具有缺陷板的船体极限强度可靠性分析
|
摘要
船体结构在建造和使用过程中很可能产生结构性缺陷(如初始变形、凹陷、开孔、裂纹等),由于设计和使用的需要,有些船板需要开孔,这些因素导致船体结构可靠性降低,而其中的某些缺陷可能产生危险的后果,导致事故发生。因此,从安全的角度考虑,如何精确地估算船体结构的实际承载能力以及产生缺陷后的极限剩余强度,并更科学、更合理地进行船舶结构设计和计算,已成为当今船舶力学界研究的一个热点课题。本文围绕这些问题开展的具体工作如下:1.结合板的非线性控制方程和有限元计算结果,讨论了具有初始缺陷(初始变形和焊接应力)、凹陷缺陷、开孔缺陷、裂纹缺陷板格的极限强度公式。给出了以完整结构极限强度和缺陷为参数的板格极限强度公式,从而便于建立具有缺陷结构的安全余量,为具有缺陷结构的可靠性分析提供理论基础。
2.给出了结构可靠性敏度分析方法,分析了各种缺陷因素(初始缺陷、凹陷、开孔、裂纹)对板格极限强度可靠性指标的影响。分析表明:(1)对于具有初始缺陷的板格,无论板格柔度如何,都应严禁使用具有严重初始变形的板格,严格控制使用具有一般初始变形的板格,尽量减少使用具有轻微初始变形的板格。在板格柔度较小时,尽量减小焊接残余应力,在板格柔度相对较大时,应严格控制焊接残余应力;(2)对于具有凹陷的板格,要严格控制凹陷直径的大小,合理控制凹陷的深度;(3)对于具有开孔的板格,应尽量开圆孔,减小开孔尺寸,以保证板格具有足够的安全裕度;(4)对于具有初始裂纹的板格,无论载荷和裂纹的形式如何都应严格控制裂纹尺寸。
3.结合具有缺陷板格的极限强度公式,给出了具有缺陷的板元减缩刚阵和反向节点力的显性表达式,为结构系统在失效过程中的力学分析提供参考,使残余结构的力学分析更加符合工程实际。
4.建立随机船舶结构可靠性分析的一般模型,将结构力学计算的基本变量,如位移、弹性模量、单元的几何参数等直接放到安全余量中,使安全余量的数学模型更贴近原始状态(不是简单写成抗力和内力的关系,如Z=R(抗力)-S(内力)),给出了用基本变量显示的表达式,提高结构系统可靠性的计算精度。结合某型船舶的结构形式,考虑板格初始缺陷、凹陷、开孔、初始裂纹等因素,对某型船舶结构中的一个舱段进行具有缺陷结构的系统可靠性分析,并与完整结构系统可靠性进行比较。分析表明,由于缺陷的存在,舱段结构系统可靠度有明显的降低,特别是在假定的具有几何变形部位处板的可靠性指标降低的程度更大。因此,要严格控制初始缺陷的大小使其在一般缺陷范围内,对于重要结构一定要将缺陷控制在小缺陷范围内。
Structural defectiveness occurs in the process of building and use of hull in all probability,such as initial distortion,concavity,hole,crackle and so on. Because of the requirements of design and use,some holes need to be drilled in the plate.The decrease of the reliability of hull structure is induced by those factors.And the danger may occur as a result of some defectiveness.Indeed,the accident may be also induced.Therefore,considering the safety,how to accurately estimate the actual carrying capacity of the hull and the ultimate remnant v after the defectiveness occurring,and also how to carry out the design and computation of the marine structure more scientifically and reasonably,all of these have been a pop topic in the field of ship mechanics.The work concerning these problems has been done in this paper,such as follows:
1.Combining the nonlinear control equation of plate and the results of the FEM,the expressions of ultimate strength of the plate grid,which has initial defectiveness(initial distortion and welded stress),concavity,hole,or crackle,are discussed separately.Taking the ultimate strength of integral structure and the defectiveness as parameters,the formulae of ultimate strength of plate grid are given.Consequently,it is convenient for establishing the safety margins of defective structure,and all those provide the theoretical basis for reliability analysis of defective structure.
2.The sensitivity analysis method of the structural reliability is given.The influence of every kind of defectiveness(initial distortion,concavity,hole,and crackle) on the reliability index is analyzed.The analysis indicates that,(1) for the plate grid with initial defectiveness,whatever the flexibility is,the use of that with severe initial distortion should be declined,and the use of that with general initial distortion should be controlled strictly,and also the use of that with slight initial distortion should be limited furthest.When the flexibility of plate grid is less,the welded remnant stress should minish furthest,and when the flexibility is larger, the welded remnant stress should be controlled strictly;(2) for the plate grid with concavity,the diameter of concavity should be controlled strictly,and the depth of that should be controlled reasonably;(3) for the plate grid with hole,the dimension of the hole should be controlled strictly and be less than a certain range, in order to ensure the plate grid with enough reliability reserves.If the circinal hole can be made,do it.Or if not,the dimension of the hole should be minish furthest;(4) for the plate grid with initial crackle,whatever the load and the form of crackle are,the dimension of crackle should be controlled strictly.
3.Combining the formula of ultimate strength of plate grid with defectiveness,the reducing stiffness matrix and the obvious expression of reverse node force of the plate unit with defectiveness are given,which provides reference to mechanics analysis of the structural system in the progress of failure,and makes the mechanics analysis of the remanent structure more coincident with engineering practice.
