大深度载人潜水器钛合金耐压球壳疲劳可靠性分析
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摘要
大深度潜水器的耐压壳体是保证潜水器正常作业的主要承力结构,其疲劳寿命及可靠性指标将直接影响潜水器的整体安全性能。本文基于断裂力学方法对大深度载人潜水器钛合金耐压球壳的疲劳寿命进行预测,并对其疲劳可靠性进行分析,为潜水器结构设计优化提供依据和参考。
选用最大设计下潜深度为4500米的美国Alvin号潜水器的下潜历史数据作为参考,由此确定该深度级别潜水器的疲劳载荷谱。通过不同概率模型的对比研究,选择了Gumbel分布作为深潜器下潜深度的概率分布模型,并通过潜水器所受压力与下潜深度的关系得到了耐压球壳的疲劳载荷谱。
分别基于板壳理论方法和有限元数值方法对耐压球壳的应力水平进行分析,通过计算,该耐压球壳满足潜水器建造规范中对于其静强度的要求。结合断裂力学对钛合金耐压球壳的疲劳寿命进行估算,分别采用基于Paris裂纹扩展模型和基于Brown-Hobson模型的疲劳全寿命裂纹扩展模型对裂纹扩展进行确定性分析,结果均满足设计要求。
最后综合计算精度和计算效率选择不含交叉项的二次响应面法作为耐压球壳疲劳可靠性的计算方法,并且分别基于Paris模型和基于Brown-Hobson模型的全寿命模型进行了可靠度指标计算和参数敏感性分析,可为各参数数值的选取及下潜作业深度提供一定的参考。结合计算结果从模型分析,由于全寿命模型计及了短裂纹扩展阶段从而能更好的描述裂纹扩展的过程,比起Paris模型结果更为精确,更适合应用于潜水器耐压球壳。
Pressure hull of deep submersible as a loading-bearing structure is the primary factor to ensure the normal work of the whole system, and the reliability of which is a direct impact on the performance of the submersible. In this paper, the author predicts the fatigue life of the pressure hull and then analyzes its reliability based on fracture mechanics, which could provide references for the structural design and optimization of the submersible.
Dive data of Alvin is chosen as a reference to determine the fatigue load spectrum of the deep submersible because Alvin has the same design maximum dive depth of 4500 meters. Gumbel distribution is more suitable to be used to create the probability model for dive depth distribution of deep submersible compared with other distributions, and then the fatigue load spectrum of pressure hull could be concluded by the transformation between pressure on the submersible and the dive depth.
Then the theory of plates and shells and the finite element method are used to analyze the stress level of the pressure hull which could be used to check the strength of the pressure hull. The result shows that the strength of the pressure hull meets the requirement to submersible.
The author uses fracture mechanics to estimate the fatigue life of titanium pressure hull. Crack model based on the Paris model and Brown-Hobson model are used to do uncertainty analysis of the crack propagation. The results meet the design requirement of the pressure hull.
At last, considering accuracy and efficiency quadratic response surface method without cross terms is chosen as the approximation method of fatigue reliability for the pressure hull. And then calculate the reliability index for the hull and analyze the parameter sensitivity in the two models, which could provide a reference for the selection of parameter values and dive depth. Compared with Paris model the total fatigue life model consider the stage of short crack propagation which could describe the full process of crack propagation more precisely, so the model is more suit for the analyzing of pressure hull.
选用最大设计下潜深度为4500米的美国Alvin号潜水器的下潜历史数据作为参考,由此确定该深度级别潜水器的疲劳载荷谱。通过不同概率模型的对比研究,选择了Gumbel分布作为深潜器下潜深度的概率分布模型,并通过潜水器所受压力与下潜深度的关系得到了耐压球壳的疲劳载荷谱。
分别基于板壳理论方法和有限元数值方法对耐压球壳的应力水平进行分析,通过计算,该耐压球壳满足潜水器建造规范中对于其静强度的要求。结合断裂力学对钛合金耐压球壳的疲劳寿命进行估算,分别采用基于Paris裂纹扩展模型和基于Brown-Hobson模型的疲劳全寿命裂纹扩展模型对裂纹扩展进行确定性分析,结果均满足设计要求。
最后综合计算精度和计算效率选择不含交叉项的二次响应面法作为耐压球壳疲劳可靠性的计算方法,并且分别基于Paris模型和基于Brown-Hobson模型的全寿命模型进行了可靠度指标计算和参数敏感性分析,可为各参数数值的选取及下潜作业深度提供一定的参考。结合计算结果从模型分析,由于全寿命模型计及了短裂纹扩展阶段从而能更好的描述裂纹扩展的过程,比起Paris模型结果更为精确,更适合应用于潜水器耐压球壳。
Pressure hull of deep submersible as a loading-bearing structure is the primary factor to ensure the normal work of the whole system, and the reliability of which is a direct impact on the performance of the submersible. In this paper, the author predicts the fatigue life of the pressure hull and then analyzes its reliability based on fracture mechanics, which could provide references for the structural design and optimization of the submersible.
