiffened ship hull panel[J]. Engineering structures, 2014, 66: 89-99. DOI:10.1016/j.engstruct.2014.02.007 (0) [4] ANG A H S, CHEUNG M C, SHUGAR T A, et al. Reliability-based fatigue analysis and design of floating structures[J]. Marine structures, 2001, 14(1/2): 25-36. (0) [5] MUHAMMED A, STACEY A. Probabilistic S-N fatigue assessment methods for welded joints in offshore structures[C]//Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering. Estoril, Portugal: ASME, 2008: 335-354. http://www.researchgate.net/publication/267604823_Probabilistic_S-N_Fatigue_Assessment_Methods_for_Welded_Joints_in_Offshore_Structures (0) [6] GARBATOV Y, SOARES C G. Assessment of the uncertainties introduced by different fatigue damage models for ship structural details[C]//Proceedings of the 29th International Conference on Ocean, Offshore and Arctic Engineering. Shanghai: ASME, 2010: 549-559. https://www.researchgate.net/publication/263085873_Assessment_of_the_Uncertainties_Introduced_by_Different_Fatigue_Damage_Models_for_Ship_Structural_Details (0) [7] HE Wentao, LIU Jingxi, XIE De. Probabilistic life assessment on fatigue crack growth in mixed-mode by coupling of Kriging model and finite element analysis[J]. Engineering fracture mechanics, 2015, 139: 56-77. DOI:10.1016/j.engfracmech.2015.03.040 (0) [8] 徐帅. 基于谱分析法的LNG船疲劳可靠性分析[D]. 武汉: 华中科技大学, 2011: 24-26. XU Shuai. Fatigue reliability for LNG carrier using spectral-based analysis[D]. Wuhan: Huazhong University of Science And Technology, 2011: 24-26. http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=D187633 (0) [9] CUI Weicheng. Relation between crack growth rate curve and S-N curve for metal fatigue[J]. Journal of ship mechanics, 2002, 6(6): 93-106. (0) [10] 卢晓平, 郦云, 董祖舜. 高速三体船研究综述[J]. 海军工程大学学报, 2005, 17(2): 43-48, 52. LU Xiaoping, LI Yun, DONG Zushun. A research summary on high speed trimaran[J]. Journal of naval university of engineering, 2005, 17(2): 43-48, 52. (0) [11] FANG M C, CHEN T Y. A parametric study of wave loads on trimaran ships traveling in waves[J]. Ocean engineering, 2008, 35(8/9): 749-762. (0) [12] WANG Yingguang. Spectral fatigue analysis of a ship structural detail-A practical case study[J]. International journal of fatigue, 2010, 32(2): 310-317. DOI:10.1016/j.ijfatigue.2009.06.020 (0) [13] 甄春博, 王天霖, 于鹏垚. 基于直接计算的三体船结构疲劳强度影响因素分析[J]. 中国舰船研究, 2017, 12(3): 86-90. ZHEN Chunbo, WANG Tianlin, YU Pengyao. Influencing factor analysis for direct calculation of trimaran structure's fatigue strength[J]. Chinese journal of ship research, 2017, 12(3): 86-90. (0)