4.The general model of stochastic reliability analysis of marine structure is established.The basic variables in the calculation of structural mechanics,such as displacement,elastic modulus,geometrical parameter of the unit and so on,are taken into the safety margin directly.The mathematic model of safety margin is made more close to its original state(not be simply described as the relationship between resistance and internal force,such as Z=R-S,where,R is resistance and S is internal force).The obvious expression of safety margin with basic variables is given,and the calculational precision of the structural system reliability is increased.Combining the structural form of the certain ship and considering the factors of initial defectiveness,concavity,hole,and initial crackle etc,the system reliability analysis of one cabin block of the certain marine structure is carried out,and the cabin block is compared with the structure system which has no defectiveness.The analysis indicates that,because of the defectiveness,the reliability index of structure system of the cabin block reduces obviously,and especially,that of the plate with supposed geometrical distortion reduces more.Thus,the size of initial defectiveness should be controlled strictly and be made in the general range.For the important structure,the size of defectiveness must be controlled in the small range.
2.给出了结构可靠性敏度分析方法,分析了各种缺陷因素(初始缺陷、凹陷、开孔、裂纹)对板格极限强度可靠性指标的影响。分析表明:(1)对于具有初始缺陷的板格,无论板格柔度如何,都应严禁使用具有严重初始变形的板格,严格控制使用具有一般初始变形的板格,尽量减少使用具有轻微初始变形的板格。在板格柔度较小时,尽量减小焊接残余应力,在板格柔度相对较大时,应严格控制焊接残余应力;(2)对于具有凹陷的板格,要严格控制凹陷直径的大小,合理控制凹陷的深度;(3)对于具有开孔的板格,应尽量开圆孔,减小开孔尺寸,以保证板格具有足够的安全裕度;(4)对于具有初始裂纹的板格,无论载荷和裂纹的形式如何都应严格控制裂纹尺寸。
3.结合具有缺陷板格的极限强度公式,给出了具有缺陷的板元减缩刚阵和反向节点力的显性表达式,为结构系统在失效过程中的力学分析提供参考,使残余结构的力学分析更加符合工程实际。
4.建立随机船舶结构可靠性分析的一般模型,将结构力学计算的基本变量,如位移、弹性模量、单元的几何参数等直接放到安全余量中,使安全余量的数学模型更贴近原始状态(不是简单写成抗力和内力的关系,如Z=R(抗力)-S(内力)),给出了用基本变量显示的表达式,提高结构系统可靠性的计算精度。结合某型船舶的结构形式,考虑板格初始缺陷、凹陷、开孔、初始裂纹等因素,对某型船舶结构中的一个舱段进行具有缺陷结构的系统可靠性分析,并与完整结构系统可靠性进行比较。分析表明,由于缺陷的存在,舱段结构系统可靠度有明显的降低,特别是在假定的具有几何变形部位处板的可靠性指标降低的程度更大。因此,要严格控制初始缺陷的大小使其在一般缺陷范围内,对于重要结构一定要将缺陷控制在小缺陷范围内。
Structural defectiveness occurs in the process of building and use of hull in all probability,such as initial distortion,concavity,hole,crackle and so on. Because of the requirements of design and use,some holes need to be drilled in the plate.The decrease of the reliability of hull structure is induced by those factors.And the danger may occur as a result of some defectiveness.Indeed,the accident may be also induced.Therefore,considering the safety,how to accurately estimate the actual carrying capacity of the hull and the ultimate remnant v after the defectiveness occurring,and also how to carry out the design and computation of the marine structure more scientifically and reasonably,all of these have been a pop topic in the field of ship mechanics.The work concerning these problems has been done in this paper,such as follows:
1.Combining the nonlinear control equation of plate and the results of the FEM,the expressions of ultimate strength of the plate grid,which has initial defectiveness(initial distortion and welded stress),concavity,hole,or crackle,are discussed separately.Taking the ultimate strength of integral structure and the defectiveness as parameters,the formulae of ultimate strength of plate grid are given.Consequently,it is convenient for establishing the safety margins of defective structure,and all those provide the theoretical basis for reliability analysis of defective structure.
2.The sensitivity analysis method of the structural reliability is given.The influence of every kind of defectiveness(initial distortion,concavity,hole,and crackle) on the reliability index is analyzed.The analysis indicates that,(1) for the plate grid with initial defectiveness,whatever the flexibility is,the use of that with severe initial distortion should be declined,and the use of that with general initial distortion should be controlled strictly,and also the use of that with slight initial distortion should be limited furthest.When the flexibility of plate grid is less,the welded remnant stress should minish furthest,and when the flexibility is larger, the welded remnant stress should be controlled strictly;(2) for the plate grid with concavity,the diameter of concavity should be controlled strictly,and the depth of that should be controlled reasonably;(3) for the plate grid with hole,the dimension of the hole should be controlled strictly and be less than a certain range, in order to ensure the plate grid with enough reliability reserves.If the circinal hole can be made,do it.Or if not,the dimension of the hole should be minish furthest;(4) for the plate grid with initial crackle,whatever the load and the form of crackle are,the dimension of crackle should be controlled strictly.
3.Combining the formula of ultimate strength of plate grid with defectiveness,the reducing stiffness matrix and the obvious expression of reverse node force of the plate unit with defectiveness are given,which provides reference to mechanics analysis of the structural system in the progress of failure,and makes the mechanics analysis of the remanent structure more coincident with engineering practice.
