﻿ 大尺度异形镂空浮体疲劳强度分析方法研究
 舰船科学技术  2024, Vol. 46 Issue (10): 102-108    DOI: 10.3404/j.issn.1672-7649.2024.10.018 PDF

1. 哈尔滨工程大学 烟台研究院，山东 烟台 264000;
2. 中船重工船舶设计研究中心有限公司，北京 100081;
3. 大连理工大学 能源与动力学院，辽宁 大连 116024

Research on fatigue strength analysis method for large scale special-shaped hollow floating structure
ZHANG Shu-you1, LENG Shu-dong2,3, CHANG Xin-jiang2, QUAN Bo-lun1
1. Yantai Research Institute, Harbin Engineering University, Yantai 264000, China;
2. CSIC Ship Design and Research Center Co., Ltd., Beijing 100081, China;
3. School of Energy and Power, Dalian University of Technology, Dalian 116024, China
Abstract: The marine environment is complex and changeable, and offshore structures need to bear the alternating load caused by random waves for a long time, which is very easy to cause fatigue damage. In this paper, a large-scale special-shaped hollow floating structure is taken as the research object, and the location where the structure is prone to fatigue failure is found through calculation and analysis. In order to make the results of structural fatigue spectrum analysis more accurate, a numerical regular wave simulation method is proposed to calculate the transfer function of structural stress. On this basis, the fatigue life of the floating structure is calculated by using the spectrum analysis method based on hot spot stress and nominal stress respectively. The results show that the fatigue life of the structure based on hot spot stress method is slightly lower than that based on nominal stress method. The above research results can provide reference for the design of large offshore floating structures.
Key words: large scale special-shaped hollow floating structure     numerical regular wave simulation method     hot spot stress     nominal stress
0 引　言

1 结构疲劳分析的基本原理 1.1 谱分析法的基本原理

 $X(t) = L\left[ {\eta (t)} \right]。$ (1)

 ${G_X}(\omega ) = {\left| {H(\omega )} \right|^2}\cdot {S_\eta }(\omega )。$ (2)

1.2 传递函数计算方法

 图 1 规则波试验法计算传递函数 Fig. 1 Calculation of transfer function by the regular wave test method
1.3 波浪谱

 $S(f)=\beta_{J} H_{\frac{1}{3}}^{2} T_{P}^{-4} f^{-5} \exp \left[-\frac{5}{4}\left(T_{P} f\right)^{-4}\right] \gamma^{{{\mathrm{exp}}}\left[-\left(\frac{f}{f_{F}}-1\right)^{2} / 2 \sigma^{x}\right]}。$ (3)

 ${{B_J} =\dfrac{{0.06238}}{{0.23 + 0.0336\gamma - 0.185{{(1.9 + \gamma )}^{ - 1}}}}[1.094 - 0.01915\ln \gamma ]。}$

$\gamma$为峰高因子，本项目中取峰高因子的平均值3.3；$\sigma$为峰形参数，频率在峰值点左侧时取0.07，频率在峰值点右侧时取0.09给出有效波高与谱峰周期即可确定JONSWAP谱曲线。

 \begin{aligned}S(\omega)= & \frac{1}{2\text{π}}\beta_JH_{\frac{1}{3}}^2T_P^{-4}\left(\frac{\omega}{2\text{π}}\right)^{-5}\times \\ & \exp\Bigg[-\frac{5}{4}\left(\frac{T_P\omega}{2\text{π}}\right)^{-4}\Bigg]\gamma^{\exp[-(\frac{\omega}{2\text{π}f_P}-1)^2\mathord{\left/\vphantom{-(\frac{\omega}{2\text{π}f_P}-1)^22\sigma^2}\right.}2\sigma^2]}。\end{aligned} (4)

1.4 异形浮体疲劳累计损伤度的计算

 ${G_{XX}}\left( {{\omega _{\text{e}}}} \right) = \int_{ - \text{π} /2}^{\text{π} /2} {f\left( \beta \right)} {\left[ {H\left( {{\omega _e},\theta - \beta } \right)} \right]^2} \cdot {G_{\text{x}}}\left( \omega \right){\mathrm{d}}\beta。$ (5)

 $f\left( \beta \right) = k{\cos ^n} \beta 。$ (6)

