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1、插值方式对基于共同规范油轮疲劳评估的影响*刘俊作者简介：刘俊(1971)，女，湖北仙桃市人，博士，副教授，现从事计算结构力学以及岩土工程数值方法研究（JLIU）.，黄铭1（1上海交通大学船舶海洋与建筑工程学院，上海，200240）摘要：为了抵制低标准船舶，国际船级社协会（IACS）订立了针对散货船和油轮的共同规范（CSR）。在油轮疲劳评估部分，CSR对于热点处应力范围的计算插值方式给出了说明。由于热点处往往应力梯度很大，不同的插值方式对于应力范围计算结果的影响非常显著和直接，进而会明显影响疲劳评估的结果。文中针对某已经运营的油轮依据CSR的规定进行了疲劳评估，并与其他常用热点应力插值计算方式的
2、评估结果进行了对比，分析了插值方式对热点应力范围以及结构疲劳损伤和疲劳寿命估算的影响。研究表明，CSR对于油轮的疲劳强度要求远远高于该轮以前的入级规范，而JTP采用的求解热点应力范围的插值方式是直接影响因素，CSR所采用的插值方式是偏于保守的。关键词：热点应力法，疲劳寿命，共同规范，插值方式，油轮Influence of extrapolation method on Fatigue assessment of oil tanker based on Common Structural Rules LIU Jun1, HUANG Ming1 (1school of Naval Architec
3、ture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)Abstract: Common Structural Rules(CSR) has been developed by IACS for the purpose of rejecting lower standards oil tankers and ensuring maritime safety. The extrapolation method used to get Hot Spot Stress range
4、 is presented in the part of fatigue assessment of CSR. Since the gradient of stress is very high over the hot spot, different extrapolation method will bring on different stress range value. The choice of extrapolation method will have direct influence on the numerical outcome of the fatigue damage
5、 and fatigue life of the ship. The midship region cargo of an oil tanker, which is already in operation, has been modeled and fatigue assessment has been carried out following the instructions of the CSR. Some Different extrapolation methods have been used to get hot spot stresses ranges, furthermor
6、e, the influence of different extrapolation methods on numerical fatigue life value have been studied. The analysis shows that the fatigue strengthen requirement of CSR is far more strict then the rules of the corresponding Classification Society which the oil tanker classed. Moreover, it can be fou
7、nd that its the extrapolation method that CSR adopted resulting in such great disparity and the extrapolation method used in CSR is conservative.Keywords: Hot Spot Stress Approach；fatigue life；Common Structural Rules(CSR)；extrapolation method; oil tanker0 概述2006年4月1日生效的“油轮结构共同规范(CSR)” 是国际船级社协会（IACS）
8、为了抵制低标准船舶而制定的。众所周知，由于工作环境的原因，疲劳破坏是船舶结构破坏的主要破坏形式之一。为了保证入级油轮有足够的疲劳强度，CSR对油轮的疲劳评估在附录C中作了详细的的规定1。大多数情况下船舶结构节点的几何形状和受载情况比较复杂，常常不能在已有的S-N曲线中找到可直接比拟的类型，此时需要采用热点应力法来进行这些部位的疲劳评估。热点处的应力一般采用插值方法求取，由于热点区域一般存在应力集中现象，应力梯度很高，而且梯度的变化也比较大，所以热点应力的大小与插值方式的选择有直接关联，不同的插值方式求得的热点应力值会不一样，而且可能会有很大的差别2。共同规范中，规定在热点处精细网格区内使用尺寸
9、为（t为接头处内底板净厚度）的4节点板壳单元进行离散，热点应力值使用结构交接点第一和第二个单元的应力值内插得到，这与以往船级社的通用做法有一定差别。由于实施的时间还不长，共同规范下船体结构的热点应力法疲劳校核结果和以往各自船级社规范校核结果之间的差异，以及造成差异的影响因素等还没有得到充分的研究和认识，不利于新规范的应用和实施。基于此，本文按照共同规范的规定对某一已投入营运的油轮进行了的疲劳分析，分析表明，该油轮远不能满足CSR的疲劳强度要求，这说明CSR对于结构强度的要求更高，基于CSR设计的油轮更为安全。文中进一步采用不同的插值方式，包括其他船级社曾经采用的插值方式推求疲劳载荷下的热点处应
10、力范围，研究了不同插值方式对热点应力范围计算值以及进一步对疲劳损伤和疲劳寿命等估算值的影响，并探讨了其影响程度，研究表明，正是CSR所采用的插值方式导致该油轮的疲劳损伤和疲劳寿命的评估结果差强人意，CSR采用的求解热点应力范围的插值方式是偏于保守的。1 热点应力法由于实际结构往往比较复杂，名义应力的求得以及对应S-N曲线的获取不一定方便，所以热点应力法从上个世纪60年代后期开始应用于压力容器和焊接管接头的疲劳设计以来，应用越来越广泛，已经扩展到非管接头的结构3。所谓热点应力是指最大结构应力或“结构中危险截面上危险点应力”，一般多采用有限元计算或应变片实际测量法求解。采用有限元法时，有限元网格的