4.The general model of stochastic reliability analysis of marine structure is established.The basic variables in the calculation of structural mechanics,such as displacement,elastic modulus,geometrical parameter of the unit and so on,are taken into the safety margin directly.The mathematic model of safety margin is made more close to its original state(not be simply described as the relationship between resistance and internal force,such as Z=R-S,where,R is resistance and S is internal force).The obvious expression of safety margin with basic variables is given,and the calculational precision of the structural system reliability is increased.Combining the structural form of the certain ship and considering the factors of initial defectiveness,concavity,hole,and initial crackle etc,the system reliability analysis of one cabin block of the certain marine structure is carried out,and the cabin block is compared with the structure system which has no defectiveness.The analysis indicates that,because of the defectiveness,the reliability index of structure system of the cabin block reduces obviously,and especially,that of the plate with supposed geometrical distortion reduces more.Thus,the size of initial defectiveness should be controlled strictly and be made in the general range.For the important structure,the size of defectiveness must be controlled in the small range.
引文
[1]安伟光.结构系统可靠性和基于可靠性的优化设计.北京:国防工业出版社,1997:1页,75-80页,266-277页
[2]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计.哈尔滨:哈尔滨工程大学出版社,2005:7-11页,251-336页
[3]李杰着.随机结构系统—分析与建模.北京:科技出版社,1996:1-8页
[4]秦权.随机有限元及其进展Ⅱ:可靠度随机有限元和随机有限元的应用.工程力学,1995,12(1):1-9页
[5]孙逊,高明.基于随机有限元方法的拱坝可靠性分析.水利水运科学研究,1994(1):71-80页
[6]邵文蛟.不完整结构的可靠性分析.北京:国防工业出版社,1997:1页,185-187页
[7]Freudenthal A M.The Safety of Structures.ASCE Trans.1947,112:125-129 P
[8]Freudenthal A M.Safety and The Probability of Structural Failure.ASCE Trans.1956,121:1337-1397 P
[9]Cornell C A.Structural Safety Specification Based on Second-Moment Reliability.Sym.Int.Assoc.of Bridge and Struct.Engr.London.1969:85-105P
[10]Lind N.C..Consistent Partial Safety Factors.ASCE.1971,97(ST6):65-76P
[11]Hasofer A M,Lind N C.Exact and Invariant Second-Moment Code Format.J.Eng.Mech.Div.ASCE.1974,100(1):111-121P
[12]Zhao Y.G.and Ono T..New Approximations for SORM:Part1.J.Eng.Mech.1999,125(1):79-93P
[13]Rackwitz R.and Fiessler B..An Algorithm for Calculation of Structural Reliability under Combined Loading.Munchen.1977:36-45P
[14]Bncher C.G.and Bourgund U..A Fast and Efficient Response Surface Approach for Structural Reliability Problem.Structural Safety.1990,7:57-66P
[15]陈虬,刘先斌.随机有限元法及其工程应用.成都:西南交通大学出版社,1993:21-30页
[16]航空工业部科学技术委员会编.飞机结构损伤容限设计指南.北京:国防工业出版社,1985
[17]航空航天工业部科学技术研究院编.飞机结构耐久性及损伤容限设计手册(2).北京:国防工业出版社,1989
[18]Thoft-christensen P.and Murotsu Y..Application of Structural Systems Reliability Theory.Springer-Verlag.1986:101-126P
[19]冯元生,董聪.枚举结构主要失效模式的一种方法.航空学报.1991,12(9):A37-42页
[20]安伟光,蔡荫林.冗余桁架结构的故障分析.哈尔滨船舶工程学院学报.1992,10(4):479-485页
[21]安伟光,蔡荫林.余度结构故障概率计算的一种方法.兵工学报,1992,2:92-96页
[22]Thoft-christensen.Reliability of Structural Systems,Studies in Applied Mechanics,24:Advances in the theory of plates and shells,Elsevier Science publishers B.U.1990:156-178P
[23]Ditlevsen O.Narrow Reliability Bounds for Structural System.J.Struc.Mech.1979,7(4):453-472P
[24]A.H.-S.A.and W.H.Tang.Probability Concepts in Engineering Planning and Design.John Wiley-and Sons.1984,2:135-146P
[25]Feng Y.S..A Method for Computing Structural System Reliability with High Accuracy.Computers and Structures.1989,33(1):1-5P
[26]Song B.F..A Numerical Integration Method in Affine Space and A Method with High Accuracy for Computing Structural System Reliability.Computer & Structures.1992,42(2):255-262P
[27]蔡荫林,周健生.结构系统失效概率的近似公式.航空学报.1992,13(3):A219-223页
[28]安伟光,王金明.具有多随机变量的结构系统的可靠性分析.兵工学报. 2001增刊:68-72页
[29]Cai YinLin,An WeiGuang,Chen WeiDong.Reliability Assessment and Optimization Design for Structural Systems.Proceedings of The Second International Conference on Reliability Maintainability and Safety,Beijing,China.1994,7:344-349P
