弹性力学随机分析与可靠度分析样条虚边界元法研究
|
摘要
考虑不确定性因素，对结构进行随机分析和可靠度评估是近年来的研究热点，国内外学者针对这一课题建立了一系列随机分析和可靠度分析方法。这些方法大多以有限元法为基础，其结果精度和计算效率会受到有限元法固有缺陷的影响。本文致力于将一种改进的间接边界元法，即样条虚边界元法，引入随机分析和可靠度分析领域，开展弹性力学随机分析和可靠度研究。本文研究的主要工作包括：
（1）扼要介绍了随机分析和可靠度分析的基本概念和常用方法，并对边界元法（含样条虚边界元法）的发展和应用进行综述。对已出现的随机分析和可靠度分析边界元法进行了归纳和分类，简单介绍了它们的计算原理，并指出了它们各自的应用优势以及存在问题。
（2）介绍了确定性弹性力学样条虚边界元法的计算原理，并阐述了该方法的数值稳定性、误差估计以及凹域与复连通域处理方法，通过算例验证了样条虚边界元法在确定性分析中的有效性。
（3）在考虑材料参数小变异情况下，采用一阶近似方法将弹性力学随机控制微分方程分解为关于响应均值和偏量的两组控制微分方程；然后利用这两组方程在形式上和确定性问题控制微分方程的相似性，采用确定性问题的基本解，建立弹性力学随机分析的样条虚边界元法列式，提出了考虑随机场模型的随机样条虚边界元法。通过数值算例验证了该方法的正确性和高效性，并对随机场参数的相关结构、相关长度和变异系数等因素对随机分析结果的影响进行了分析，获得了这些因素的影响规律。
（4）结合可靠度分析的改进一次二阶矩法和样条虚边界元法，提出了弹性力学可靠度分析的一次二阶矩样条虚边界元法，其中考虑了两种输入参数模型，即随机场模型和随机变量模型。针对输入参数随机场模型，利用随机样条虚边界元法得到响应量与随机场离散向量之间的关系式后，再结合一次二阶矩法进行可靠度计算；针对输入参数随机变量模型，一次二阶矩法中所需要的功能函数梯度可以直接利用样条虚边界元法列式得到。通过数值算例对一次二阶矩样条虚边界元法的计算精度、效率以及适用性进行了考察。
（5）以样条虚边界元法作为样本试验方法，建立弹性力学可靠度分析的直接蒙特卡罗样条虚边界元法。为了提高计算效率，引入Taylor展开和Neumann展开技术，避免在大量样本计算中直接生成影响矩阵及对其进行求逆运算，降低了单次样本计算时间；同时引入重要抽样技术，在相同精度情况下减少了蒙特卡罗法的抽取样本数。通过数值算例，考察了所提出的Taylor-Neumann展开重要抽样蒙特卡罗样条虚边界元法的计算精度和效率。
研究结果表明，在随机场理论和可靠度计算方法基础上提出的弹性力学随机分析和可靠度分析样条虚边界元法，具有良好的计算精度和相当高的计算效率。本文工作一方面拓宽样条虚边界元法的应用范围，另一方面也为弹性力学随机分析和可靠度计算提供一种更为精确和具有更高计算效率的数值方法。
Stochastic analysis and reliability assessment of structures with uncertain parametershave drawn much attention in recent years. Numerical computation schemes in the frame offinite element method (FEM) have been developed in this area. The accuracy and efficiencyof such schemes are inevitably affected by the inherent defects of FEM. In this study, thespline fictitious boundary element method (SFBEM), a modified indirect boundary elementmethod (BEM), is applied to the area of stochastic analysis and reliability assessment of theelasticity problems with structural uncertainties. The work in this dissertation is described asfollows:
(1) The basic concepts and main methods of stochastic analysis and reliabilityassessment are briefly introduced, and the development and application of BEM and SFBEMare summarized. The main BEMs for stochastic analysis and reliability assessment are thenintroduced systematically, and their advantages and disadvantages are also pointed out.
(2) The formulation of deterministic SFBEM for elasticity problems is presented, and thenumerical stability, error estimates and domain-division techniques for concave andcomplex-connected domains are discussed. The effectiveness of the method in the area ofdeterministic analysis is also validated by numerical examples.
(3) The stochastic SFBEM is proposed for stochastic analysis of elasticity problems withthe input parameters modeled as random fields under the assumption of small variation of theparameters. Two sets of governing differential equations described with the means anddeviations of structural responses are first derived by including the first-order terms ofdeviations. These equations are then solved by SFBEM using deterministic fundamentalsolutions, since they are in similar forms to those of deterministic problems. Numericalexamples are given to show the accuracy and efficiency of the proposed method, and theeffects on the analytic results of various factors, including the correlation types, correlationlengths, and the coefficients of variation, are investigated and certain conclusions are obtainedregarding the influence of the above factors.
(4) The first-order-second-moment SFBEM, which is in the frame of the advancedfirst-order-second-moment (AFOSM) method in conjunction with SFBEM, is proposed forreliability analysis of elasticity problems. Two cases are considered. For the first one, theinput parameters are modeled as random fields, and the relationship between structuralresponses and the random vectors from random field discretization derived in stochasticSFBEM is utilized for reliability analysis with AFOSM method. For the second case, the input parameters are modeled as random variables, and the gradient of the performancefunction required in AFSOM method is obtained directly in the frame of SFBEM formulation.The accuracy, efficiency and applicability of the present method are investigated by numericalexamples.
(5) The direct Monte-Carlo SFBEM is proposed for reliability analysis of elasticityproblems, in which SFBEM is used as a tool for each sample experiment in Monte-Carlosimulation (MCS). In order to improve the efficiency of the method, the techniques of Taylorexpansion and Neumann expansion are adopted to avoid generating influence matrices andcalculating their inverses during the repeated sample analyses. In addition, an importantsampling technique is also incorporated in the proposed method to reduce the samplingnumber. The accuracy and efficiency of the present approach are validated by numericalexamples.
The work in this dissertation shows that a good precision and high efficiency can beobtained by SFBEM for stochastic analysis and reliability assessment. The proposed methodwill further extend the application area of SFBEM, and it will also provide a new approach tosolve the stochastic and reliability problems in elasticity analysis at high accuracy andefficiency.
