裂纹内水压对重力坝断裂特性影响的研究
|
摘要
在实际工程中,混凝土坝等结构由于温度、地震、干缩等原因不可避免地会出现表面裂纹,裂纹的出现改变了坝体的受力状态,并在裂纹尖端将产生较大的应力集中现象,对坝和结构的安全造成不利影响。水库蓄水以后裂纹内的水压力作用将引起额外的材料损伤而降低结构抵抗开裂的能力。尽管人们已经认识到裂纹内水压可能改变结构的抗力强度,但是由于缺少现场实测、实验室试验、数值分析的数据,裂纹内水压力对结构的影响仍然是结构设计和安全评价中的一个不确定因素。因此,研究裂纹内水压力对结构安全性的影响将具有重要的意义。
比例边界有限元法(Scaled Boundary Finite Elemem Method,简称SBFEM)是最近发展起来的一种新的数值方法,它不仅集合了传统有限元法和边界元法的优点,同时具有自己独特的优势。首先,它只需离散部分边界使问题降低一维,从而减小了计算工作量以及前处理的工作量。其次它避免了基本解求解的复杂性和奇异积分,可以方便地处理各向异性材料。在无限域模拟方面,它精确满足无穷远处的辐射条件,且不需要增加任何计算量就能够方便地模拟一类非均质无限地基。在断裂力学方面当相似中心选在裂尖处时裂纹面不需要离散,且在径向位移和应力具有完全精确的解析解,使得裂纹尖端应力强度因子的计算既准确又方便,处理应力奇异性问题是比例边界有限元法的另一个突出优点。
本文应用比例边界有限元法在断裂力学应用中的优势,联合子结构法(超单元)对弹性多裂纹问题进行了分析,进一步推广了比例边界有限元法的应用范围,使得应用比例边界有限元法分析水坝的水力劈裂问题成为可能。由于比例边界有限元法具有半解析的特点,对于一大类体荷载和面荷载可以解析地求解不需要引入额外的近似,本文建立了含裂纹内水压的重力坝应力强度因子的比例边界有限元计算方程,该方程由二阶齐次常微分方程转变为二阶非齐次常微分方程,求解方法发生一定的变化,通过典型算例验证了收敛性和精度。并计算了正交异性材料,双材料交界面及多裂纹有裂纹面荷载作用情况下的应力强度因子。最后研究了不同裂纹长度、不同水压分布、不同坝体坝基弹模比的情况下应力强度因子的变化规律,得到一些有意义的结论。
在研究坝体的地震响应时,通常要研究无限地基对坝体响应的影响,一般计算公式中只包含了弹性刚度与阻尼项,而忽略了迟滞效应。本文应用比例边界有限元方法建立了考虑迟滞效应影响的无限地基动力相互作用方程。通过一种新的高阶透射边界对无限地基进行模拟。该透射边界是基于无限域动力刚度矩阵的连分式解形式。连分式的系数通过以动力刚度矩阵表示的比例边界有限元方程递推计算。数值算例验证了该透射边界的收敛性,并与解析解进行比较表明该方法具有较高的精度。并将该透射边界应用于重力坝—地基—库水系统动力分析,将计算结果与工程上常用的无质量地基进行了对比。该方法可以方便有效的进行二维和三维大型结构—地基相互作用分析。
在以上研究的基础上,本文充分利用比例边界有限元法在结构—地基相互作用分析中及断裂力学中应用的两大优势,对重力坝—地基—库水系统进行了动态断裂分析,给出了裂纹尖端应力强度因子时程变化规律,以及坝体的最大应力分布。表明比例边界有限元法可以有效应用于坝体的动态断裂分析。
In the practical engineering, the concrete dam will suffer various kinds of damage such as dents, corrosion pits, cracks, deformation, etc. through years of environmental impact of soil reactions, earthquakes, water pressure, etc. The presence of these cracks or geometrical changes, such as notches may result in reduction of the stiffness of the cracked structures, and thus influence the degree of safety. Furthermore, any water pressure inside cracks will cause additional material damage and therefore reduce resistance against further cracking. Although it is anticipated that water pressure in cracks might change the strength of the structures, due to lack of historical, experimental and numerical evidences the influence of water pressure in cracks on the structures remains a major factor of uncertainty in the design and safety assessment of concrete structures. Therefore it has very important meaning to study the effect of the water pressure in the crack on the safety of the structure.