[30]陈卫东,王善,蔡荫林.杆板结构系统的可靠性分析.哈尔滨工程大学学报.1997,18(6):68-74页
[31]An WeiGuang and Cai YinLin.Failure Analysis in Tall Redundant Truss Structures.Proceedings of the Fourth International Conference on Tall Buildings.Hong Kong & Shanghai.1988.04:358-363P
[32]安伟光.荷载效应组合时的失效概率.哈尔滨船舶工程学院学报.1988,9(2):126-136页
[33]蔡荫林,安伟光.随机组合力下冗余结构的故障概率计算.哈尔滨船舶工程学院学报.10(2):135-144页
[34]安伟光,陈卫东.结构系统在随机组合力作用下的可靠性分析.哈尔滨工程大学学报.1996,17(1):15-23页
[35]AN Wei-guang,SUN Ke-lin,CHEN Wei-dong,WANG Bin-sheng,CAI Yin-lin.Optilnum Design Based on Reliability in Stochastic Structure Systems.Applied Mathematics and Mechanics.2005,26(10):1293-1302P
[36]安伟光,孙克淋,王滨生.梁板结构系统可靠性分析的关键问题研究.宇航学报.2003,24(6):621-624页
[37]Jeom Kee Paik,Jae Myung Lee,Dong Hoon Lee.Ultimate strength of dented steel plates under axial compressive loads.International Journal of Mechanical Sciences.2003,45:433-448P
[38]Jeom Kee Paik,Bong Ju Kim.Ultimate strength formulations for stiffenedpanels under combined axial load,in-plane bending and lateral pressure.Thin-Walled Structures.2002,40:45-83P
[39]Jeom Kee Paik,Y.V.Satish Kumar,Jae Myung Lee.Ultimate strength of cracked plate elements underaxial compression or tension.Thin-Walled Structures.2005,45:237-272P
[40]Jeom Kee Paik,,Anil K.Thayamballi,Do Hyung Kim.An analytical method for the ultimate compressive strength and effective plating ofstiffened panels.Journal of Constructional Steel Research.1999,49:43-68P
[41]Jeom Kee Paik,Y.V.Satish Kumar,Jae Myung Lee.Ultimate strength of cracked plate elements under axial compression or tension.Thin-Walled Structures.2005,43:237-272P
[42]束长庚,周国华.船舶结构的屈曲强度.北京:国防工业出版社,2003:212-214页
[43]邵文蛟.初裂纹尺寸对疲劳可靠性影响.船舶力学,2001,5(6):50-54页
[44]邵文蛟,邹劲松.初挠度对平面刚架系统可靠性影响.中国造船,1992,2:72-80页
[45]石理国,姚木林.管节点焊接残余应力研究.舰船性能研究,1991,3:49-57页
[46]石理国,包荪蓉.海洋平台有损杆件的承载能力研究.舰船性能研究,1992,3:91-101页
[47]沈世钊,陈昕,林有军,汤建南.单层球面网壳的稳定性.空间结构,1997,3(3):3-12页
[48]林有军,沈世钊.短程线型球面网壳结构的稳定性.哈尔滨建筑大学学报,1999,32(3):30-33页
[49]吴轶,沈世钊.单层双曲扁网壳的稳定性.哈尔滨建筑大学学报,1999,32(4):24-28页
[50]赵维涛.飞行器结构可靠性分析与优化设计研究.哈尔滨工程大学博士学位论文,2006:7-24页
[51]赵国藩.工程结构可靠性理论与应用.大连:大连理工大学出版社,1996:51-62页
[52]Paik,J.K.and Thayamballi,A.K.An empirical formulation for predicting the ultimate compressive strength of stiffened panels,Proc.of International Offshore and Polar Engineering Conference,Honolulu,May,1997:328-338P
[53]Paik,J.K.,Thayamballi,A.K.and Park YI.Local buckling of stiffeners in ship plating,J.of Ship Research.1998.42:56-67P
[54]Paik,J.K.,Thayamballi,A.K.and Lee,W.H.A numerical investigation of tripping,Marine Structures.December,1998:159-183P
[55]Paik,J.K.,Thayamballi,A.K.and Kim,D.H.An analytical method for the ultimate compressive plating of stiffened panels,J.of Constructional Steel Research.1999,49:43-68P
[56]Paik,J.K.,Thayamballi,A.K.,Wang,G and Kim,B.J.On advanced buckling and ultimate strength design of ship plating,Trans.SNAME.2000:108P
[57]Paik,J.K.,Thayamballi,A.K.Buckling strength of steel plating with elastically restrained edges,Thin-Walled Structures.2000,137(1):27-57P
[58]Paik,J.K.,Thayamballi,A.K.and Kim,B.J.Advanced ultimate strength formulations for ship plating under combined biaxial compression/tension,edge shear and lateral pressure loads.Marine technology.2001,138:9-25P
[59]Paik,J.K.,Thayamballi,A.K.and Kim,B.J.Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure,Thin-Walled Structures.2001,215-246P
[60]Cui,W.C.and Mansour A.E.Effects of Welding Distortion and Residual Stress on the Ultimate Strength of Ship Plates under Un-axial Compression.Marine Structures.1998,11:251-269
[61]张少雄,余友谊.有凹陷的板在轴向压力作用下的极限强度.武汉理工大学学报.2004,28(3):315-333页
[62]徐力,刘荣桂,韦芳芳.开孔板的有限元分析.江苏大学学报.2002,23(5):28-30页
[63]O'Dowd N.Elastic-plastic analysis of biaxial loaded center-cracked plate[J].International Journal of Solids and Structures.1999,36:5639-5661P
[64]胡勇,崔维成.具有裂纹缺陷的板和加筋板格在联合载荷作用下的剩余极限强度.船舶力学.2003,7(1):63-78页
[65]孙克淋,安伟光,王滨生等.航天飞机薄壁结构的可靠性分析.哈尔滨工程大学学报.2004,25(3):327-331页
[66]安伟光,孙克淋,陈卫东等.随机结构系统基于可靠性的优化设计.应用数学和力学.2005,26(10):1175-1182页.