（1）扼要介绍了随机分析和可靠度分析的基本概念和常用方法，并对边界元法（含样条虚边界元法）的发展和应用进行综述。对已出现的随机分析和可靠度分析边界元法进行了归纳和分类，简单介绍了它们的计算原理，并指出了它们各自的应用优势以及存在问题。
（2）介绍了确定性弹性力学样条虚边界元法的计算原理，并阐述了该方法的数值稳定性、误差估计以及凹域与复连通域处理方法，通过算例验证了样条虚边界元法在确定性分析中的有效性。
（3）在考虑材料参数小变异情况下，采用一阶近似方法将弹性力学随机控制微分方程分解为关于响应均值和偏量的两组控制微分方程；然后利用这两组方程在形式上和确定性问题控制微分方程的相似性，采用确定性问题的基本解，建立弹性力学随机分析的样条虚边界元法列式，提出了考虑随机场模型的随机样条虚边界元法。通过数值算例验证了该方法的正确性和高效性，并对随机场参数的相关结构、相关长度和变异系数等因素对随机分析结果的影响进行了分析，获得了这些因素的影响规律。
（4）结合可靠度分析的改进一次二阶矩法和样条虚边界元法，提出了弹性力学可靠度分析的一次二阶矩样条虚边界元法，其中考虑了两种输入参数模型，即随机场模型和随机变量模型。针对输入参数随机场模型，利用随机样条虚边界元法得到响应量与随机场离散向量之间的关系式后，再结合一次二阶矩法进行可靠度计算；针对输入参数随机变量模型，一次二阶矩法中所需要的功能函数梯度可以直接利用样条虚边界元法列式得到。通过数值算例对一次二阶矩样条虚边界元法的计算精度、效率以及适用性进行了考察。
（5）以样条虚边界元法作为样本试验方法，建立弹性力学可靠度分析的直接蒙特卡罗样条虚边界元法。为了提高计算效率，引入Taylor展开和Neumann展开技术，避免在大量样本计算中直接生成影响矩阵及对其进行求逆运算，降低了单次样本计算时间；同时引入重要抽样技术，在相同精度情况下减少了蒙特卡罗法的抽取样本数。通过数值算例，考察了所提出的Taylor-Neumann展开重要抽样蒙特卡罗样条虚边界元法的计算精度和效率。
研究结果表明，在随机场理论和可靠度计算方法基础上提出的弹性力学随机分析和可靠度分析样条虚边界元法，具有良好的计算精度和相当高的计算效率。本文工作一方面拓宽样条虚边界元法的应用范围，另一方面也为弹性力学随机分析和可靠度计算提供一种更为精确和具有更高计算效率的数值方法。
Stochastic analysis and reliability assessment of structures with uncertain parametershave drawn much attention in recent years. Numerical computation schemes in the frame offinite element method (FEM) have been developed in this area. The accuracy and efficiencyof such schemes are inevitably affected by the inherent defects of FEM. In this study, thespline fictitious boundary element method (SFBEM), a modified indirect boundary elementmethod (BEM), is applied to the area of stochastic analysis and reliability assessment of theelasticity problems with structural uncertainties. The work in this dissertation is described asfollows:
(1) The basic concepts and main methods of stochastic analysis and reliabilityassessment are briefly introduced, and the development and application of BEM and SFBEMare summarized. The main BEMs for stochastic analysis and reliability assessment are thenintroduced systematically, and their advantages and disadvantages are also pointed out.
(2) The formulation of deterministic SFBEM for elasticity problems is presented, and thenumerical stability, error estimates and domain-division techniques for concave andcomplex-connected domains are discussed. The effectiveness of the method in the area ofdeterministic analysis is also validated by numerical examples.
(3) The stochastic SFBEM is proposed for stochastic analysis of elasticity problems withthe input parameters modeled as random fields under the assumption of small variation of theparameters. Two sets of governing differential equations described with the means anddeviations of structural responses are first derived by including the first-order terms ofdeviations. These equations are then solved by SFBEM using deterministic fundamentalsolutions, since they are in similar forms to those of deterministic problems. Numericalexamples are given to show the accuracy and efficiency of the proposed method, and theeffects on the analytic results of various factors, including the correlation types, correlationlengths, and the coefficients of variation, are investigated and certain conclusions are obtainedregarding the influence of the above factors.
(4) The first-order-second-moment SFBEM, which is in the frame of the advancedfirst-order-second-moment (AFOSM) method in conjunction with SFBEM, is proposed forreliability analysis of elasticity problems. Two cases are considered. For the first one, theinput parameters are modeled as random fields, and the relationship between structuralresponses and the random vectors from random field discretization derived in stochasticSFBEM is utilized for reliability analysis with AFOSM method. For the second case, the input parameters are modeled as random variables, and the gradient of the performancefunction required in AFSOM method is obtained directly in the frame of SFBEM formulation.The accuracy, efficiency and applicability of the present method are investigated by numericalexamples.
(5) The direct Monte-Carlo SFBEM is proposed for reliability analysis of elasticityproblems, in which SFBEM is used as a tool for each sample experiment in Monte-Carlosimulation (MCS). In order to improve the efficiency of the method, the techniques of Taylorexpansion and Neumann expansion are adopted to avoid generating influence matrices andcalculating their inverses during the repeated sample analyses. In addition, an importantsampling technique is also incorporated in the proposed method to reduce the samplingnumber. The accuracy and efficiency of the present approach are validated by numericalexamples.
The work in this dissertation shows that a good precision and high efficiency can beobtained by SFBEM for stochastic analysis and reliability assessment. The proposed methodwill further extend the application area of SFBEM, and it will also provide a new approach tosolve the stochastic and reliability problems in elasticity analysis at high accuracy andefficiency.