Dive data of Alvin is chosen as a reference to determine the fatigue load spectrum of the deep submersible because Alvin has the same design maximum dive depth of 4500 meters. Gumbel distribution is more suitable to be used to create the probability model for dive depth distribution of deep submersible compared with other distributions, and then the fatigue load spectrum of pressure hull could be concluded by the transformation between pressure on the submersible and the dive depth.
Then the theory of plates and shells and the finite element method are used to analyze the stress level of the pressure hull which could be used to check the strength of the pressure hull. The result shows that the strength of the pressure hull meets the requirement to submersible.
The author uses fracture mechanics to estimate the fatigue life of titanium pressure hull. Crack model based on the Paris model and Brown-Hobson model are used to do uncertainty analysis of the crack propagation. The results meet the design requirement of the pressure hull.
At last, considering accuracy and efficiency quadratic response surface method without cross terms is chosen as the approximation method of fatigue reliability for the pressure hull. And then calculate the reliability index for the hull and analyze the parameter sensitivity in the two models, which could provide a reference for the selection of parameter values and dive depth. Compared with Paris model the total fatigue life model consider the stage of short crack propagation which could describe the full process of crack propagation more precisely, so the model is more suit for the analyzing of pressure hull.
引文
[1]潘涛.深潜器耐压结构强度分析与优化设计[D].哈尔滨:哈尔滨工程大学, 2010.
[2]中国船级社.潜水系统和潜水器入级与建造规范[S].北京:人民交通出版社, 1996.
[3] Rules for classification and constructione, 1-Ship technology, 5-Underwater technology, 2-Manned submersibles[S]. Published Germanischer Lloyd Aktiengesellschaft(GL) in 2009, 2009.
[4] Rules and regulations for the construction and classification of submersibles and underwater systems[S]. London: Lloyd’s Register of Shipping, 1989.
[5] Rules for building and classing underwater vehicles, systems and hyperbaric facilities[S]. Huston: American Bureau of Shipping, 2010.
[6]徐秉汉,朱邦俊等.现代潜艇结构强度的理论与试验[M].北京:国防工业出版社, 2007.
[7]李良碧,王仁华.深海载人潜水器耐压球壳的非线性有限元分析[J].中国造船, 2005, 46(4): 11-18.
[8]陆蓓,刘涛,崔维成.深海载人潜水器耐压球壳极限强度研究[J].船舶力学, 8(1): 51-58.
[9]俞铭华,王仁华,王自力等.深海载人潜水器有开孔耐压球壳的极限强度[J].中国造船, 2005, 46(4): 92-96.
[10]熊志鑫,佟福山.钛合金深潜器耐压球壳极限强度的切线模量因子算法[J].哈尔滨工程大学学报, 2010, 31(2): 177-181.
[11] V.Sinha, C.Mercer, W.O.Soboyejo. An investigation of short and long fatigue crack growth behavior of Ti-6Al-4V[J]. Materials Science and Engineering, 2000, A287: 30-42.
[12]赵永翔.低周疲劳短裂纹行为和可靠性分析[D].成都:西南交通大学, 1998.
[13] Shankman, A.D.. Materials for hydrospace pressure hulls, present and future. Ocean Systems Operations of North American Rockwell Corporation, California, 1968: 1-17.
[14] Garland, C.. Design and fabrication of deep-diving submersible pressure hulls. SNAME Transactions, 1968, 76: 161-179.
[15]俞铭华,王自力,李良碧,等.大深度载人潜水器耐压壳结构研究进展[J].华东船舶工业学院学报, 2004, 18(4): 1-6.
[16]李良碧,罗广恩,王自力.大深度载人潜水器疲劳寿命有限元分析[J].江苏科技大学学报(自然科学版), 2006, 20(3): 1-5.
[17]栗明,许金泉.残余应力对压力容器破坏模式的影响分析[J].力学季刊, 2007, 28(1): 92-97.