[67]O.F.休斯著.张祥孝译.船舶结构设计.广州:华南理工大学出版社,1988:1-6页,61-83页,360-368页,330-336页,369-382页,241页,279页,322页
[68]J.W.Davies.,A Finite Element to Model the In-Pane Response of Ribbed Rectangular Panels.M.Eng.Sc.thesis,University of New South Walse,Sydney.1976
[69]龙兵.船舶结构可靠性分析方法研究.哈尔滨工程大学硕士学位论文,2002:13-14页
[70]余建星.船体横框架的可靠性分析.天津大学硕士学位论文,1990
[71]ShinozukaM,LenceE.A probabilistic model for spatial distribution of material properties.Engng.Feactuec Mech.1976(8):217-227P
[72]Cambou B.Application of first order uncertainty analysis in the finite element method in linear elasticity.Proc.Second Int.Conf.on Applications of Stastistics and Probability in Scil and Struct.Engng.London England 1971:117-122P
[73]Dendrou B A,Houstis E N.An inference finite element model for field applications.Applied Mathematical Modeling,1,Guildford,England 1978:49-55P
[74]Baecher G B,Ingra T S.Stochastic FEM in settlement predictions.J.Geotech.Engng.107,GT 1981(4):449-463P
[75]Handa K,Anderson,K.Applications of finite element methods in statistical analysisof structures.Proc.3~(rd) Int.Conf.on Struct.Safety and Reliability.Trondhrim,Norway(June 1981):409-417P
[76]Hisada T,Nakagiri,S.Stochastic finite element method developed for struct.safety and reliability.Proc.3~(rd) Int.Conf.on Struct.Safety and Reliability.Trondhrim,Norway(June 1981):395-408P
[77]Nakagiri S,Hisada T.Stochastic finite element method developed for struct.analysis with uncertain parameters.Proc,Int.Conf.on FRM Australia (August 1982):206-211P
[78]Hisada T,Nakagiri S.Role of stochastic finite element method in struct.safety and reliability.Proc.4~(rd) Int.Conf.on Struct.Safety and Reliability.Kobe,Japan(May 1985):213-219P
[79]Hisada T,Nakagiri S.Stochastic finite element analysis of uncertain struct.system.Proc.4~(rd) Int.Conf.on FEM,Austrialia 1982:133-138P
[80]Shinozuka M,Deodatis G.Response variability of stochastic finite element systems.J.engng.Mech.ASCE.114,1988(3):499-519P
[81]Yammazzaki F,Shinozuka M,Dasgupta G.Neumann expansion for stochastic finite element analysis.J.engng.Mech.ASCE.114,1988(8):1335-1354P
[82]Der Kiureghian A,Ke J.Finite element based reliability of frame structures.Proc.4~(rd) Int.Conf.on Struct.Safety and Reliability.Kobe,Japan(May 1985):395-404P
[83]Der Kiureghian A,Ke J.Stochastic finite element method in structural reliability.Probabilistic Engng.Mech.1988(3):83-91P
[84]Der Kiureghian A,Ke J.Finite element method in structural safety studies.Structural Safety Studies(Ed James,Yao T P) 1986:40-52P
[85]Rackwitz R,Fiessler B.Structural reliability under combined random load sequence.Comput.& Struct.1978:489-494P
[86]Spanos P D,Ghanem R.Stochastic finite element expansion for random media.J.Engng.Mech.ASCE.115,1989(5):1035-1053P
[87]Ishii K,Suzuki M.Stochastic FEM for slope stability analysis.Struct.Safety.1978(2):111-129P
[88]Bazant Z P,Wang T S.Spectral finite element analysis of random shrinkage in concrete.J.Struct.Engng.ASCE.1984(9):2196-2211P
[89]Langley R S.A finite element method for the statistics of non-linear random vibration.J.Sound Vib.1985(1):41-54P
[90]Liu W K,Besterfield G,Mani A.Probabilistic finite element methods in nonlinear dynamics.Coumputer Methods in Applied Mech.and Engng.1986(57):61-81P
[91]姜晋庆,张铎.结构塑性有限元分析.北京:宇航出版社,1990
[92]刘宁.可靠度随机有限元法及其工程应用.北京:中国水利水电出版社,2001:1-10页,34-43页
[93]安伟光,苗晗,孙克淋.随机参数压电桁架结构的稳定可靠性分析.哈尔滨 工程大学学报,2006,27(4):519-522页
[94]赵维涛,安伟光.随机空间梁板结构系统静强度可靠性分析.兵工学报,2007,28(8):953-956页
[95]严心池,安伟光,陈卫东.大型舰船结构的可靠性研究.哈尔滨工程大学学报.2004,25(2):147-150页