引文
[1-1]国家自然科学基金委员会.自然科学学科发展战略调研报告:水利学科[M].北京:科学出版社,1994
[1-2]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[1-3]赵国藩,贡金鑫,赵尚传.我国土木工程结构可靠性研究的一些进展[J].大连理工大学学报,2005,40(3):253-258
[1-4]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[1-5] Schu ller G I. A state-of-the-art report on computational stochastic mechanics[J].Probabilistic Engineering Mechnics,1997,12(4):194-321
[1-6]刘宁,郑建清.工程随机力学与工程可靠性中的若干问题(上)[J].河海大学学报,1999,27(5):1-7
[1-7]刘宁.工程随机力学与工程可靠性中的若干问题(下)[J].河海大学学报,2000,28(1):1-7
[1-8] Grigoriu M. Stochastic mechanics[J]. Solids and Structures,2000(37):197-214
[1-9] Schu ller G I. Computational stochastic mechanics—recent advances[J]. Computersand Structures,2001,79(22-25):2225-2234
[1-10]秦权.随机有限元及其进展(I)—随机场的离散和反应矩计算[J].工程力学,1994,11(4):1-10
[1-11]刘章军.工程随机动力作用的正交展开理论及应用研究[D].上海:同济大学,2007
[1-12]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[1-13]秦权,林道锦,梅刚.结构可靠度随机有限元:理论及工程应用[M].北京:清华大学出版社,2006
[1-14] Shinozuka M, Wen Y K. Monte Carlo solution of nonlinear vibrations[J]. AIAAJoumal,1972,10(l):37-40
[1-15] Shinozuka M, Lenoe E. A probabilistic model for spatial distribution of materialproperties[J]. Engineering Fracture Mechanics,1976,8(l):217-227
[1-16] Shinozuka M, Deodatis G. Response variability of stochastic finite elementsystems[J]. Journal of Engineering Mechanics ASCE,1988,114(3):499-519
[1-17] Yamazaki F, Shinozuka M, Dasgupta G. Neumann expansion for stochastic finiteelement systems[J]. Journal of Engineering Mechanics ASCE,1988,114(8):1335-1354
[1-18] Caflisch R E. Monte Carlo and quasi-Monte Carlo methods[J]. Acta Numerica,1998,7:1-49
[1-19] Keese A, Matthies H G. Hierarchical parallel solution of stochastic systems[A].Bathe K J. Computational Fluid and Solid Mechanics2003[C], Amsterdam: Elsevier,2003:2023-2025
[1-20] Keese A, Matthies H G. Parallel computation of stochastic groundwater flow[A].Wolf D, Münster G, Kremer M. NIC Symposium2004[C]. Jülich: John von NeumannInstitute for Computing,2003:399-408
[1-21] Keese A, Matthies H G. Parallel solution of stochastic PDEs[J]. Proceedings inApplied Mathematics and Mechanics,2003,2:485-486
[1-22]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].成都:西南交通大学.1996
[1-23]郝志明.随机结构有限元法及可靠性研究[D].成都:西南交通大学:2001
[1-24] Hart G C, Collins J D. The treatment of randomness in finite element modeling[A].SAE National Aeronautic and Space Engineering and Manufacturing Meeting[C]. LosAngeles,1970:1-12
[1-25] Hasselman T K, Hart G C. Model analysis of random structural systems[J].Probabilistic Engineering Mechanics,1972,98(2):561-586
[1-26] Handa K, Anderson K. Application of finite element methods in the statisticalanalysis of structures[J]. Proc.3rdInt. Conf. on Structural Safety and Reliability,1981:409-417
[1-27] Nakagiri S, Hisada T, Toshimitsu K. Stochasitc time history analysis of structuralvibration with uncertain damping[J]. Probalilistic Structural Analysis,1984,93:109-120
[1-28]张汝清,高行山.随机变量的变分原理及有限元法[J].应用数学与力学,1992,13(5):383-388
[1-29]张汝清,高行山.有限变形弹性理论随机变量变分原理及有限元法[J].应用数学与力学,1994,15(10):855-862
[1-30]秦权,林道锦,梅刚.结构可靠度随机有限元法:理论及工程应用[M].北京:清华大学出版社,2006
[1-31] Sun T C. A finite element method for random differential equations with randomcoefficients[J]. Journal of Numerical Analysis,1979,16(6):1019-1035
[1-32] Ghanem R, Spanos P D. Polynomial chaos in stochastic finite elements[J]. Journal ofApplied Mechanics,1990,57(1):197-202
[1-33]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3):263-267
[1-34]杨杰.非线性结构随机分析数值模拟的方法研究[D].成都:西南交通大学.2004
[1-35]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000
[1-36] Freudenthal A M. The safety of structures[J]. Transactions ASCE,1947,112:125-129
[1-37]张新培.建筑结构可靠度分析与设计[M].北京:科学出版社,2001
[1-38] Cornell C A. A probability-based structural code[J]. ACI Journal Proceedings,1969,66(12):974-985
[1-39] Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. Journalof Engineering Mechanics Division ASCE,1974,100(1):111-121
[1-40] Ang A H-S, Tang W H. Probability Concepts in Engineering Planning andDesign[M]. New York: John Eiley&Sons,1984
[1-41] Rackwitz R, Fiessler B. Structural reliability combined random load sequences[J].Computers and Structures,1974,9(5):489-494
[1-42]余大胜,康海贵.响应面法计算结构可靠度的回顾[J].工业建筑,2006,36(S1):238-242
[1-43] Deng J, Gu D S, Li X B, et al. Structural reliability analysis for implicit performancefunctions using artificial network[J]. Strucutural Safety,2005,27(1):25-48
[1-44]金伟良,唐纯喜,陈进.基于SVM的结构可靠度分析响应面方法[J].计算力学学报,2007,24(6):713-718
[1-45]金伟良,袁雪霞.基于LS-SVM的结构可靠度响应面分析方法[J].浙江大学学报,2007,41(1):44-47
[1-46] Rizzo F J. An integral equation approach to boundary value problems of classicalelastostatics[J]. Quarterly of Applied Mathematics,1967,25:83-95
[1-47] Cheng A H D, Cheng D T. Heritage and early history of the boundary elementmethod[J]. Enginerring Analysis with Boundary Elements,2005,29(3):268-302
[1-48] Bannerjee P K, Butterfield R. Boundary Element Methods in EngineeringScience[M]. London: McGraw-Hill,1981
[1-49] Brebbia C A. The boundary Element Method for Engineers[M]. London: Pretech,1978
[1-50] Brebbia C A, Telles J, Wrobel L C. Boundary Element Techniques: Theory andApplications in Engineering[M]. Berlin: Springer-Verlag,1984
[1-51] Manolis G D, Beskos D E. Boundary Element Methods in Elastodynamics[M].London: Unwin-Hyman,1988
[1-52]杜庆华,嵇醒,岑章志等.边界积分方程-边界元法的力学基础与工程应用[M].北京:高等教育出版社,1989
[1-53]嵇醒,臧跃龙,程玉民.边界元法进展及通用程序[M].上海:同济大学出版社,1997
[1-54]郑建军.边界元法及其在结构分析中的应用[M].合肥:安徽科学技术出版社,2006
[1-55]祝家麟,袁政强.边界元分析[M].北京:科学出版社,2009
[1-56]余德浩.自然边界元方法的数学理论[M].北京:科学出版社,1993
[1-57]金伏生,秦庆华.非线性Reissner板杂交元及边界元解[J].计算力学学报,1992,9(2):148-152