 $f\left( \beta \right) = \frac{2}{\text{π} }{\cos ^2} \beta 。$ (7)

 ${\nu _0}{\text{ = }}\frac{1}{{2\text{π} }}\sqrt {\frac{{{m_2}}}{{{m_0}}}}。$ (8)

 ${m_n} = \int\limits_0^{ + \infty } {\omega _e^n} \cdot {G_{XX}}({\omega _e}){\mathrm{d}}{\omega _e}。$ (9)

 $f(x) = \frac{x}{{{\sigma ^2}}}\exp \left( { - \frac{{{x^2}}}{{2{\sigma ^2}}}} \right)\begin{array}{*{20}{c}} {}&{0 \leqslant x < + \infty } 。\end{array}$ (10)

 $S = 2x。$ (11)

 ${f_S}(S) = \frac{S}{{4{\sigma ^2}}}\exp \left( { - \frac{{{S^2}}}{{8{\sigma ^2}}}} \right)\begin{array}{*{20}{c}}，\end{array}0 \leqslant S < + \infty。$ (12)

 $D_{ij}=\frac{T_{ij}.\nu_{0ij}}{A}\int_0^{+\infty}S^mf_{Sij}(S)\mathrm{d}S。$ (13)

 $N \cdot {S^m} = A 。$ (14)

 \begin{aligned} {D_{ij}} = &\frac{{{T_{ij}}.{\nu _{0ij}}}}{A}\cdot{(2\sqrt 2 {\sigma _{Xij}})^m}\cdot \Gamma \Bigg(1 + \frac{m}{2}\Bigg) = \\ &\frac{{{T_{ij}}.{\nu _{0ij}}}}{A}\cdot {(2\sqrt {2{m_{0ij}}} )^m}\cdot \Gamma \Bigg(1 + \frac{m}{2}\Bigg)。\end{aligned} (15)

 ${T_{ij}} = T\cdot{p_i}\cdot{p_j}。$ (16)

 \begin{aligned} D = &\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{D_{ij}}} } = \frac{T}{A}\cdot \Gamma \Bigg (1 + \frac{m}{2}\Bigg )\cdot \\ &\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{p_i}.{p_j}.} } {\nu _{0ij}}.{(2\sqrt {2{m_{0ij}}} )^m}。\end{aligned} (17)
2 异形浮体疲劳位置的选取 2.1 异形浮体模型的建立

 图 2 浮体有限元模型 Fig. 2 Floating body finite element model

2.2 异形浮体的水动力分析

 图 3 异形浮体水动力模型 Fig. 3 Hydrodynamic model of a shaped buoyant body

 图 4 异形浮体中部垂向弯矩的传递函数 Fig. 4 Transfer function of vertical bending moment in the middle of shaped floating body
2.3 疲劳位置的确定

 图 5 波浪荷载下浮体应力云图 Fig. 5 Stress cloud of floating body under wave loading

 图 6 应力最大位置 Fig. 6 Position of maximum stress

 图 7 浮体结构分段 Fig. 7 Floating body structure segmentatio

 图 8 网格细化 Fig. 8 Mesh refinement
3 传递函数的数值模拟

1）名义应力法：名义应力可以由提取疲劳点计算得到的应力乘以应力集中系数SCF（stress concentration factor）得到，针对不同的位置有不同的系数计算公式，具体的应力集中系数可查阅CCS《海洋工程结构物疲劳强度评估技术指南》3.2～3.4节得到[14]。采用名义应力法得到的响应曲线，如图9所示。

 图 9 名义应力法计算应力的响应拟合曲线 Fig. 9 Response fitting curves for stresses calculated by the nominal stress method

2）热点应力法：焊缝处的热点应力值是通过插值的方法求出的，具体方法如图10所示。采用热点应力法得到的响应曲线，如图11所示。求焊缝1号点的热点应力，不能直接读取1号点的应力，需要分别计算2条路径（由3到2到1或者由5到4到1）的线性插值，取其中较大值为1号点的热点应力。具体可由下式求得：

 图 10 疲劳位置热点应力求解路径 Fig. 10 Fatigue location hotspot stress solution paths

 图 11 热点应力法计算应力的响应拟合曲线 Fig. 11 Response fitting curve of stress calculated by hot spot stress method
 ${\sigma _1} = \max \left\{ \begin{gathered} 1.5{\sigma _2} - 0.5{\sigma _3}，\\ 1.5{\sigma _4} - 0.5{\sigma _5}。\\ \end{gathered} \right.$ (18)
3.1 名义应力法计算的传递函数