[18]卞如冈,崔维成,万正权等.焊接残余应力对疲劳寿命影响的定量研究[J].船舶力学, 2011, 15(7): 776-783.
[19]李向阳,崔维成,张文明.钛合金载人球壳的疲劳寿命可靠性分析[J].船舶力学, 2006, 10(2): 82-86.
[20]林杰威.航空发动机叶片疲劳寿命和可靠性研究[D].天津:天津大学, 2009.
[21]匡卫红,倪侃,张圣坤.给定置信度下的三参数P-S-N曲线[J].上海交通大学学报, 2002, 36(11): 1583-1586.
[22]闫相祯,刘锦昆,许志倩,等.服役海底管道钢疲劳可靠性试验与海底管道寿命预测[J].中国石油大学学报(自然科学版), 2010, 34(5): 109-113.
[23]谢里阳,林文强.线性累积损伤的概率准则[J].机械强度, 1993, 15(3): 41-44.
[24]吕海波,姚卫星.元件疲劳可靠性估算的剩余强度模型[J].航空学报, 2000, 21(1): 74-77.
[25] Broutman L J, Sahu S. A new theory to predict cumulative fatigue damage in fibre-glass reinforced plastics[C]. Composite materials: testing and design, ASTM STP497, 1972: 170-188.
[26] Yang J N, Jones D L. Load sequence Fatigue of Fibrous Composite Materials on the fatigue unnotched composite materials[C]. ASTM STP723, 1981: 213-232.
[27] Hashin Z. Cumulative damage theory for composite materials,residual life and residual strength methods[J]. Composite Science and Technology, 1985, 23: 1-19.
[28] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics, 1945, 12(3): A159-A164.
[29] Langer B F. Fatigue failure from stress cycles of varying amplitude [J]. Journal of Applied Mechanic, 1937, 59: A160-A152.
[30] Marco S M, Starkey W J. A concept of fatigue damage[C]. Transaction ASME, 1954, 76: 627-632.
[31] Altus E. Fatigue, Fractals and a Modified Miner’s Rule[J]. Journal of Applied Mechanics, 1991, 58(3): 571-579.
[32] Zhao Z W, Haldar A, Florence L B Jr. Fatigue-reliability evaluation of steel bridges[J]. Journal of Structural Engineering, ASCE, 1994, 120(5): 1608-1623.
[33] Wirsching P H. Fatigue Reliability for offshore structures[J]. Journal of Structural Engineering, ASCE, 1984, 110(10): 2340-2356.
[34]董聪,杨庆雄.结构系统疲劳可靠性分析理论与算法[J].航空学报, 1993, 14(5): 247-253.
[35]董聪,何庆芝.自治型随机疲劳累积损伤可靠性分析模型[J].机械强度, 1995, 17(1): 6-8.
[36]倪侃,张圣坤.二维Miner准则与Wirsching模型[J].船舶力学, 2002, 6(5): 38-43.
[37]谢里阳,李翠玲.应力—强度干涉模型在系统失效概率分析中的应用及相关问题[J].机械强度, 2005, 27(4): 492-497.
[38]李四超,张代国,张强.机械结构可靠性计算方法[J].船舰科学技术, 2011, 33(5): 63-65.
[39]孙权,赵建印,周经纶.复合应力作用下强度退化的应力—强度干涉模型可靠性统计分析[J].计算力学学报, 2007, 24(5): 358-361.
[40]安宗文,郑堃,黄建龙.多级疲劳载荷作用下的应力—强度干涉模型[J].电子科技大学学报, 2010, 39(6): 956-960.
[41]唐家银,赵永翔,宋冬利.应力—强度相关性干涉的静态和动态可靠度计算模型[J].西南交通大学学报, 2010, 45(3): 384-388.
[42] Wirsching P H. Probability-based fatigue design criteria for offshore structures. Final report, APIPRAC Project 81-15, 1983.
[43] Martindale S G, Wirsching P H. Reliability-based progressive fatigue collapse[J]. J Structural Engineering, ASCE, 1983, 109(8): 1792-1811.
[44] Karamchandani A, Dalane J I, Bjerager P. Systems reliability approach to fatigue of structures[J]. Journal of Structural Engineering, ASCE, 1992, 118(3): 684-700.
[45]邓洪洲,王肇民.结构系统疲劳可靠性分析方法及其应用[J].同济大学学报, 1997, 25(1): 17-22.
[46]丁克勤,柳春图.重要性抽样法在管节点疲劳可靠性分析中的应用[J].力学学报, 1996, 28(3): 359-362.