[1-58]秦庆华,黄玉盈.任意外型薄板非线性后屈曲问题的边界元解[J].固体力学学报,1990,11(1):47-56
[1-59] Qin Q H. The Trefftz Finite and Boundary Element Method[M]. Southampton: WIT.2000
[1-60] Qin Q H. Fracture Mechanics of Piezoelectric Materials[M]. Southampton: WIT.2001
[1-61] Zhang C H, Wolf J P. Dynamic Soil-Structure Interaction: Current Research in Chinaand Switzerland[M]. Amsterdam: Elsevier,1998
[1-62] Zhang C H. Numerical Modeling of Oncrete Dam-Foundation-Reservoir Systems[M].Beijing: Tsinghua University,2001
[1-63]姚振汉,杜庆华.边界元法应用的若干近期研究及国际新进展[J].清华大学学报(自然科学版),2001:89-93
[1-64]姚振汉,王海涛.边界元法[M].北京:高等教育出版社,2010
[1-65] Su C, Han D J. Analysis of elastic plane problems by the spline fictitious boundaryelement method[A]. Computational Method in Engineering and Science—Theory andPractice[C]. Guangzhou: South China University of Technology Press,1997:538-542
[1-66] Su C, Han D J. Multidomain SFBEM and its application in elastic plane problems[J].Journal of Engineering Mechanics ASCE,2000,126(10):1057-1063
[1-67] Su C, Han D J. Elastic analysis of orthotropic plane problems by the spline fictitiousboundary element method[J]. Applied Mathematics and Mechanics,2002;23(4):446-453
[1-68]苏成,韩大建.高层建筑筏板基础分析的样条虚边界元法[J].土木工程学报,2001,34(1):61-66
[1-69]苏成,郑淳.应力强度因子计算的样条虚边界元法[J].工程力学,2007,24(8):49-53
[1-70]苏成,郑淳.基于Erdogan基本解边界元法计算应力强度因子[J].力学学报,2007,39(1):93-99
[1-71] Burczyński T. Stochastic boundary value problems of elastostatics in terms of theboundary integral equation method[J]. Papers of the Institution of Civil Engineering inWroc aw Technical University,1981,1(28):61-68(in Polish)
[1-72] Nakagiri S, Suzuki K, Hisada T. Stochastic boundary element method applied tostress analysis[A]. Brebbia C A, Futugami T, Tanaka M. Boundary Elements V[C]. NewYork: Springer-Verlag,1983:439-448
[1-73]王金根.基于形状摄动技术的边界元法[J].计算结构力学及其应用,1990,7(2):77-84
[1-74] Etlouney M, Benaroga H, Wright J. Boundary element methods in probabilisticstructural analysis (PBEM)[J]. Applied Mathematical Modeling,1989,13(7):432-440
[1-75] Kaljevi I, Saigal S. Stochastic boundary elements in elastostatics[J]. ComputerMethods in Applied Mechanics and Engineering,1993,109(3-4):259-280
[1-76] Kamiński M. Stochastic second-order BEM perturbation formulation[J]. EngineeringAnalysis with Boundary Elements,1999,23(2):123-129
[1-77] Kamiński M. Application of the generalized perturbation-based stochastic boundaryelement method to the elastostatics[J]. Engineering Analysis with Boundary Elements,2007,31(6):514-527
[1-78] Kamiński M. Least squares stochastic boundary element method[J]. EngineeringAnalysis with Boundary Elements,2011,35(5):776-784
[1-79] Dasgupta G, Papusha A N, Malsch E. First order stochasticity in boundary geometry:a computer algebra BE development[J]. Engineering Analysis with Boundary Elements,2001,25(9):741-751
[1-80] Kaljevi I, Saigal S. Stochastic boundary elements for two-dimensional potentialflow in homogeneous domains[J]. International Journal of Solids and Structures,1995,32(13):1873-1892
[1-81] Emery A F. Solving stochastic heat transfer problems[J]. Engineering Analysis withBoundary Elements,2004,28(3):279-291
[1-82] Manolis G D, Shaw R P. Boundary integral formulation for2D and3D thermalproblems exhibiting a linearly varying stochastic conductivity[J]. ComputationalMechanics,1996,17(6):406-417
[1-83] Manolis G D, Shaw R P. Harmonic elastic waves in continuously heterogeneousrandom layers[J]. Engineering Analysis with Boundary Elements,1997,19(3),181-198
[1-84] Manolis G D, Pavlou S. Fundamental solutions for SH-waves in a continuum withlarge randomness[J]. Engineering Analysis with Boundary Elements,1999,23(9),721-736
[1-85] Breitung K, Casciati F, Farávelli L. A random field description for stochasticboundary elements[J]. Engineering Analysis with Boundary Elements,1997,19(3):223-229
[1-86]江爱民,丁皓江.扁壳统计分析的随机边界元法[J].土木工程学报,1996,29(4):57-63
[1-87]江爱民,朱劲松,丁皓江等.薄板统计分析的随机边界元法[J].上海力学,1997,18(4):321-326
[1-88]江爱民,沈晓安.中厚板统计分析的随机边界元法[J].计算力学学报,2001,18(2):179-183
[1-89] Burczyński T. The boundary element method for stochastic potential problems[J].Applied Mathematical Modelling,1985,9(3):189-194
[1-90] Burczyński T. Stochastic boundary element method for wave propagation throughcontinuous random media[A]. Connor J J, Brebbia C A. BETECH86MIT[C]. Cambridge:CML Publications,1986:733-741
[1-91] Burczyński T, John A. Stochastic dynamic analysis of elastic and viscoelastic systemby means of the boundary element method[A]. Brebbia C A, Maier G. Boundary ElementsⅦ[C]. Berlin: Springer-Verlag,1985:53-61
[1-92] Burczyński T. Boundary element method for deterministic and stochastic shapedesign sensitivity analysis[A]. Cruse T A. Advanced Boundary Element Method[C]. Belin:Springer-Verlag,1988:73-80
[1-93] Burczyński T, Fedeliński P. Boundary elements in shape design sensitivity analysisand optimal design of vibrating structures[J]. Engineering Analysis with BoundaryElements,1992,9(3):195-202
[1-94] Burczyński T, Kane J H, Balakrishna C. Comparison of shape design sensitivityanalysis formulation via material derivative-adjoint variable and implicit differentiationtechniques for3-D and2-D curved boundary element[J]. Computer Methods in AppliedMechanics and Engineering,1997,168(1-42):89-109
[1-95] Bonnet M, Burczyński T, Nowakowski M. Sensitivity analysis for shape perturbationof cavity or internal crack using BIE and adjoint variable approach[J]. Iternational Journalof Solids and Structures,2002,39(9):2365-2385