The scaled Boundary Finite Element Method (abbr. SBFEM) is a new numerical method developed in recently. It has the advantages of both the finite element method and the boundary element method, at the same time it has its own characters. Firstly, it discretizes only boundaries of the investigated domain, reduces the cost of prepare process. Secondly, no fundamental solution and its complexity are required, anisotropic materials are handled without additional computational efforts. In the modeling of unbounded domain, the method permits the boundary condition at infinity to be enforced analytically, non-homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates can be considered easily. When it is applied to fracture mechanics problems, the scaling centre is chosen on the part of the boundary, no discretization is required. In the radial direction the displacements and stress can be evaluated analytically, the stress intensity factors and T-stress can be calculated based on their determination. It is another prominent character of SBFEM to represent the stress singularities.
In the paper the elastic multi-crack problem is analyzed using SBFEM combining the sub-technique (or super-element). The scope of application of the SBFEM has been extended, and it makes it feasible to analyze the hydraulic fracture problem using the SBFEM. For a kind of loads varying as power functions in the radial coordinate, the SBFEM remains semi-anlytical and no additional approximations are introduced. The scaled boundary finite element equations for evaluating the SIF of the gravity dam with the effect of water pressure inside the crack is established and solved. The equation is the second order heterogeneous ordinary differential equation. Its solving process is different from the second order homogeneous ordinary differential equation. The comparison with the analytical solution and numerical examples show that SBFEM is effective and possesses high accuracy for the calculation of stress intensity factor with the contribution of surface tractions. The stress intensity factors of the anisotropic materials and bi-material with the contribution of surface tractions are also evaluated. The fracture analysis for the interfacial cracks in the vicinity of the dam heel combining the sub-structure technique (or super-element) is made. The effect of different water pressure distributing in the crack is studied and some useful conclusions are obtained by comparisons.
When subjected to earthquake ground motion, wether considering the dynamic interaction of structure-foundation plays a vital important role to the response of the dam. Generally, the formula for calculating the interaction force includes the elastic stiffness matrix and damp matrix only, the lingering effect is disregarded. The equation of the structure-unbounded foundation interaction which can consider the lingering effect, namely the action of the time coupling, is established. In the paper the unbounded foundation is considered by a new high-order transmitting boundary based on the continued-fraction solution of the dynamic-stiffness matrix. The coefficient matrices of the continued fraction are evaluated recursively through the scaled boundary finite element equation in dynamic stiffness. The convergence of the high-order transmitting boundary is demonstrated by the numerical examples. Comparisons with the analytical solutions show that the method possesses high accuracy. The system of the gravity dam-reservoir-foundation is calculated and the results are compared with the mass-less base model. In conclusion the approach is effective and suitable for 2D and 3D large-scale structure-foundation interaction analysis.
At last, making the best use of advantage that SBFEM can simulate the unbounded media and the stress singularity expediently, the system of the gravity dam-reservoir-foundation with the crack in the dam heel is evaluated dynamically, the time history of the DSIFs and the stress distributing of the dam with crack are provided for the infinite foundation and mass-less foundation. The approach is applicable for the 2D dynamic fracture analysis.