[47]靳慧,王立彬,王金诺.弹塑性随机有限元在低周疲劳分析中的应用[J].工程力学, 2004, 21(3): 196-200.
[48]董玉革.机械模糊可靠性设计[M].北京:机械工业出版社, 2001.
[49]赵少汴,王忠保.局部应力—应变法如何推广应用于高周疲劳.第六届全国疲劳学术会议论文集,厦门, 1993: 282-284.
[50]聂宏,常龙.基于局部应力应变法估算高周疲劳寿命[J].南京航空航天大学学报, 2000, 32(1): 75-79.
[51]姚卫星.金属材料疲劳行为的应力场强法描述[J].固体力学学报, 1997, 18(1): 38-48.
[52]陈凌,蒋家羚,范志超,等.低周疲劳寿命预测的能量模型探讨[J].金属学报, 2006, 42(2): 195-200.
[53] http://www.whoi.edu[OL].
[54]李向阳,刘涛,等.大深度载人潜水器在人耐压球壳的疲劳载荷谱分析[J].船舶力学, 2004, 8(1): 49-70.
[55] Mckee, A.I.. Recent submarine design practices and problems. SNAME Transactions, 1959, 67: 623-652.
[56]拉宾诺维奇.厚壁球壳的近似计算方法[J].壳体结构文汇(第四册).北京:中国工业出版社, 1965: 81-109.
[57] Paris P, Erdogan F. A critical analysis of crack propagation laws[J]. ASME Transactions, Journal of basic engineering, Series D, 1963, 85D(4): 528-534.
[58] Miller K J. Short crack problem[J]. Fatigue of Eng. Materials and Stru, 1982, 5(3): 223-232.
[59] Miller K J. The behaviour of short fatigue cracks and their initiation[J]. Fatigue Fract Master Struct, 1987, 10(2): 93-113.
[60] Angelova D, Akid R. A note on modelling short fatigue crack behaviour[J]. Fatigue Fract Engng Master Struct, 1998, 21(1): 771-779.
[61]刘建中,丁传富,吴学仁,等.钛合金TC4的疲劳小裂纹行为及其预测[C].第十一届全国疲劳和断裂学术会议, 2002.
[62]李良巧,顾唯明.机械可靠性设计与分析[M].北京:国防工业出版社, 1998.
[63]刘惟信.机械可靠性设计[M].北京:清华大学出版社, 2002.
[64]吕震宙,赵洁,岳珠峰.机械可靠性分析的高精度响应面法[J].应用数学和力学, 2007, 28(1): 17-24.
[65] Bucher C G. A fast and efficient response surface approach for structural reliability problems [J]. Structural Safety, 1990, 7(1): 57-66.
[66] Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J]. Somputational Structure, 1978, 9: 484-494.
[67]何恩山,刘勤,钱云鹏,等.基于仿真的动作机构可靠性灵敏度分析[J].机械设计, 2008, 25(11): 35-37.
[68] GB50153-2008,工程结构可靠性统一设计标准[M].中华人民共和国建设部,北京, 2008.
[69] GB50068-2001,建筑结构可靠性统一设计标准[M].中华人民共和国建设部,北京, 2001.
[2]中国船级社.潜水系统和潜水器入级与建造规范[S].北京:人民交通出版社, 1996.
[3] Rules for classification and constructione, 1-Ship technology, 5-Underwater technology, 2-Manned submersibles[S]. Published Germanischer Lloyd Aktiengesellschaft(GL) in 2009, 2009.
[4] Rules and regulations for the construction and classification of submersibles and underwater systems[S]. London: Lloyd’s Register of Shipping, 1989.
[5] Rules for building and classing underwater vehicles, systems and hyperbaric facilities[S]. Huston: American Bureau of Shipping, 2010.
[6]徐秉汉,朱邦俊等.现代潜艇结构强度的理论与试验[M].北京:国防工业出版社, 2007.
[7]李良碧,王仁华.深海载人潜水器耐压球壳的非线性有限元分析[J].中国造船, 2005, 46(4): 11-18.
[8]陆蓓,刘涛,崔维成.深海载人潜水器耐压球壳极限强度研究[J].船舶力学, 8(1): 51-58.
[9]俞铭华,王仁华,王自力等.深海载人潜水器有开孔耐压球壳的极限强度[J].中国造船, 2005, 46(4): 92-96.
[10]熊志鑫,佟福山.钛合金深潜器耐压球壳极限强度的切线模量因子算法[J].哈尔滨工程大学学报, 2010, 31(2): 177-181.