[1-96] Bialecki R A, Burczyński T, Dlugosz A. Evolutionary shape optimization ofthernoelastic bodies exchanging heat by convection and radiation[J]. Computer Methodsin Applied Mechanics and Engineering,2005,194(17):1839-1859
[1-97] Burczyński T, Skrzypczyk J. Theoretical and computational aspects of the stochasticboundary element method[J]. Computer Methods in Applied Mechanics and Engineering,1999,168(1-4):321-344
[1-98] Honda R. Stochastic BEM with spectral approach in elastostatic and elastodynamicproblems with geometrical uncertainty[J]. Engineering Analysis with Boundary Elements,2005,29(5):415-427
[1-99] Agarwal N, Aluru N R. Stochastic modeling of coupled electromechanicalinteraction for uncertainty quantification in electrostatically actuated MEMS[J]. ComputerMethods in Applied Mechanics and Engineering,2008,197(43-44):3456-3471
[1-100]江爱民,任永坚.结构可靠性分析的随机边界元法[J].浙江大学学报,1994,22(6):708-715
[1-101]江爱民,丁皓江.随机边界元法在大坝可靠性分析中的应用[J].工程力学,1996,13(1):81-85
[1-102]江爱民,汪小超,陈瑞生.随机边界元法在薄板可靠性分析中的应用[J].力学季刊,2002,23(2):272-274
[1-103]温卫东,陈伟,高德平.二维弹性随机边界元法与可靠度分析[J].应用力学学报.1995,12(1):9-14
[1-104]陈伟,温卫东,陈卓.二维弹性接触问题中随机边界元法与可靠性分析[J].应用力学学报,1998,15(1):109-112
[1-105] Zhang M, Wu Q G. Stochastic boundary element analysis of concrete gravity dam[J].Tsinghua Science and Technology,2002,7(3):254-257
[2-1] Su Cheng, Han Dajian. Analysis of elastic plane problems by the spline fictitiousboundary element method[A]. Computational Method in Engineering and Science—Theory and Practice[C]. Guangzhou: SCUT Press,1997:538-542
[2-2] Su Cheng, Han Dajian. Multidomain SFBEM and its application in elastic planeproblems[J]. Journal of Engineering Mechanics ASCE,2000,126(10):1057-1063
[2-3]苏成,韩大建.正交各向异性弹性力学平面问题的样条虚边界元法[J].应用数学和力学,2002,23(4):400-406
[2-4]苏成,韩大建.高层建筑侧向刚度计算的分域样条虚边界元法[J].华南理工大学学报(自然科学版),1998,26(6):81-85
[2-5]苏成,韩大建.高层建筑筏板基础分析的样条虚边界元法[J].土木工程学报,2001,34(1):61-66
[2-6]苏成,郑淳.样条虚边界元法的数值稳定性与误差估计[J].华南理工大学学报,2003,31(8):53-58
[2-7]郑淳.样条虚边界元法在线弹性断裂力学中的应用[D].广州:华南理工大学,2004
[2-8]苏成,韩大建.弹性力学平面问题的分域样条虚边界元法—边界子段法[J].华南理工大学学报,1998,26(3):22-26
[2-9] Banerjee P K, Butterfield R. Boundary Element Method in Engineering Science[M].London: McGraw-Hill,1981
[2-10] Brebbia C A. The Boundary Element Method for Engineers[M]. London: PentechPress.1978
[2-11] Brebbia C A, Walker S. Boundary Element Method in Engineering[M]. London:Butterworths.1980
[2-12]王能超.数值分析简明教程[M].北京:高等教育出版社,1984
[2-13]许文焕,陈虬.加权余量法在结构分析中的应用[M].北京:中国铁道出版社.1985
[2-14]姚振汉,钟晓光.边界元法中边界变量的确定与误差直观度量[M].华中理工大学学报.1989,17(6):97~103
[2-15]西田正孝.应力集中(增补版)[M].李安定,郭廷玮.北京:机械工业出版社.1986
[2-16]邓攀.二维弹性动力学的样条虚边界元法[D].广州:华南理工大学,2005
[3-1] Vanmarcke E H. Random Fields[M]. Cambridge: MIT Press,1983
[3-2] Vanmarcke E H, Shinozuka M. Random fields and stochastic finite element method[J].Structural Safety,1986,3(3-4):143-166
[3-3] Vanmarcke E H. Probabilistic modeling of soil profiles[J]. Journal of GeotechnicalEngineering Division,1977,103(11):1227-1246
[3-4] Shinozuka M. Probabilistic modeling of concrete structures[J]. Journal of EngineeringMechanics Division,1972,98(6):1433-1451
[3-5]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[3-6]秦权.随机有限元及其进展(I)—随机场的离散和反应矩的计算[J].工程力学,1994,11(4):1-10
[3-7] Liu P L, Kiureghian A D. Finite element reliability of geometrically nonlinearuncertain structures[J]. Journal of Engineering Mechanics,1991,117(8):1806-1825
[3-8] Liu P L, Kiureghian A D. Multi-variate distribution models with prescribed marginalsand covariances[J]. Probabilistic Engineering Mechanics,1986,1(2):105-112
[3-9] Spanos P D, Ghanem R G. Stochastic finite element expansion for random media[J].Journal of Engineering Mechanics,1989,115(5):1035-1053
[3-10] Ghanem R G, Spanos P D. Stochastic Finite Element: A Spectral Approach[M]. NewYork: Springer-Verlag,1991
[4-1]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[4-2] Hasofer A M，Lind N C. Exact and invariant second-moment code format[J]. Journalof Engineering Mechanics，1974，100(1):111-121
[4-3]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990
[4-4]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
[4-5]张新培.建筑结构可靠度分析与设计[M].北京:科学出版社,2001
[4-6] Rackwitz R, Fiessler B. Structural relizbility under combined random loadsequences[J]. Computers and Structures,1978,9(5):489-494
[4-7] GBJ68-84，建筑结构设计统一标注[S].北京：中国建筑工业出版社，1984
[4-8] GB\T50283-1999，公路工程结构可靠度设计统一标准[S].北京：中国计划出版社，1999
[4-9]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000
[4-10] Rosenblatt. Remarks on a multivariate transformation[J]. Annals of MathematicalStatistics,1952,23:470-472
[4-11] Chen X, Lind N C. Fast probability integration by three parameter normal tailapproximation[J]. Structural Safety,1983,1(4):269-276
[4-12] Nowak A S, Collins K R. Reliability of Structures. NewYork: McGraw-Hill,2000
[5-1]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京：人民交通出版社,2003
[5-2] Rosenblatt. Remarks on a multivariate transformation[J]. Annals of MathematicalStatistics,1952,23:470-472
[5-3] Chen X, Lind N C. Fast probability integration by three parameter normal tailapproximation[J]. Structural Safety,1983,1(4):269-276
[5-4]李鹏飞.结构可靠度分析的响应面—蒙特卡罗法研究[D].广州:华南理工大学,2008
[5-5] Shinozuka M, Deodatis G． Response variability of stochastic finite elementsystems[J]. Journal of Engineering Mechanics ASCE.1988,114(3):499-519
[5-6] Yamazaki F, Shinozuka M, Dasgupta G．Neumann expansion for stochastic finiteelement systems[J]. Journal of Engineering Mechanics ASCE.1988,114(8):1335-1354
[5-7]金伟良.结构可靠度数值模拟的新方法[J].建筑结构学报,1996,14(3):63-72
[5-8]贡金鑫,仲伟秋,赵国藩.工程结构可靠度基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4),2-9