比例边界有限元法(Scaled Boundary Finite Elemem Method,简称SBFEM)是最近发展起来的一种新的数值方法,它不仅集合了传统有限元法和边界元法的优点,同时具有自己独特的优势。首先,它只需离散部分边界使问题降低一维,从而减小了计算工作量以及前处理的工作量。其次它避免了基本解求解的复杂性和奇异积分,可以方便地处理各向异性材料。在无限域模拟方面,它精确满足无穷远处的辐射条件,且不需要增加任何计算量就能够方便地模拟一类非均质无限地基。在断裂力学方面当相似中心选在裂尖处时裂纹面不需要离散,且在径向位移和应力具有完全精确的解析解,使得裂纹尖端应力强度因子的计算既准确又方便,处理应力奇异性问题是比例边界有限元法的另一个突出优点。
本文应用比例边界有限元法在断裂力学应用中的优势,联合子结构法(超单元)对弹性多裂纹问题进行了分析,进一步推广了比例边界有限元法的应用范围,使得应用比例边界有限元法分析水坝的水力劈裂问题成为可能。由于比例边界有限元法具有半解析的特点,对于一大类体荷载和面荷载可以解析地求解不需要引入额外的近似,本文建立了含裂纹内水压的重力坝应力强度因子的比例边界有限元计算方程,该方程由二阶齐次常微分方程转变为二阶非齐次常微分方程,求解方法发生一定的变化,通过典型算例验证了收敛性和精度。并计算了正交异性材料,双材料交界面及多裂纹有裂纹面荷载作用情况下的应力强度因子。最后研究了不同裂纹长度、不同水压分布、不同坝体坝基弹模比的情况下应力强度因子的变化规律,得到一些有意义的结论。
在研究坝体的地震响应时,通常要研究无限地基对坝体响应的影响,一般计算公式中只包含了弹性刚度与阻尼项,而忽略了迟滞效应。本文应用比例边界有限元方法建立了考虑迟滞效应影响的无限地基动力相互作用方程。通过一种新的高阶透射边界对无限地基进行模拟。该透射边界是基于无限域动力刚度矩阵的连分式解形式。连分式的系数通过以动力刚度矩阵表示的比例边界有限元方程递推计算。数值算例验证了该透射边界的收敛性,并与解析解进行比较表明该方法具有较高的精度。并将该透射边界应用于重力坝—地基—库水系统动力分析,将计算结果与工程上常用的无质量地基进行了对比。该方法可以方便有效的进行二维和三维大型结构—地基相互作用分析。
在以上研究的基础上,本文充分利用比例边界有限元法在结构—地基相互作用分析中及断裂力学中应用的两大优势,对重力坝—地基—库水系统进行了动态断裂分析,给出了裂纹尖端应力强度因子时程变化规律,以及坝体的最大应力分布。表明比例边界有限元法可以有效应用于坝体的动态断裂分析。
In the practical engineering, the concrete dam will suffer various kinds of damage such as dents, corrosion pits, cracks, deformation, etc. through years of environmental impact of soil reactions, earthquakes, water pressure, etc. The presence of these cracks or geometrical changes, such as notches may result in reduction of the stiffness of the cracked structures, and thus influence the degree of safety. Furthermore, any water pressure inside cracks will cause additional material damage and therefore reduce resistance against further cracking. Although it is anticipated that water pressure in cracks might change the strength of the structures, due to lack of historical, experimental and numerical evidences the influence of water pressure in cracks on the structures remains a major factor of uncertainty in the design and safety assessment of concrete structures. Therefore it has very important meaning to study the effect of the water pressure in the crack on the safety of the structure.
The scaled Boundary Finite Element Method (abbr. SBFEM) is a new numerical method developed in recently. It has the advantages of both the finite element method and the boundary element method, at the same time it has its own characters. Firstly, it discretizes only boundaries of the investigated domain, reduces the cost of prepare process. Secondly, no fundamental solution and its complexity are required, anisotropic materials are handled without additional computational efforts. In the modeling of unbounded domain, the method permits the boundary condition at infinity to be enforced analytically, non-homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates can be considered easily. When it is applied to fracture mechanics problems, the scaling centre is chosen on the part of the boundary, no discretization is required. In the radial direction the displacements and stress can be evaluated analytically, the stress intensity factors and T-stress can be calculated based on their determination. It is another prominent character of SBFEM to represent the stress singularities.
In the paper the elastic multi-crack problem is analyzed using SBFEM combining the sub-technique (or super-element). The scope of application of the SBFEM has been extended, and it makes it feasible to analyze the hydraulic fracture problem using the SBFEM. For a kind of loads varying as power functions in the radial coordinate, the SBFEM remains semi-anlytical and no additional approximations are introduced. The scaled boundary finite element equations for evaluating the SIF of the gravity dam with the effect of water pressure inside the crack is established and solved. The equation is the second order heterogeneous ordinary differential equation. Its solving process is different from the second order homogeneous ordinary differential equation. The comparison with the analytical solution and numerical examples show that SBFEM is effective and possesses high accuracy for the calculation of stress intensity factor with the contribution of surface tractions. The stress intensity factors of the anisotropic materials and bi-material with the contribution of surface tractions are also evaluated. The fracture analysis for the interfacial cracks in the vicinity of the dam heel combining the sub-structure technique (or super-element) is made. The effect of different water pressure distributing in the crack is studied and some useful conclusions are obtained by comparisons.