11、划分只模拟结构整体尺寸，不反映局部细微尺寸变化，计算求得结构中的工作应力，不包括焊缝形状、裂纹、缺口等引起强烈局部应力集中，只依赖于构件接头处的宏观尺寸和载荷参量。实际应用中，由于采用不同的热点应力插值方法和不同的有限元网格，不同研究者得到的疲劳评估结果相差较大。从以往研究者的工作和作者已做过的对比来看4，共同规范规定的网格精度是合适的，故仅在此讨论插值方式的影响。2 热点应力求解的插值方式热点应力法求解时，比较普遍的是将热点应力定义为焊趾处的应力值，此应力值又由距焊趾一定距离的两个点的应力值线性外插得到。由于热点附近应力梯度往往很大，求解出的热点处应力范围大小受插值方式的影响非常明显。常用比
12、较典型的插值方式有： （1） 针对焊接结构中焊趾位于板的表面的a型热点，国际焊接学会推荐采用距离焊趾0.4t和1.0t处应力值线性外推计算焊趾处的热点应力5-6，如图1(a)示。 （2） 采用距离焊趾0.5t和1.5t处应力值线性外推计算焊趾处的应力作为热点应力也很常见，见图1(b)，这也是很多船级社采用7-9的。（3） 在管接头进行疲劳强度分析时，如C点为焊趾位置，A、B为外插点，如图1（c），则一般A与C之间的距离取0.4-0.5t，A与B之间的距离取为t，其中t为弦管壁厚，焊缝趾端处的热点应力也是通过外插法得到 10。(a) (b) (c)图1 插值示意图Fig.1 Extrapolat
13、ion of hot spot stress公同规范中规定，对焊接结构节点，热点应力范围指距焊趾位置处、与焊接方向垂直的表面应力（图2），而此值使用结构交接点的第一和第二个单元各自的应力通过线性内插法得到，其中单元应力取自高斯积分点1,11。可以看出，在CSR中计算热点应力的位置的表述以及插值方式都有所不同。前述3种方法都是外推（插），而共同规范规定为内插，根据热点应力的分布特征可知外插方式得到的计算值会小于内插方式，所以可以定性判断共同规范采用的求解热点应力范围的插值方式较之以前的常用方法严格，这有助于保证油轮建造的高标准。图2 CSR热点应力示意Fig.2 Hot spot stress
14、defined in CSR3 有限元模型和不同插值方式针对某油轮采用板梁单元建立了三舱段模型（图3）进行疲劳评估，热点应力范围采用局部细化模型进行计算（图4）。油轮有限元计算模型的建立，包括腐蚀余量折减，工况选取以及约束和载荷的施加等等都按照共同规范的规定进行，热点的定义也按照共同规范采用，分析中唯一不同的只是热点应力范围计算方法。考虑到上文（3）针对的是管接头，不是板连接件，所以研究中采用了表1所示的四种热点应力范围的求解方式进行对比研究。 图3 油轮三舱段模型 图4 局部细化模型(tt)Fig.3 FE model of the midship region cargo Fig.4 Lo
15、cal refined model(tt)表1 热点应力范围的求解方式Tab. 1 Different calculating methods of hot spot stresses range方法编号具体描述1油轮共同规范规定方法2船级社通常采用方法，上文（2）3国际焊接学会推荐的针对焊接结构中焊趾位于板表面的a型热点的插值方法，上文（1）4直接计算值4 插值方式的影响分析采用表1所列的不同热点应力范围计算方式进行了疲劳分析，评估结果列于表2。从计算结果可以看出：（1） 不同方法得到的评估结果相差很大，基于共同规范插值方式（方法1）计算得出的设计年限内疲劳损伤（2.416）是船级社以往常用
16、方式（方法2）得出的设计年限内疲劳损伤计算值（1.067）的2.264倍，而方法2预期疲劳寿命估算值（23.44年）是方法1预期疲劳寿命估算值（10.35年）的2.267倍；（2） 基于共同规范插值方式（方法1）的热点应力范围计算结果最大，相应的设计年限内（25年）疲劳损伤最大（2.416）而预期疲劳寿命最短（10.35年），远远低于共同规范关于油轮疲劳强度要求，其计算结果和以直接计算结果作为热点应力值方式（方法4）的计算结果比较接近；（3） 按照船级社以往常用方式（方法2）计算热点应力范围，得到的设计年限（25年）内疲劳损伤最小（1.067）和预期疲劳寿命最长（23.44年），接近共同规范设
17、计寿命25年的要求，同时可以看出该油轮确实满足当时的入级标准；（4） 按照焊接学会推荐的热点插值计算方法（方法3）得到的评估结果与方法2比较接近。上面4种计算热点应力范围的方法中，除方法4是直接采用计算值外，方法2和方法3采用距交接点远于热点的两点应力外推（插）的方式，方法1采用与交接点距离分别大于和小于热点的两点处应力范围值内插的方式，由于与交接点越近应力和应力梯度越大，所以方法2和3确定的热点应力范围小于直接计算值；反之方法1确定的计算值则大于直接计算值，由于计算得到的热点应力范围不同，疲劳评估结果也出现了差异。上述结果说明，不同的插值方式得到的疲劳评估结果差异很大，插值方式的选取直接影响
18、了疲劳损伤和疲劳寿命的计算值。表2 不同插值方式下疲劳评估Tab. 2 Fatigue assessments with different interpolation or extrapolation methods插值方法热点处应力范围(MPa)边舱折角接头疲劳评估满载工况压载工况设计寿命下损伤寿命（年）Se1Se2SixSiySizSR1Se1Se2SR2满载压载总和1354.951.8待添加的隐藏文字内容30.5535.689.1265.0205.953.094.62.3540.0622.41610.352275.640.00.4628.067.7206.0156.842.271.91
19、.0480.0191.06723.443296.943.50.4830.374.5221.6167.045.277.91.3300.0271.35718.424344.050.30.5334.786.3256.8199.551.591.72.1330.0542.18811.435 结论研究表明，该油轮尽管满足入级时相应的疲劳强度要求，却不能满足共同规范的疲劳强度规定，造成这种矛盾的直接原因是，依循不同规范计算热点应力范围时采用的插值方式不同。共同规范规定的热点应力范围插值方式有助于提高油轮的建造标准，保障海上安全，但校核结果偏于保守。参考文献1 IACS. Common Structural
20、Rules for Oil TankersR. International Association of Classification Societies, 2006. 2 Wolfgang Fricke, Adrian Kahl. Comparison of different structural stress approaches for fatigue assessment of welded ship structures. Marine Structures. 2005.9-11, 18(7-8), 473-4883 Zhi-Gang Xiao, Kentaro Yamada. A