[5-9]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[1-2]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[1-3]赵国藩,贡金鑫,赵尚传.我国土木工程结构可靠性研究的一些进展[J].大连理工大学学报,2005,40(3):253-258
[1-4]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[1-5] Schu ller G I. A state-of-the-art report on computational stochastic mechanics[J].Probabilistic Engineering Mechnics,1997,12(4):194-321
[1-6]刘宁,郑建清.工程随机力学与工程可靠性中的若干问题(上)[J].河海大学学报,1999,27(5):1-7
[1-7]刘宁.工程随机力学与工程可靠性中的若干问题(下)[J].河海大学学报,2000,28(1):1-7
[1-8] Grigoriu M. Stochastic mechanics[J]. Solids and Structures,2000(37):197-214
[1-9] Schu ller G I. Computational stochastic mechanics—recent advances[J]. Computersand Structures,2001,79(22-25):2225-2234
[1-10]秦权.随机有限元及其进展(I)—随机场的离散和反应矩计算[J].工程力学,1994,11(4):1-10
[1-11]刘章军.工程随机动力作用的正交展开理论及应用研究[D].上海:同济大学,2007
[1-12]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[1-13]秦权,林道锦,梅刚.结构可靠度随机有限元:理论及工程应用[M].北京:清华大学出版社,2006
[1-14] Shinozuka M, Wen Y K. Monte Carlo solution of nonlinear vibrations[J]. AIAAJoumal,1972,10(l):37-40
[1-15] Shinozuka M, Lenoe E. A probabilistic model for spatial distribution of materialproperties[J]. Engineering Fracture Mechanics,1976,8(l):217-227
[1-16] Shinozuka M, Deodatis G. Response variability of stochastic finite elementsystems[J]. Journal of Engineering Mechanics ASCE,1988,114(3):499-519
[1-17] Yamazaki F, Shinozuka M, Dasgupta G. Neumann expansion for stochastic finiteelement systems[J]. Journal of Engineering Mechanics ASCE,1988,114(8):1335-1354
[1-18] Caflisch R E. Monte Carlo and quasi-Monte Carlo methods[J]. Acta Numerica,1998,7:1-49
[1-19] Keese A, Matthies H G. Hierarchical parallel solution of stochastic systems[A].Bathe K J. Computational Fluid and Solid Mechanics2003[C], Amsterdam: Elsevier,2003:2023-2025
[1-20] Keese A, Matthies H G. Parallel computation of stochastic groundwater flow[A].Wolf D, Münster G, Kremer M. NIC Symposium2004[C]. Jülich: John von NeumannInstitute for Computing,2003:399-408
[1-21] Keese A, Matthies H G. Parallel solution of stochastic PDEs[J]. Proceedings inApplied Mathematics and Mechanics,2003,2:485-486
[1-22]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].成都:西南交通大学.1996
[1-23]郝志明.随机结构有限元法及可靠性研究[D].成都:西南交通大学:2001
[1-24] Hart G C, Collins J D. The treatment of randomness in finite element modeling[A].SAE National Aeronautic and Space Engineering and Manufacturing Meeting[C]. LosAngeles,1970:1-12
[1-25] Hasselman T K, Hart G C. Model analysis of random structural systems[J].Probabilistic Engineering Mechanics,1972,98(2):561-586
[1-26] Handa K, Anderson K. Application of finite element methods in the statisticalanalysis of structures[J]. Proc.3rdInt. Conf. on Structural Safety and Reliability,1981:409-417
[1-27] Nakagiri S, Hisada T, Toshimitsu K. Stochasitc time history analysis of structuralvibration with uncertain damping[J]. Probalilistic Structural Analysis,1984,93:109-120
[1-28]张汝清,高行山.随机变量的变分原理及有限元法[J].应用数学与力学,1992,13(5):383-388
[1-29]张汝清,高行山.有限变形弹性理论随机变量变分原理及有限元法[J].应用数学与力学,1994,15(10):855-862
[1-30]秦权,林道锦,梅刚.结构可靠度随机有限元法:理论及工程应用[M].北京:清华大学出版社,2006
[1-31] Sun T C. A finite element method for random differential equations with randomcoefficients[J]. Journal of Numerical Analysis,1979,16(6):1019-1035
[1-32] Ghanem R, Spanos P D. Polynomial chaos in stochastic finite elements[J]. Journal ofApplied Mechanics,1990,57(1):197-202
[1-33]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3):263-267
[1-34]杨杰.非线性结构随机分析数值模拟的方法研究[D].成都:西南交通大学.2004
[1-35]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000
[1-36] Freudenthal A M. The safety of structures[J]. Transactions ASCE,1947,112:125-129
[1-37]张新培.建筑结构可靠度分析与设计[M].北京:科学出版社,2001
[1-38] Cornell C A. A probability-based structural code[J]. ACI Journal Proceedings,1969,66(12):974-985
[1-39] Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. Journalof Engineering Mechanics Division ASCE,1974,100(1):111-121
[1-40] Ang A H-S, Tang W H. Probability Concepts in Engineering Planning andDesign[M]. New York: John Eiley&Sons,1984
[1-41] Rackwitz R, Fiessler B. Structural reliability combined random load sequences[J].Computers and Structures,1974,9(5):489-494
[1-42]余大胜,康海贵.响应面法计算结构可靠度的回顾[J].工业建筑,2006,36(S1):238-242
[1-43] Deng J, Gu D S, Li X B, et al. Structural reliability analysis for implicit performancefunctions using artificial network[J]. Strucutural Safety,2005,27(1):25-48
[1-44]金伟良,唐纯喜,陈进.基于SVM的结构可靠度分析响应面方法[J].计算力学学报,2007,24(6):713-718
[1-45]金伟良,袁雪霞.基于LS-SVM的结构可靠度响应面分析方法[J].浙江大学学报,2007,41(1):44-47
[1-46] Rizzo F J. An integral equation approach to boundary value problems of classicalelastostatics[J]. Quarterly of Applied Mathematics,1967,25:83-95
[1-47] Cheng A H D, Cheng D T. Heritage and early history of the boundary elementmethod[J]. Enginerring Analysis with Boundary Elements,2005,29(3):268-302
[1-48] Bannerjee P K, Butterfield R. Boundary Element Methods in EngineeringScience[M]. London: McGraw-Hill,1981
[1-49] Brebbia C A. The boundary Element Method for Engineers[M]. London: Pretech,1978
[1-50] Brebbia C A, Telles J, Wrobel L C. Boundary Element Techniques: Theory andApplications in Engineering[M]. Berlin: Springer-Verlag,1984
[1-51] Manolis G D, Beskos D E. Boundary Element Methods in Elastodynamics[M].London: Unwin-Hyman,1988
[1-52]杜庆华,嵇醒,岑章志等.边界积分方程-边界元法的力学基础与工程应用[M].北京:高等教育出版社,1989
[1-53]嵇醒,臧跃龙,程玉民.边界元法进展及通用程序[M].上海:同济大学出版社,1997
[1-54]郑建军.边界元法及其在结构分析中的应用[M].合肥:安徽科学技术出版社,2006
[1-55]祝家麟,袁政强.边界元分析[M].北京:科学出版社,2009
[1-56]余德浩.自然边界元方法的数学理论[M].北京:科学出版社,1993
[1-57]金伏生,秦庆华.非线性Reissner板杂交元及边界元解[J].计算力学学报,1992,9(2):148-152