When subjected to earthquake ground motion, wether considering the dynamic interaction of structure-foundation plays a vital important role to the response of the dam. Generally, the formula for calculating the interaction force includes the elastic stiffness matrix and damp matrix only, the lingering effect is disregarded. The equation of the structure-unbounded foundation interaction which can consider the lingering effect, namely the action of the time coupling, is established. In the paper the unbounded foundation is considered by a new high-order transmitting boundary based on the continued-fraction solution of the dynamic-stiffness matrix. The coefficient matrices of the continued fraction are evaluated recursively through the scaled boundary finite element equation in dynamic stiffness. The convergence of the high-order transmitting boundary is demonstrated by the numerical examples. Comparisons with the analytical solutions show that the method possesses high accuracy. The system of the gravity dam-reservoir-foundation is calculated and the results are compared with the mass-less base model. In conclusion the approach is effective and suitable for 2D and 3D large-scale structure-foundation interaction analysis.
At last, making the best use of advantage that SBFEM can simulate the unbounded media and the stress singularity expediently, the system of the gravity dam-reservoir-foundation with the crack in the dam heel is evaluated dynamically, the time history of the DSIFs and the stress distributing of the dam with crack are provided for the infinite foundation and mass-less foundation. The approach is applicable for the 2D dynamic fracture analysis.
引文
[1]潘家铮.关于高拱坝建设中若干问题的探讨.科技导报.1997,2:17-19.
[2]凡耐理M,李进平,刘忠清.高拱坝对基础裂缝的敏感性研究.水利水电快报.1999,20(21):12-16.
[3]李瓒.石门拱坝的坝踵裂缝.水利学报.1999,11:61-65.
[4]Kaplan M F.Crack propagation and the fracture of concrete.ACI Journal,1961,58:591-610.
[5]潘家铮.重力坝设计.北京:水利水电出版社,1987.
[6]徐世娘.混凝土断裂机理:大连:大连理工大学,1988.
[7]徐世娘.混凝土断裂力学.大连:大连理工大学,1991.
[8]徐世娘,赵国藩.混凝_十结构裂缝扩展的双K断裂准则.土木工程学报.1992,25(2):32-38.
[9]徐世娘,赵国藩.混凝土断裂力学研究.大连:大连理工大学出版社,1991.
[10]Hillerborg A,Modeerand M,Petersson P E,et al.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.Cement and Concrete Research,1976,6(6):773-782.
[11]Bazant Z P.Crack band theory for fracture of concrete.Materials and Structures,1983,16(93):155-177.
[12]Swartz S E,Go C G.Validity of compliance calibration to cracked concrete beams in bending tests.Experimental Mechanics,1984,24(2):129-134.
[13]Swartz S E,Refai T M.Influence of size on opening mode fracture parameters for precracked concrete beams in bending.Proceedings of ESM-RILEM International conference on fracture of concrete and rock,Houston,Texas,1987:242-254.
[14]Jenq Y S,Shah S P.Two parameter fracture model for concrete,ASCE.Journal of Engineering Mechanics,1985,111(10):1227-1241.
[15]Bazant Z P,Kazemi M T.Size dependence of concrete fracture energy determined by Rilem work-of-fracture method.International Journal of Fracture,1991,51(2):121-138.
[16]Bazant Z P,Kazemi M T.Determination of fracture energy,process zone length and brittleness number from size effect,with application to rock and concrete.International Journal of Fracture,1990,44(2):111-131.
[17]Karihaloo B L.Fracture mechanics and structural concrete.New York:Copublished in the United States with John Wiley & Sons,1995.
[18]Bruhwiler E,Saomna V E.Water fracture interaction in concrete Part I:Fracture Properties.ACI Materials Journal,1995,92(3).
[19]Bruhwiler E,Saouma V E.Water fracture interaction in concrete Part II:Hydrostatic Pressure in Cracks.ACI Materials Journal,1995,92(4).
[20]Reinhardt H W,Sosoro M,Zhu X,et al.Cracked and repaired concrete subject to fluid penetration.Materials and Structures,1998,31:74-93.