[96]董聪.现代结构系统可靠性理论及其应用.北京:科学出版社,2001:35-45页
[97]胡云昌,郭振邦.结构系统可靠性分析原理及应用.天津:天津大学出版社,1992:1页,6-7页,76-155页,80-95页
[98]何水清,王善.结构可靠性分析与设计.北京:国防工业出版社,1993:55-98页
[99]黄兴棣.工程结构可靠性设计.北京:人民交通出版社,1992:112-136页
[100]吴香国.具有初始几何缺陷的不完整结构系统可靠性分析.哈尔滨工程大学硕士学位论文,2004:37-48页
[101]蔡荫林,安伟光,陈卫东.舰船结构可靠性分析与优化设计.中国船舶科技报告,1997:86-95页
[102]安伟光,洪国钧,蔡荫林,陈卫东等.基于随机有限元的舰船结构的可靠性优化设计方法.中国国防科学技术报告,2002:135-155页
[2]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计.哈尔滨:哈尔滨工程大学出版社,2005:7-11页,251-336页
[3]李杰着.随机结构系统—分析与建模.北京:科技出版社,1996:1-8页
[4]秦权.随机有限元及其进展Ⅱ:可靠度随机有限元和随机有限元的应用.工程力学,1995,12(1):1-9页
[5]孙逊,高明.基于随机有限元方法的拱坝可靠性分析.水利水运科学研究,1994(1):71-80页
[6]邵文蛟.不完整结构的可靠性分析.北京:国防工业出版社,1997:1页,185-187页
[7]Freudenthal A M.The Safety of Structures.ASCE Trans.1947,112:125-129 P
[8]Freudenthal A M.Safety and The Probability of Structural Failure.ASCE Trans.1956,121:1337-1397 P
[9]Cornell C A.Structural Safety Specification Based on Second-Moment Reliability.Sym.Int.Assoc.of Bridge and Struct.Engr.London.1969:85-105P
[10]Lind N.C..Consistent Partial Safety Factors.ASCE.1971,97(ST6):65-76P
[11]Hasofer A M,Lind N C.Exact and Invariant Second-Moment Code Format.J.Eng.Mech.Div.ASCE.1974,100(1):111-121P
[12]Zhao Y.G.and Ono T..New Approximations for SORM:Part1.J.Eng.Mech.1999,125(1):79-93P
[13]Rackwitz R.and Fiessler B..An Algorithm for Calculation of Structural Reliability under Combined Loading.Munchen.1977:36-45P
[14]Bncher C.G.and Bourgund U..A Fast and Efficient Response Surface Approach for Structural Reliability Problem.Structural Safety.1990,7:57-66P
[15]陈虬,刘先斌.随机有限元法及其工程应用.成都:西南交通大学出版社,1993:21-30页
[16]航空工业部科学技术委员会编.飞机结构损伤容限设计指南.北京:国防工业出版社,1985
[17]航空航天工业部科学技术研究院编.飞机结构耐久性及损伤容限设计手册(2).北京:国防工业出版社,1989
[18]Thoft-christensen P.and Murotsu Y..Application of Structural Systems Reliability Theory.Springer-Verlag.1986:101-126P
[19]冯元生,董聪.枚举结构主要失效模式的一种方法.航空学报.1991,12(9):A37-42页
[20]安伟光,蔡荫林.冗余桁架结构的故障分析.哈尔滨船舶工程学院学报.1992,10(4):479-485页
[21]安伟光,蔡荫林.余度结构故障概率计算的一种方法.兵工学报,1992,2:92-96页
[22]Thoft-christensen.Reliability of Structural Systems,Studies in Applied Mechanics,24:Advances in the theory of plates and shells,Elsevier Science publishers B.U.1990:156-178P
[23]Ditlevsen O.Narrow Reliability Bounds for Structural System.J.Struc.Mech.1979,7(4):453-472P
[24]A.H.-S.A.and W.H.Tang.Probability Concepts in Engineering Planning and Design.John Wiley-and Sons.1984,2:135-146P
[25]Feng Y.S..A Method for Computing Structural System Reliability with High Accuracy.Computers and Structures.1989,33(1):1-5P
[26]Song B.F..A Numerical Integration Method in Affine Space and A Method with High Accuracy for Computing Structural System Reliability.Computer & Structures.1992,42(2):255-262P
[27]蔡荫林,周健生.结构系统失效概率的近似公式.航空学报.1992,13(3):A219-223页
[28]安伟光,王金明.具有多随机变量的结构系统的可靠性分析.兵工学报. 2001增刊:68-72页
[29]Cai YinLin,An WeiGuang,Chen WeiDong.Reliability Assessment and Optimization Design for Structural Systems.Proceedings of The Second International Conference on Reliability Maintainability and Safety,Beijing,China.1994,7:344-349P
[30]陈卫东,王善,蔡荫林.杆板结构系统的可靠性分析.哈尔滨工程大学学报.1997,18(6):68-74页
[31]An WeiGuang and Cai YinLin.Failure Analysis in Tall Redundant Truss Structures.Proceedings of the Fourth International Conference on Tall Buildings.Hong Kong & Shanghai.1988.04:358-363P
[32]安伟光.荷载效应组合时的失效概率.哈尔滨船舶工程学院学报.1988,9(2):126-136页
[33]蔡荫林,安伟光.随机组合力下冗余结构的故障概率计算.哈尔滨船舶工程学院学报.10(2):135-144页
[34]安伟光,陈卫东.结构系统在随机组合力作用下的可靠性分析.哈尔滨工程大学学报.1996,17(1):15-23页