[1-58]秦庆华,黄玉盈.任意外型薄板非线性后屈曲问题的边界元解[J].固体力学学报,1990,11(1):47-56
[1-59] Qin Q H. The Trefftz Finite and Boundary Element Method[M]. Southampton: WIT.2000
[1-60] Qin Q H. Fracture Mechanics of Piezoelectric Materials[M]. Southampton: WIT.2001
[1-61] Zhang C H, Wolf J P. Dynamic Soil-Structure Interaction: Current Research in Chinaand Switzerland[M]. Amsterdam: Elsevier,1998
[1-62] Zhang C H. Numerical Modeling of Oncrete Dam-Foundation-Reservoir Systems[M].Beijing: Tsinghua University,2001
[1-63]姚振汉,杜庆华.边界元法应用的若干近期研究及国际新进展[J].清华大学学报(自然科学版),2001:89-93
[1-64]姚振汉,王海涛.边界元法[M].北京:高等教育出版社,2010
[1-65] Su C, Han D J. Analysis of elastic plane problems by the spline fictitious boundaryelement method[A]. Computational Method in Engineering and Science—Theory andPractice[C]. Guangzhou: South China University of Technology Press,1997:538-542
[1-66] Su C, Han D J. Multidomain SFBEM and its application in elastic plane problems[J].Journal of Engineering Mechanics ASCE,2000,126(10):1057-1063
[1-67] Su C, Han D J. Elastic analysis of orthotropic plane problems by the spline fictitiousboundary element method[J]. Applied Mathematics and Mechanics,2002;23(4):446-453
[1-68]苏成,韩大建.高层建筑筏板基础分析的样条虚边界元法[J].土木工程学报,2001,34(1):61-66
[1-69]苏成,郑淳.应力强度因子计算的样条虚边界元法[J].工程力学,2007,24(8):49-53
[1-70]苏成,郑淳.基于Erdogan基本解边界元法计算应力强度因子[J].力学学报,2007,39(1):93-99
[1-71] Burczyński T. Stochastic boundary value problems of elastostatics in terms of theboundary integral equation method[J]. Papers of the Institution of Civil Engineering inWroc aw Technical University,1981,1(28):61-68(in Polish)
[1-72] Nakagiri S, Suzuki K, Hisada T. Stochastic boundary element method applied tostress analysis[A]. Brebbia C A, Futugami T, Tanaka M. Boundary Elements V[C]. NewYork: Springer-Verlag,1983:439-448
[1-73]王金根.基于形状摄动技术的边界元法[J].计算结构力学及其应用,1990,7(2):77-84
[1-74] Etlouney M, Benaroga H, Wright J. Boundary element methods in probabilisticstructural analysis (PBEM)[J]. Applied Mathematical Modeling,1989,13(7):432-440
[1-75] Kaljevi I, Saigal S. Stochastic boundary elements in elastostatics[J]. ComputerMethods in Applied Mechanics and Engineering,1993,109(3-4):259-280
[1-76] Kamiński M. Stochastic second-order BEM perturbation formulation[J]. EngineeringAnalysis with Boundary Elements,1999,23(2):123-129
[1-77] Kamiński M. Application of the generalized perturbation-based stochastic boundaryelement method to the elastostatics[J]. Engineering Analysis with Boundary Elements,2007,31(6):514-527
[1-78] Kamiński M. Least squares stochastic boundary element method[J]. EngineeringAnalysis with Boundary Elements,2011,35(5):776-784
[1-79] Dasgupta G, Papusha A N, Malsch E. First order stochasticity in boundary geometry:a computer algebra BE development[J]. Engineering Analysis with Boundary Elements,2001,25(9):741-751
[1-80] Kaljevi I, Saigal S. Stochastic boundary elements for two-dimensional potentialflow in homogeneous domains[J]. International Journal of Solids and Structures,1995,32(13):1873-1892
[1-81] Emery A F. Solving stochastic heat transfer problems[J]. Engineering Analysis withBoundary Elements,2004,28(3):279-291
[1-82] Manolis G D, Shaw R P. Boundary integral formulation for2D and3D thermalproblems exhibiting a linearly varying stochastic conductivity[J]. ComputationalMechanics,1996,17(6):406-417
[1-83] Manolis G D, Shaw R P. Harmonic elastic waves in continuously heterogeneousrandom layers[J]. Engineering Analysis with Boundary Elements,1997,19(3),181-198
[1-84] Manolis G D, Pavlou S. Fundamental solutions for SH-waves in a continuum withlarge randomness[J]. Engineering Analysis with Boundary Elements,1999,23(9),721-736
[1-85] Breitung K, Casciati F, Farávelli L. A random field description for stochasticboundary elements[J]. Engineering Analysis with Boundary Elements,1997,19(3):223-229
[1-86]江爱民,丁皓江.扁壳统计分析的随机边界元法[J].土木工程学报,1996,29(4):57-63
[1-87]江爱民,朱劲松,丁皓江等.薄板统计分析的随机边界元法[J].上海力学,1997,18(4):321-326
[1-88]江爱民,沈晓安.中厚板统计分析的随机边界元法[J].计算力学学报,2001,18(2):179-183
[1-89] Burczyński T. The boundary element method for stochastic potential problems[J].Applied Mathematical Modelling,1985,9(3):189-194
[1-90] Burczyński T. Stochastic boundary element method for wave propagation throughcontinuous random media[A]. Connor J J, Brebbia C A. BETECH86MIT[C]. Cambridge:CML Publications,1986:733-741
[1-91] Burczyński T, John A. Stochastic dynamic analysis of elastic and viscoelastic systemby means of the boundary element method[A]. Brebbia C A, Maier G. Boundary ElementsⅦ[C]. Berlin: Springer-Verlag,1985:53-61
[1-92] Burczyński T. Boundary element method for deterministic and stochastic shapedesign sensitivity analysis[A]. Cruse T A. Advanced Boundary Element Method[C]. Belin:Springer-Verlag,1988:73-80
[1-93] Burczyński T, Fedeliński P. Boundary elements in shape design sensitivity analysisand optimal design of vibrating structures[J]. Engineering Analysis with BoundaryElements,1992,9(3):195-202
[1-94] Burczyński T, Kane J H, Balakrishna C. Comparison of shape design sensitivityanalysis formulation via material derivative-adjoint variable and implicit differentiationtechniques for3-D and2-D curved boundary element[J]. Computer Methods in AppliedMechanics and Engineering,1997,168(1-42):89-109
[1-95] Bonnet M, Burczyński T, Nowakowski M. Sensitivity analysis for shape perturbationof cavity or internal crack using BIE and adjoint variable approach[J]. Iternational Journalof Solids and Structures,2002,39(9):2365-2385