[21]Slowik V,Saouma V E.Water pressure in propagating concrete cracks.Journal of Structural Engineering,2000,126(2):235-242.
[22]柏承新,赵代深.二次奇性边界元及其在重力坝坝踵断裂分析中的应用.土木工程学报,1988, (02):43-50.
[23]李庆斌,林皋,周鸿钧.异弹模界面裂缝的边界元分析及其应用.大连理工大学学报,1991,(02):1 99-204.
[24]刘光廷,王宗敏,周鸿钧.缝端奇异边界单元和界面裂缝的应力强度因子计算.清华大学学报(自然科学版),1996,(01):34-40.
[25]贾金生,李新宇,郑璀莹.特高重力坝考虑高压水劈裂影响的初步研究.水利学报.2006,(12):1509-1515
[26]Griffth A A.The phenomena of rupture and flow in solids.Philosophical Transactions Royal Society of London,1921,Series A221:163-168.
[27]Lawn B R.Fracture of Brittle Solids-Second Edition.Cambridge:Cambridge University,1993.
[28]Irwin G R.Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics,1957,24(4):361-364.
[29]20世纪理论和应用力学十大进展.力学进展,2001,31(03):322-326.
[30]柳春图,蒋持平.当前断裂力学发展的几个问题:固体力学发展趋势.黄克智,徐秉业.北京:北京理工大学出版社,1995322-326.
[31]Sih G C.Mechanics of fracture,Vol.1,Methods of analysis and solutions of crack problem.Leyden:Noordhoff International Publishing,1973.
[32]Rooke D P,Cartwright D J.Compendium of stress intensity factors.London:England:the Hillingdon,1976.
[33]中国航空研究院.应力强度因子手册.北京:科学出版社,1981.
[34]张行.断裂力学中应力强度因子的解法.北京:国防工业出版社,1992.
[35]Sih G C.Handbook of stress intensity factors.Bethlehem:Leheigh University,1973.
[36]Tada H,Paris P C,Irwin G R,et al.The stress analysis of cracks.Hellertown:Del Research Corp,1973.
[37]Murakami Y.Stress intensity factor handbook.New York:Pergamon Press,1987.
[38]余德浩.计算数学与科学工程计算及其在中国的若干发展.数学进展,2002,(01):1-6.
[39]Aliabadi M H,Rooke D P.Numerical Fracture Mechanics.Southampton/Boston:Kluwer Academic Pubsishers,1991.
[40]黎在良,王元汉,李廷芥.断裂力学中的边界数值方法.北京:地震出版社,1996.
[41]Zhu Z,Xie H,Ji S,et al.The mixed boundary problems for a mixed mode crack in a finite plate.Engineering Fracture Mechanics,1997,56(5):647-655.
[42]Fett T.Stress intensity factors and T-stress in edge-cracked rectangular plates under mixed boundary conditions.Engineering Fracture Mechanics,1998,60(5-6):625-630.
[43]Fett T,Bahr H.Mode I stress intensity factors and weight functions for short plates under different boundary conditions.Engineering Fracture Mechanics,1999,62(6):593-606.
[44]Fett T.Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions.Engineering Fracture Mechanics,2001,68(9):1119-1136.
[45]Fett T.Stress intensity factors and T-stress for single and double-edge-cracked circular disks under mixed boundary conditions.Engineering Fracture Mechanics,2002,69(1):69-83.
[46]Liebowitz H,Sandhu J S,Lee J D,et al.Computational fracture mechanics:Research and application. Engineering Fracture Mechanics,1995,50(5-6):653-670.
[47]Chen Y M.Numerical computation of dynamic stress intensity factors,by a Lagrangian finite-difference method(the HEMP code).Engineering Fracture Mechanics,1975,7(4):653-660.
[48]Lin X,Ballmann J.Re-consideration of Chen's problem by finite difference method.Engineering Fracture Mechanics,1993,44(5):735-739.
[49]Altus E.The finite difference technique for solving crack problems.Engineering Fracture Mechanics,1984,19(5):947-957.
[50]Liebowitz H,Moyer E T.Finite Element Methods in Fracture Mechanics.Computers & Structures,1989,31(1):1-9.
[51]Mowbray D F.A note on the finite element method in linear fracture mechanics.Engineering Fracture Mechanics,1970,2(2):173-176.