[35]AN Wei-guang,SUN Ke-lin,CHEN Wei-dong,WANG Bin-sheng,CAI Yin-lin.Optilnum Design Based on Reliability in Stochastic Structure Systems.Applied Mathematics and Mechanics.2005,26(10):1293-1302P
[36]安伟光,孙克淋,王滨生.梁板结构系统可靠性分析的关键问题研究.宇航学报.2003,24(6):621-624页
[37]Jeom Kee Paik,Jae Myung Lee,Dong Hoon Lee.Ultimate strength of dented steel plates under axial compressive loads.International Journal of Mechanical Sciences.2003,45:433-448P
[38]Jeom Kee Paik,Bong Ju Kim.Ultimate strength formulations for stiffenedpanels under combined axial load,in-plane bending and lateral pressure.Thin-Walled Structures.2002,40:45-83P
[39]Jeom Kee Paik,Y.V.Satish Kumar,Jae Myung Lee.Ultimate strength of cracked plate elements underaxial compression or tension.Thin-Walled Structures.2005,45:237-272P
[40]Jeom Kee Paik,,Anil K.Thayamballi,Do Hyung Kim.An analytical method for the ultimate compressive strength and effective plating ofstiffened panels.Journal of Constructional Steel Research.1999,49:43-68P
[41]Jeom Kee Paik,Y.V.Satish Kumar,Jae Myung Lee.Ultimate strength of cracked plate elements under axial compression or tension.Thin-Walled Structures.2005,43:237-272P
[42]束长庚,周国华.船舶结构的屈曲强度.北京:国防工业出版社,2003:212-214页
[43]邵文蛟.初裂纹尺寸对疲劳可靠性影响.船舶力学,2001,5(6):50-54页
[44]邵文蛟,邹劲松.初挠度对平面刚架系统可靠性影响.中国造船,1992,2:72-80页
[45]石理国,姚木林.管节点焊接残余应力研究.舰船性能研究,1991,3:49-57页
[46]石理国,包荪蓉.海洋平台有损杆件的承载能力研究.舰船性能研究,1992,3:91-101页
[47]沈世钊,陈昕,林有军,汤建南.单层球面网壳的稳定性.空间结构,1997,3(3):3-12页
[48]林有军,沈世钊.短程线型球面网壳结构的稳定性.哈尔滨建筑大学学报,1999,32(3):30-33页
[49]吴轶,沈世钊.单层双曲扁网壳的稳定性.哈尔滨建筑大学学报,1999,32(4):24-28页
[50]赵维涛.飞行器结构可靠性分析与优化设计研究.哈尔滨工程大学博士学位论文,2006:7-24页
[51]赵国藩.工程结构可靠性理论与应用.大连:大连理工大学出版社,1996:51-62页
[52]Paik,J.K.and Thayamballi,A.K.An empirical formulation for predicting the ultimate compressive strength of stiffened panels,Proc.of International Offshore and Polar Engineering Conference,Honolulu,May,1997:328-338P
[53]Paik,J.K.,Thayamballi,A.K.and Park YI.Local buckling of stiffeners in ship plating,J.of Ship Research.1998.42:56-67P
[54]Paik,J.K.,Thayamballi,A.K.and Lee,W.H.A numerical investigation of tripping,Marine Structures.December,1998:159-183P
[55]Paik,J.K.,Thayamballi,A.K.and Kim,D.H.An analytical method for the ultimate compressive plating of stiffened panels,J.of Constructional Steel Research.1999,49:43-68P
[56]Paik,J.K.,Thayamballi,A.K.,Wang,G and Kim,B.J.On advanced buckling and ultimate strength design of ship plating,Trans.SNAME.2000:108P
[57]Paik,J.K.,Thayamballi,A.K.Buckling strength of steel plating with elastically restrained edges,Thin-Walled Structures.2000,137(1):27-57P
[58]Paik,J.K.,Thayamballi,A.K.and Kim,B.J.Advanced ultimate strength formulations for ship plating under combined biaxial compression/tension,edge shear and lateral pressure loads.Marine technology.2001,138:9-25P
[59]Paik,J.K.,Thayamballi,A.K.and Kim,B.J.Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure,Thin-Walled Structures.2001,215-246P
[60]Cui,W.C.and Mansour A.E.Effects of Welding Distortion and Residual Stress on the Ultimate Strength of Ship Plates under Un-axial Compression.Marine Structures.1998,11:251-269
[61]张少雄,余友谊.有凹陷的板在轴向压力作用下的极限强度.武汉理工大学学报.2004,28(3):315-333页
[62]徐力,刘荣桂,韦芳芳.开孔板的有限元分析.江苏大学学报.2002,23(5):28-30页
[63]O'Dowd N.Elastic-plastic analysis of biaxial loaded center-cracked plate[J].International Journal of Solids and Structures.1999,36:5639-5661P
[64]胡勇,崔维成.具有裂纹缺陷的板和加筋板格在联合载荷作用下的剩余极限强度.船舶力学.2003,7(1):63-78页
[65]孙克淋,安伟光,王滨生等.航天飞机薄壁结构的可靠性分析.哈尔滨工程大学学报.2004,25(3):327-331页
[66]安伟光,孙克淋,陈卫东等.随机结构系统基于可靠性的优化设计.应用数学和力学.2005,26(10):1175-1182页.