[11] V.Sinha, C.Mercer, W.O.Soboyejo. An investigation of short and long fatigue crack growth behavior of Ti-6Al-4V[J]. Materials Science and Engineering, 2000, A287: 30-42.
[12]赵永翔.低周疲劳短裂纹行为和可靠性分析[D].成都:西南交通大学, 1998.
[13] Shankman, A.D.. Materials for hydrospace pressure hulls, present and future. Ocean Systems Operations of North American Rockwell Corporation, California, 1968: 1-17.
[14] Garland, C.. Design and fabrication of deep-diving submersible pressure hulls. SNAME Transactions, 1968, 76: 161-179.
[15]俞铭华,王自力,李良碧,等.大深度载人潜水器耐压壳结构研究进展[J].华东船舶工业学院学报, 2004, 18(4): 1-6.
[16]李良碧,罗广恩,王自力.大深度载人潜水器疲劳寿命有限元分析[J].江苏科技大学学报(自然科学版), 2006, 20(3): 1-5.
[17]栗明,许金泉.残余应力对压力容器破坏模式的影响分析[J].力学季刊, 2007, 28(1): 92-97.
[18]卞如冈,崔维成,万正权等.焊接残余应力对疲劳寿命影响的定量研究[J].船舶力学, 2011, 15(7): 776-783.
[19]李向阳,崔维成,张文明.钛合金载人球壳的疲劳寿命可靠性分析[J].船舶力学, 2006, 10(2): 82-86.
[20]林杰威.航空发动机叶片疲劳寿命和可靠性研究[D].天津:天津大学, 2009.
[21]匡卫红,倪侃,张圣坤.给定置信度下的三参数P-S-N曲线[J].上海交通大学学报, 2002, 36(11): 1583-1586.
[22]闫相祯,刘锦昆,许志倩,等.服役海底管道钢疲劳可靠性试验与海底管道寿命预测[J].中国石油大学学报(自然科学版), 2010, 34(5): 109-113.
[23]谢里阳,林文强.线性累积损伤的概率准则[J].机械强度, 1993, 15(3): 41-44.
[24]吕海波,姚卫星.元件疲劳可靠性估算的剩余强度模型[J].航空学报, 2000, 21(1): 74-77.
[25] Broutman L J, Sahu S. A new theory to predict cumulative fatigue damage in fibre-glass reinforced plastics[C]. Composite materials: testing and design, ASTM STP497, 1972: 170-188.
[26] Yang J N, Jones D L. Load sequence Fatigue of Fibrous Composite Materials on the fatigue unnotched composite materials[C]. ASTM STP723, 1981: 213-232.
[27] Hashin Z. Cumulative damage theory for composite materials,residual life and residual strength methods[J]. Composite Science and Technology, 1985, 23: 1-19.
[28] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics, 1945, 12(3): A159-A164.
[29] Langer B F. Fatigue failure from stress cycles of varying amplitude [J]. Journal of Applied Mechanic, 1937, 59: A160-A152.
[30] Marco S M, Starkey W J. A concept of fatigue damage[C]. Transaction ASME, 1954, 76: 627-632.
[31] Altus E. Fatigue, Fractals and a Modified Miner’s Rule[J]. Journal of Applied Mechanics, 1991, 58(3): 571-579.
[32] Zhao Z W, Haldar A, Florence L B Jr. Fatigue-reliability evaluation of steel bridges[J]. Journal of Structural Engineering, ASCE, 1994, 120(5): 1608-1623.
[33] Wirsching P H. Fatigue Reliability for offshore structures[J]. Journal of Structural Engineering, ASCE, 1984, 110(10): 2340-2356.
[34]董聪,杨庆雄.结构系统疲劳可靠性分析理论与算法[J].航空学报, 1993, 14(5): 247-253.
[35]董聪,何庆芝.自治型随机疲劳累积损伤可靠性分析模型[J].机械强度, 1995, 17(1): 6-8.
[36]倪侃,张圣坤.二维Miner准则与Wirsching模型[J].船舶力学, 2002, 6(5): 38-43.
[37]谢里阳,李翠玲.应力—强度干涉模型在系统失效概率分析中的应用及相关问题[J].机械强度, 2005, 27(4): 492-497.
[38]李四超,张代国,张强.机械结构可靠性计算方法[J].船舰科学技术, 2011, 33(5): 63-65.