[52]Chan S K,Tuba I S,Wilson W K,et al.On the finite element method in linear fracture mechanics.Engineering Fracture Mechanics,1970,2(1):1-17.
[53]Banks-sills L.Application of the finite element method to linear elastic fracture mechanics.Applied Mechanics Reviews,1991,44(10):447-461.
[54]Henshell R D,Shaw K G.Crack tip finite elements are unnecessary.International Journal for Numerical Methods in Engineering,1975,9:495-507.
[55]Barsoum R S.On the use of isoparametric finite elements in linear fracture mechanics.International Journal for Numerical Methods in Engineering,1976,10:25-37.
[56]Barsoum R S.Trangular quarter-point elements as elastic and perfectly-plastic crack tip elements.International Journal for Numerical Methods in Engineering,1977,11:85-98.
[57]Owen D R,Fawkes A J.Engineering Fracture Mechanics:Numerical Methods and Application.Swansea,U.K.:Pineridge Press Ltd,1982.
[58]姚敬之.有限元法中的过渡单元.固体力学学报,1985,(04):541-548.
[59]姚敬之.奇应变拟协调元.河海大学学报(自然科学版),1988,(04):72-83.
[60]姚敬之.关于奇应变拟协调元的一点注记.河海大学学报:自然科学版,1991,19(4):127-129.
[61]陈万吉,陈伦元,杨健.拟协调奇异元.固体力学学报,1984,(03):351-366.
[62]李英治,柳春图.Reissner型平板弯曲断裂问题分析.力学学报,1983,(04):366-375.
[63]李英治,柳春图.用应力杂交法计算Reissner型板复合型弯曲应力强度因子.航空学报,1986,(06):553-558.
[64]李英治,李敏华,柳春图.含表面裂纹三维体裂纹尖端应力应变场及应力强度因子计算.中国科学A辑,1988,(08):828-842.
[65]冯金辉,柳春图.含裂纹有限结构的局部.整体分析.应用力学学报,1999,(02):145-150.
[66]Tracey D M.Finite elements,for determination of crack tip elastic stress intensity factors.Engineering Fracture Mechanics,1971,3(3):255-265.
[67]Tracey D M,Cook T S.Analysis of power type singularities using finite elements.International Journal Numerical Method in Engineering,1977,11:1225-1233.
[68]Pu S L,Hussain M A,Lorensen W E,et al.The collapsed cubic isoparametric element as a singular element for crack problems.International Journal Numerical Method in Engineering,1978,12:1727-1742.
[69]Lin K Y,Tong P.Singular finite elements for the fracture analysis of V-notched plate.International Journal Numerical Method in Engineering,1980,15:1343-1354.
[70]Givoli D,Rivkin L.The DtN finite element method for elastic domains with cracks and reentrant comers.COMPUTERS & Structures,1993,49:633-642.
[71]王志超,张理苏.一种新的准谐调有限元列式方法及在断裂力学中的应用.力学学报,1990,22(4):457-462.
[72]钟万勰,张洪武.平面断裂解析元的列式.机械强度,1995,17(3):1-6.
[73]Meguid S A,Tan M,Zh Z H,et al.Analysis of cracks perpenticular to biomaterial interfaces using a novel FE.International Journal Of Fracture,1995,.
[74]Rahulkumar P,Saigal S,Yunus S,et al.SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS.International Journal for Numerical Methods ir Engineering,1997,40(6):1091-1114.
[75]Munaswamy K,Pullela R.Computation of stress intensity factors for through cracks in plates using p-version finite element method.Communications in Numerical Methods in Engineering,2007.
[76]Xiao Q Z,Karihaloo B L,Williams F W,et al.Application of penalty-equilibrium hybrid stress element method to crack problems.Engineering Fracture Mechanics,1999,63(1):1-22.
[77]Wu C C,Cheung Y K.On optimization approaches of hybrid stress elements.Finite Elements ir Analysis and Design,1995,21(1-2):111-128.
[78]Yamada Y,Okumura H.Finite element analysis of stress and strain singularity eigenstate in inhomogeneous media or composite materials.Hybrid and Mixed Finite Methods,New York,1983:325-343.
[79]平学成,陈梦成.楔形体尖端近似场的非协调有限元特征法.华东交通大学学报,2001,(04):6-11.