[67]O.F.休斯著.张祥孝译.船舶结构设计.广州:华南理工大学出版社,1988:1-6页,61-83页,360-368页,330-336页,369-382页,241页,279页,322页
[68]J.W.Davies.,A Finite Element to Model the In-Pane Response of Ribbed Rectangular Panels.M.Eng.Sc.thesis,University of New South Walse,Sydney.1976
[69]龙兵.船舶结构可靠性分析方法研究.哈尔滨工程大学硕士学位论文,2002:13-14页
[70]余建星.船体横框架的可靠性分析.天津大学硕士学位论文,1990
[71]ShinozukaM,LenceE.A probabilistic model for spatial distribution of material properties.Engng.Feactuec Mech.1976(8):217-227P
[72]Cambou B.Application of first order uncertainty analysis in the finite element method in linear elasticity.Proc.Second Int.Conf.on Applications of Stastistics and Probability in Scil and Struct.Engng.London England 1971:117-122P
[73]Dendrou B A,Houstis E N.An inference finite element model for field applications.Applied Mathematical Modeling,1,Guildford,England 1978:49-55P
[74]Baecher G B,Ingra T S.Stochastic FEM in settlement predictions.J.Geotech.Engng.107,GT 1981(4):449-463P
[75]Handa K,Anderson,K.Applications of finite element methods in statistical analysisof structures.Proc.3~(rd) Int.Conf.on Struct.Safety and Reliability.Trondhrim,Norway(June 1981):409-417P
[76]Hisada T,Nakagiri,S.Stochastic finite element method developed for struct.safety and reliability.Proc.3~(rd) Int.Conf.on Struct.Safety and Reliability.Trondhrim,Norway(June 1981):395-408P
[77]Nakagiri S,Hisada T.Stochastic finite element method developed for struct.analysis with uncertain parameters.Proc,Int.Conf.on FRM Australia (August 1982):206-211P
[78]Hisada T,Nakagiri S.Role of stochastic finite element method in struct.safety and reliability.Proc.4~(rd) Int.Conf.on Struct.Safety and Reliability.Kobe,Japan(May 1985):213-219P
[79]Hisada T,Nakagiri S.Stochastic finite element analysis of uncertain struct.system.Proc.4~(rd) Int.Conf.on FEM,Austrialia 1982:133-138P
[80]Shinozuka M,Deodatis G.Response variability of stochastic finite element systems.J.engng.Mech.ASCE.114,1988(3):499-519P
[81]Yammazzaki F,Shinozuka M,Dasgupta G.Neumann expansion for stochastic finite element analysis.J.engng.Mech.ASCE.114,1988(8):1335-1354P
[82]Der Kiureghian A,Ke J.Finite element based reliability of frame structures.Proc.4~(rd) Int.Conf.on Struct.Safety and Reliability.Kobe,Japan(May 1985):395-404P
[83]Der Kiureghian A,Ke J.Stochastic finite element method in structural reliability.Probabilistic Engng.Mech.1988(3):83-91P
[84]Der Kiureghian A,Ke J.Finite element method in structural safety studies.Structural Safety Studies(Ed James,Yao T P) 1986:40-52P
[85]Rackwitz R,Fiessler B.Structural reliability under combined random load sequence.Comput.& Struct.1978:489-494P
[86]Spanos P D,Ghanem R.Stochastic finite element expansion for random media.J.Engng.Mech.ASCE.115,1989(5):1035-1053P
[87]Ishii K,Suzuki M.Stochastic FEM for slope stability analysis.Struct.Safety.1978(2):111-129P
[88]Bazant Z P,Wang T S.Spectral finite element analysis of random shrinkage in concrete.J.Struct.Engng.ASCE.1984(9):2196-2211P
[89]Langley R S.A finite element method for the statistics of non-linear random vibration.J.Sound Vib.1985(1):41-54P
[90]Liu W K,Besterfield G,Mani A.Probabilistic finite element methods in nonlinear dynamics.Coumputer Methods in Applied Mech.and Engng.1986(57):61-81P
[91]姜晋庆,张铎.结构塑性有限元分析.北京:宇航出版社,1990
[92]刘宁.可靠度随机有限元法及其工程应用.北京:中国水利水电出版社,2001:1-10页,34-43页
[93]安伟光,苗晗,孙克淋.随机参数压电桁架结构的稳定可靠性分析.哈尔滨 工程大学学报,2006,27(4):519-522页
[94]赵维涛,安伟光.随机空间梁板结构系统静强度可靠性分析.兵工学报,2007,28(8):953-956页
[95]严心池,安伟光,陈卫东.大型舰船结构的可靠性研究.哈尔滨工程大学学报.2004,25(2):147-150页
[96]董聪.现代结构系统可靠性理论及其应用.北京:科学出版社,2001:35-45页
[97]胡云昌,郭振邦.结构系统可靠性分析原理及应用.天津:天津大学出版社,1992:1页,6-7页,76-155页,80-95页
[98]何水清,王善.结构可靠性分析与设计.北京:国防工业出版社,1993:55-98页
[99]黄兴棣.工程结构可靠性设计.北京:人民交通出版社,1992:112-136页
[100]吴香国.具有初始几何缺陷的不完整结构系统可靠性分析.哈尔滨工程大学硕士学位论文,2004:37-48页
[101]蔡荫林,安伟光,陈卫东.舰船结构可靠性分析与优化设计.中国船舶科技报告,1997:86-95页
[102]安伟光,洪国钧,蔡荫林,陈卫东等.基于随机有限元的舰船结构的可靠性优化设计方法.中国国防科学技术报告,2002:135-155页