[39]孙权,赵建印,周经纶.复合应力作用下强度退化的应力—强度干涉模型可靠性统计分析[J].计算力学学报, 2007, 24(5): 358-361.
[40]安宗文,郑堃,黄建龙.多级疲劳载荷作用下的应力—强度干涉模型[J].电子科技大学学报, 2010, 39(6): 956-960.
[41]唐家银,赵永翔,宋冬利.应力—强度相关性干涉的静态和动态可靠度计算模型[J].西南交通大学学报, 2010, 45(3): 384-388.
[42] Wirsching P H. Probability-based fatigue design criteria for offshore structures. Final report, APIPRAC Project 81-15, 1983.
[43] Martindale S G, Wirsching P H. Reliability-based progressive fatigue collapse[J]. J Structural Engineering, ASCE, 1983, 109(8): 1792-1811.
[44] Karamchandani A, Dalane J I, Bjerager P. Systems reliability approach to fatigue of structures[J]. Journal of Structural Engineering, ASCE, 1992, 118(3): 684-700.
[45]邓洪洲,王肇民.结构系统疲劳可靠性分析方法及其应用[J].同济大学学报, 1997, 25(1): 17-22.
[46]丁克勤,柳春图.重要性抽样法在管节点疲劳可靠性分析中的应用[J].力学学报, 1996, 28(3): 359-362.
[47]靳慧,王立彬,王金诺.弹塑性随机有限元在低周疲劳分析中的应用[J].工程力学, 2004, 21(3): 196-200.
[48]董玉革.机械模糊可靠性设计[M].北京:机械工业出版社, 2001.
[49]赵少汴,王忠保.局部应力—应变法如何推广应用于高周疲劳.第六届全国疲劳学术会议论文集,厦门, 1993: 282-284.
[50]聂宏,常龙.基于局部应力应变法估算高周疲劳寿命[J].南京航空航天大学学报, 2000, 32(1): 75-79.
[51]姚卫星.金属材料疲劳行为的应力场强法描述[J].固体力学学报, 1997, 18(1): 38-48.
[52]陈凌,蒋家羚,范志超,等.低周疲劳寿命预测的能量模型探讨[J].金属学报, 2006, 42(2): 195-200.
[53] http://www.whoi.edu[OL].
[54]李向阳,刘涛,等.大深度载人潜水器在人耐压球壳的疲劳载荷谱分析[J].船舶力学, 2004, 8(1): 49-70.
[55] Mckee, A.I.. Recent submarine design practices and problems. SNAME Transactions, 1959, 67: 623-652.
[56]拉宾诺维奇.厚壁球壳的近似计算方法[J].壳体结构文汇(第四册).北京:中国工业出版社, 1965: 81-109.
[57] Paris P, Erdogan F. A critical analysis of crack propagation laws[J]. ASME Transactions, Journal of basic engineering, Series D, 1963, 85D(4): 528-534.
[58] Miller K J. Short crack problem[J]. Fatigue of Eng. Materials and Stru, 1982, 5(3): 223-232.
[59] Miller K J. The behaviour of short fatigue cracks and their initiation[J]. Fatigue Fract Master Struct, 1987, 10(2): 93-113.
[60] Angelova D, Akid R. A note on modelling short fatigue crack behaviour[J]. Fatigue Fract Engng Master Struct, 1998, 21(1): 771-779.
[61]刘建中,丁传富,吴学仁,等.钛合金TC4的疲劳小裂纹行为及其预测[C].第十一届全国疲劳和断裂学术会议, 2002.
[62]李良巧,顾唯明.机械可靠性设计与分析[M].北京:国防工业出版社, 1998.
[63]刘惟信.机械可靠性设计[M].北京:清华大学出版社, 2002.
[64]吕震宙,赵洁,岳珠峰.机械可靠性分析的高精度响应面法[J].应用数学和力学, 2007, 28(1): 17-24.
[65] Bucher C G. A fast and efficient response surface approach for structural reliability problems [J]. Structural Safety, 1990, 7(1): 57-66.
[66] Rackwitz R, Fiessler B. Structural reliability under combined random load sequences[J]. Somputational Structure, 1978, 9: 484-494.
[67]何恩山,刘勤,钱云鹏,等.基于仿真的动作机构可靠性灵敏度分析[J].机械设计, 2008, 25(11): 35-37.
[68] GB50153-2008,工程结构可靠性统一设计标准[M].中华人民共和国建设部,北京, 2008.
[69] GB50068-2001,建筑结构可靠性统一设计标准[M].中华人民共和国建设部,北京, 2001.