[80]梁平英,陈梦成.一种新的计算各向异性材料裂纹尖端应力强度因子杂交元法.计算力学学报,2007,(02):209-214.
[81]张武,林胜良.多参量断裂力学广义杂交/混合裂纹有限元法.应用力学学报,2004,(01):62-67.
[82]Noor A K,Babuska I.Quality assessment and control of finite element solutions.Finite Elements in Analysis and Design,1987,3(1):1-26.
[83]lyer N R,Appa R T.A review of error analysis and adaptive refinement methodologies in finite element applications.Part I:Error analysis.Journal of Structural Engineering,1992,19:77-94.
[84]lyer N R,Appa R T.A review of error analysis and adaptive refinement methodologies in finite element applications.Part II:Adaptive refinements.Journal of Structural Engineering,1992,19:125-137.
[85]Babuka I,Rheinboldt W C.A-posteriori error estimates for the finite element method.International Journal for Numerical Methods in Engineering,1978,12(10):1597-1615.
[86]Zienkiewicz O C,Zhu J Z.A simple error estimator and adaptive procedure for practical engineerng analysis.International Journal for Numerical Methods in Engineering,1987,24(2):337-357.
[87]Zienkiewicz O C,Zhu J Z.The superconvergent patch recovery and a posteriori error estimators.Part Ⅰ:The recovery technique;PartII:Error estimates and adaptivity.International Journal For Numerical Methods In Engineering,1992,33:1331-1382.
[88]Wiberg N E,Abdulwahab F.Patch recovery based on superconvergent derivatives and equilibrium. International Journal for Numerical Methods in Engineering, 1993, 36(16): 2703-2724.
[89] Wiberg N E, Abdulwahab F. Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. International Journal for Numerical Methods in Engineering, 1994, 37(20): 3417-3440.
[90] Wiberg N E, Li X D, Abdulwahab F, et al. Adaptive finite element procedures in elasticity and plasticity. Engineering Computations, 1996, 12: 120 - 141.
[91] Wiberg N E, Li X D. Adaptive finite element procedures for linear and non-linear dynamics. International Journal for Numerical Methods in Engineering, 1999, 46(10): 1781-1802.
[92] Blacker T, Belytschko T. Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 1994, 37(3): 517-536.
[93] Schleupen A, Ramm E. Local and global error estimations in linear structural dynamics. Computers & Structures, 2000, 76(6): 741-756.
[94] Zienkiewicz O C, Taylor R L. The finite element method, vol. I: The basis, vol. II: Solid mechanics. Oxford: Butterworth-Hienemann Ltd, 2000.
[95] Ainsworth M, Oden J T. Posteriori Error Estimation in Finite Element Analysis. New York: Wiley-Interscience, 2000.
[96] Palani G S, Iyer N R, Dattaguru B, et al. New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems. Engineering Fracture Mechanics, 2006, 73(6): 802-819.
[97] Min J B, Bass J M, Spradley L W, et al. Adaptive finite element methods for two-dimensional problems in computational fracture mechanics. Computers & Structures, 1994, 50(3): 433-445.
[98] Koenke C, Harte R, Kratzig W B, et al. On adaptive remeshing techniques for crack simulation problems. Engineering Computations, 1998, 15: 74-88.
[99] Murthy K, Mukhopadhyay M. Unification of stress intensity factor (SIF) extraction methods with an h-adaptive finite element scheme. Communications in Numerical Methods in Engineering, 2001, 17(7): 509-520.
[100] Lim I L, Johnston I W, Choi S K, et al. Comparison between various displacement-based stress intensity factor computation techniques. International Journal of Fracture, 1992, 58: 193 - 120.
[101] Meshii T, Watanabe K. Stress intensity factor error index for finite element analysis with singular elements. Engineering Fracture Mechanics, 2002, 70(5): 657-669.
[102] Palani G S, Dattaguru B, Iyer N R, et al. Numerically integrated modified virtual crack closure integral technique for 2-D crack problems. Structural Engineering and Mechanics, 2004, 18(6): 731-744.
[103] Gallimard L, Panetier J. Error estimation of stress intensity factors for mixed-mode cracks. International Journal for Numerical Methods in Engineering, 2006, 68(3): 299-316.