[1-96] Bialecki R A, Burczyński T, Dlugosz A. Evolutionary shape optimization ofthernoelastic bodies exchanging heat by convection and radiation[J]. Computer Methodsin Applied Mechanics and Engineering,2005,194(17):1839-1859
[1-97] Burczyński T, Skrzypczyk J. Theoretical and computational aspects of the stochasticboundary element method[J]. Computer Methods in Applied Mechanics and Engineering,1999,168(1-4):321-344
[1-98] Honda R. Stochastic BEM with spectral approach in elastostatic and elastodynamicproblems with geometrical uncertainty[J]. Engineering Analysis with Boundary Elements,2005,29(5):415-427
[1-99] Agarwal N, Aluru N R. Stochastic modeling of coupled electromechanicalinteraction for uncertainty quantification in electrostatically actuated MEMS[J]. ComputerMethods in Applied Mechanics and Engineering,2008,197(43-44):3456-3471
[1-100]江爱民,任永坚.结构可靠性分析的随机边界元法[J].浙江大学学报,1994,22(6):708-715
[1-101]江爱民,丁皓江.随机边界元法在大坝可靠性分析中的应用[J].工程力学,1996,13(1):81-85
[1-102]江爱民,汪小超,陈瑞生.随机边界元法在薄板可靠性分析中的应用[J].力学季刊,2002,23(2):272-274
[1-103]温卫东,陈伟,高德平.二维弹性随机边界元法与可靠度分析[J].应用力学学报.1995,12(1):9-14
[1-104]陈伟,温卫东,陈卓.二维弹性接触问题中随机边界元法与可靠性分析[J].应用力学学报,1998,15(1):109-112
[1-105] Zhang M, Wu Q G. Stochastic boundary element analysis of concrete gravity dam[J].Tsinghua Science and Technology,2002,7(3):254-257
[2-1] Su Cheng, Han Dajian. Analysis of elastic plane problems by the spline fictitiousboundary element method[A]. Computational Method in Engineering and Science—Theory and Practice[C]. Guangzhou: SCUT Press,1997:538-542
[2-2] Su Cheng, Han Dajian. Multidomain SFBEM and its application in elastic planeproblems[J]. Journal of Engineering Mechanics ASCE,2000,126(10):1057-1063
[2-3]苏成,韩大建.正交各向异性弹性力学平面问题的样条虚边界元法[J].应用数学和力学,2002,23(4):400-406
[2-4]苏成,韩大建.高层建筑侧向刚度计算的分域样条虚边界元法[J].华南理工大学学报(自然科学版),1998,26(6):81-85
[2-5]苏成,韩大建.高层建筑筏板基础分析的样条虚边界元法[J].土木工程学报,2001,34(1):61-66
[2-6]苏成,郑淳.样条虚边界元法的数值稳定性与误差估计[J].华南理工大学学报,2003,31(8):53-58
[2-7]郑淳.样条虚边界元法在线弹性断裂力学中的应用[D].广州:华南理工大学,2004
[2-8]苏成,韩大建.弹性力学平面问题的分域样条虚边界元法—边界子段法[J].华南理工大学学报,1998,26(3):22-26
[2-9] Banerjee P K, Butterfield R. Boundary Element Method in Engineering Science[M].London: McGraw-Hill,1981
[2-10] Brebbia C A. The Boundary Element Method for Engineers[M]. London: PentechPress.1978
[2-11] Brebbia C A, Walker S. Boundary Element Method in Engineering[M]. London:Butterworths.1980
[2-12]王能超.数值分析简明教程[M].北京:高等教育出版社,1984
[2-13]许文焕,陈虬.加权余量法在结构分析中的应用[M].北京:中国铁道出版社.1985
[2-14]姚振汉,钟晓光.边界元法中边界变量的确定与误差直观度量[M].华中理工大学学报.1989,17(6):97~103
[2-15]西田正孝.应力集中(增补版)[M].李安定,郭廷玮.北京:机械工业出版社.1986
[2-16]邓攀.二维弹性动力学的样条虚边界元法[D].广州:华南理工大学,2005
[3-1] Vanmarcke E H. Random Fields[M]. Cambridge: MIT Press,1983
[3-2] Vanmarcke E H, Shinozuka M. Random fields and stochastic finite element method[J].Structural Safety,1986,3(3-4):143-166
[3-3] Vanmarcke E H. Probabilistic modeling of soil profiles[J]. Journal of GeotechnicalEngineering Division,1977,103(11):1227-1246
[3-4] Shinozuka M. Probabilistic modeling of concrete structures[J]. Journal of EngineeringMechanics Division,1972,98(6):1433-1451
[3-5]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[3-6]秦权.随机有限元及其进展(I)—随机场的离散和反应矩的计算[J].工程力学,1994,11(4):1-10
[3-7] Liu P L, Kiureghian A D. Finite element reliability of geometrically nonlinearuncertain structures[J]. Journal of Engineering Mechanics,1991,117(8):1806-1825
[3-8] Liu P L, Kiureghian A D. Multi-variate distribution models with prescribed marginalsand covariances[J]. Probabilistic Engineering Mechanics,1986,1(2):105-112
[3-9] Spanos P D, Ghanem R G. Stochastic finite element expansion for random media[J].Journal of Engineering Mechanics,1989,115(5):1035-1053
[3-10] Ghanem R G, Spanos P D. Stochastic Finite Element: A Spectral Approach[M]. NewYork: Springer-Verlag,1991
[4-1]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001
[4-2] Hasofer A M，Lind N C. Exact and invariant second-moment code format[J]. Journalof Engineering Mechanics，1974，100(1):111-121
[4-3]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990
[4-4]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
[4-5]张新培.建筑结构可靠度分析与设计[M].北京:科学出版社,2001
[4-6] Rackwitz R, Fiessler B. Structural relizbility under combined random loadsequences[J]. Computers and Structures,1978,9(5):489-494
[4-7] GBJ68-84，建筑结构设计统一标注[S].北京：中国建筑工业出版社，1984
[4-8] GB\T50283-1999，公路工程结构可靠度设计统一标准[S].北京：中国计划出版社，1999
[4-9]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000
[4-10] Rosenblatt. Remarks on a multivariate transformation[J]. Annals of MathematicalStatistics,1952,23:470-472
[4-11] Chen X, Lind N C. Fast probability integration by three parameter normal tailapproximation[J]. Structural Safety,1983,1(4):269-276
[4-12] Nowak A S, Collins K R. Reliability of Structures. NewYork: McGraw-Hill,2000
[5-1]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京：人民交通出版社,2003
[5-2] Rosenblatt. Remarks on a multivariate transformation[J]. Annals of MathematicalStatistics,1952,23:470-472
[5-3] Chen X, Lind N C. Fast probability integration by three parameter normal tailapproximation[J]. Structural Safety,1983,1(4):269-276
[5-4]李鹏飞.结构可靠度分析的响应面—蒙特卡罗法研究[D].广州:华南理工大学,2008
[5-5] Shinozuka M, Deodatis G． Response variability of stochastic finite elementsystems[J]. Journal of Engineering Mechanics ASCE.1988,114(3):499-519
[5-6] Yamazaki F, Shinozuka M, Dasgupta G．Neumann expansion for stochastic finiteelement systems[J]. Journal of Engineering Mechanics ASCE.1988,114(8):1335-1354
[5-7]金伟良.结构可靠度数值模拟的新方法[J].建筑结构学报,1996,14(3):63-72
[5-8]贡金鑫,仲伟秋,赵国藩.工程结构可靠度基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4),2-9
[5-9]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001