21、 method of determining geometric stress for fatigue strength evaluation of steel welded joints. International Journal of Fatigue. 26 (2004), 127712934 刘俊，薛鸿祥，陈芳，某油轮基于共同规范疲劳评估及网格精度上海交通大学学报，2008.6. 42(6): 910-913LIU Jun, XUE Hong-xiang, CHEN Fang. Fatigue Assessment of an Oil Tanker Based on Common St
22、ructural Rules and the Influence of Mesh Size. Journal Of Shanghai Jiaotong University. 2008.6. 42(6): 910-9135 贾法勇，霍立兴，张玉凤等，热点应力有限元分析的主要影响因素焊接学报，2003.6. 24(3): 27-30JIA Fa-yong, HUO Li-xing, ZHANG Yu-feng etc. Key influence factors in hot spot stress FEM analysis. Transactions of the China Welding
23、Institution. 2003.6. 24(3): 27-30 6 Ilkka Poutiainen, Pasi Tanskanen, Gary Marquis. Finite element methods for structural hot spot stress. International Journal of Fatigue, 26 (2004): 114711577 ABS. Guide for building and classing membrane tank lng vessels. 2002,175-1768 DNV. Fatigue assessment of s
24、hip structuresS/Det Norske Veritas Classification Notes No30. 20039 BV. Part Bhull and stabilityS/Bureau Veritas Rules for the Classification of Steel Ships. 200310 刘刚，郑云龙，赵德有等，BINGO9000半潜式钻井平台疲劳强度分析船舶力学，2002.4 6(2): 54-63LIU Gang, ZHENG Yun-long, ZHAO De-you etc. Fatigue Strength Analysis of BINGO9
25、000 Semisubmersible Drilling Rig. Journal of Ship Mechanics. 2002.4 6(2): 54-6311 罗广恩，王自力，张延昌等，基于JTP规范中热点应力的油船船体疲劳强度分析江苏科技大学学报(自然科学版)，2007.2，21(1): 17-20LUO Guang-en，WANG Zi-li，ZHANG Yan-chang etc. Fatigue Assessment of Oil Tanker Based on Hot Spot Stress in JTP Rules. Journal of Jiangsu University
26、of Science and Technology(Natural Science Edition). 2007.2，21(1): 17-20作者简介：刘俊，女，博士，上海交通大学船舶海洋与建筑工程学院副教授。研究方向为船舶与海洋工程计算结构力学和岩土工程数值方法。通讯地址：上海市东川路800号上海交通大学船舶海洋与建筑工程学院 邮编：200240Email：jliu; Tel: 021-62933375，34204470Editors note: Judson Jones is a meteorologist, journalist and photographer. He has free
27、lanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputn
28、ik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized
29、 space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a c
30、rane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at wo
31、rk glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a
32、 journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his
33、pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded superson
34、ic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent cou
35、ld happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the a
36、tmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary la
37、yer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Oly
38、mpic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver
39、preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes
40、 too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute succ
41、essfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachu
42、te is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