 图 12 异形浮体结构1号疲劳点的传递函数 Fig. 12 Transfer function for fatigue point 1 of shaped floating body structure

 图 13 异形浮体结构2号疲劳点的传递函数 Fig. 13 Transfer function for fatigue point 2 of the shaped floating body structure

 图 14 异形浮体结构3号疲劳点的传递函数 Fig. 14 Transfer function for fatigue point 3 of the shaped floating body structure

 图 15 异形浮体结构4号疲劳点的传递函数 Fig. 15 Transfer function for fatigue point 4 of the shaped floating body structure
3.2 热点应力法计算的传递函数

 图 16 异形浮体结构1号疲劳点的传递函数 Fig. 16 Transfer function for fatigue point 1 of the shaped floating body structure

 图 17 异形浮体结构2号疲劳点的传递函数 Fig. 17 Transfer function for fatigue point 2 of the shaped floating body structure

 图 18 异形浮体结构3号疲劳点的传递函数 Fig. 18 Transfer function for fatigue point 3 of the shaped floating body structure

 图 19 异形浮体结构4号疲劳点的传递函数 Fig. 19 Transfer function for fatigue point 4 of the shaped floating body structure
4 浮体疲劳疲劳寿命的计算

5 结　语

1）浮体的疲劳位置基本都产生在焊缝位置，提高焊接技术有利提高结构的疲劳寿命。

2）当浮体受到150°方向的波浪荷载时，结构的应力值最大，可以基于此对结构进行针对性的加强。

3）采用热点应力法计算的结构疲劳寿命要小于采用名义应力法所计算的结构疲劳寿命，结果偏于保守。在未能准确对焊缝进行建模时，建议采取热点应力法计算结构的疲劳寿命。

 [1] MATSUISHI M, ENDO T. Fatigue of metals subjected to varying stress [J]. Japan Society of Mechanical Engineers, 1967, 54(1): 84–91. [2] RYCHLIK I. A new definition of the rainflow cycle counting method[J]. International Journal of Fatigue, 1987, 9(2): 119–121. [3] DOWLING N E. Fatigue-failure predictions for complicated stress–strain histories[J]. Journal of Materials, 1972, 7(1): 71–87. [4] WATSON P, DABELL B J. Cycle counting and fatigue damage [J]. Warwick University, 1976. [5] BRACCESI C, CIANETTI F, LORI G, etal. A frequency method for fatigue life estimation of mechanical components under bimodal random stress process[J]. SDHM Structural Durability and Health Monitoring, 2005, 1(4): 277–290. [6] MRŠNIK M, SLAVIC J, BOLTEZAR M. Frequency-domain methods for a vibration-fatigue-life estimation. Application to real data[J]. International Journal Fatigue, 2013, 4(7): 8–17. [7] WANG M, YAO W. Frequency domain method for fatigue life analysis on notched specimens under random vibration loading[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2008, 40(4): 489–492. [8] 张朝阳, 刘俊, 白艳彬, 等. 基于谱分析法的深水半潜式平台疲劳强度分析[J]. 海洋工程, 2012(1): 53-59. DOI:10.3969/j.issn.1005-9865.2012.01.008 [9] 马网扣, 王志青, 张海彬, 等. 深水半潜式钻井平台节点疲劳寿命谱分析研究[J]. 海洋工程, 2008(3): 1-8. DOI:10.3969/j.issn.1005-9865.2008.03.001 [10] 谢文会, 谢彬, 王世圣, 等. 深水半潜式钻井平台典型节点谱疲劳分析[J]. 中国海洋平台, 2009(5): 28-33. DOI:10.3969/j.issn.1001-4500.2009.05.006 [11] 冯国庆. 船舶结构疲劳评估方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2003. [12] 冯国庆. 船舶结构疲劳强度评估方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2006. [13] 周蕊. 近海海浪的建模仿真研究[D]. 昆明: 昆明理工大学, 2015. [14] 中国船级社. 海洋工程结构物疲劳强度评估技术指南[S]. 2022. [15] 中国船级社. 基于谱分析的船体结构疲劳强度评估指南[S]. 2018.