[104] Stern M, Becker E B, Dunham R S, et al. A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture, 1976, 12(3): 359 - 368.
[105] Giner E, Fhenmayor F J, Tarancon J E, et al. An improvement of the EDI method in linear elastic fracture mechanics by means of a posteriori and an error estimator in G. International Journal for Numerical Methods in Engineering, 2004, 59(4): 533-558.
[106] Xuan Z C, Par N, Peraire J, et al. Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity. Computer Methods in Applied Mechanics and Engineering, 2006, 195(4-6): 430-443.
[107]Oden J T,Demkowiez L,Strouboulis T,et al.Adaptive methods for problems in solid and fluid mechanics.Accuracy estimates and adaptive refinements in finite element computations,Chichester,1986:249-280.
[108]Ogen G,Schiff B.Constrained finite elements for singular boundary value problems.Journal of Computational Physics,1983,51(1):65-82.
[109]Yosibash Z,Schiff B.A superelement for two-dimensional singular boundary value problems in linear elasticity.International Journal of Fracture,1993,62(4):325-340.
[110]Yosibash Z,Schiff B.Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities.Finite Elements in Analysis and Design,1997,26(4):315-335.
[111]Go C G,Lin C I,Lin Y S,et al.Formulation of a super-element for the dynamic problem of a cracked plate.Communications in Numerical Methods in Engineering,1998,14(12):1143-1154.
[112]Song C M.A super-element for crack analysis in the time domain.International Journal for Numerical Methods in Engineering,2004,61(8):1332-1357.
[113]Thatcher R W.Singularities in the solution of Laplace's equation in two dimensions.Journal of the Institute of Mathematics and Its AoDlications,1975,16:303-319.
[114]应隆安.计算应力强度因子的无限相似单元法.中国科学A辑,1977,(06):517-535.
[115]Houde H.The numerical solutions of interface problems by infinite element method.Numerische Mathematik,1982,39:39-50.
[116]应隆安.无限元方法.北京:北京大学出版社,1992.
[117]Ying L.Infinite Element Methods.Beijing/Braunschweig:Peking University Press/Vieweg Publishing,1995.
[118]李有堂.平面断裂问题的相似单元理论及其应用研究:博士.兰州:兰州大学,1997.
[119]Liu D S,Chiou D Y.A coupled IEM/FEM approach for solving elastic problems with multiple cracks.International Journal of Solids and Structures,2003,40(8):1973-1993.
[120]Panagiotopoulos P D.Fractal geometry in solids and structures.International Journal of Solids and Structures,1992,29(17):2159-2175.
[121]Panagiotopoulos P D,Panagouli O K,Mistakidis E S,et al.Fractal geometry and fractal material behavior in Solids and Structures.Archive of Applied Mechanics,1993,63(1):1-24.
[122]Leung A Y,Wong S C.Two-level finite element method for plane cracks.Communications in Applied Numerical Methods,1989,5(4):263-274.
[123]Leung A Y,Su R K.Mode I crack problems by fractal two level finite element methods.Engineering Fracture Mechanics,1994,48(6):847-856.
[124]Leung A Y,Su R K.Mixed-mode two-dimensional crack problem by fractal two level finite element method.Engineering Fracture Mechanics,1995,51(6):889-895.
[125]Leung A Y,Su R K.Body-force linear elastic stress intensity factor calculation using fractal two level finite element method.Engineering Fracture Mechanics,1995,51(6):879-888.
[126]Leung A Y,Su R K.Fractal two-level finite element method for 2-D cracks.Microcomputers in Civil Engineering,1996,11:249-257.
[127]Williams M L.Stress singularities resulting from various boundary conditions in angular comers of plates in extensions.Journal of Applied Mechanics,1957,24:109-114.
[128] Leung A Y, Su R K. Fractal two-level finite element method for free vibration of cracked beams. Journal of Shock and Vibration, 1998, 5(1): 61 - 68.
[129] Leung A Y, Su R K. Eigenfunction expansion for penny-shaped and circumferential cracks. International Journal of Fracture, 1998, 89(3): 205-222.
[130] Leung A Y, Su R K. Two-level finite element study of axisymmetric cracks. International Journal Of Fracture, 1998, 89(2).
[131] Leung A Y, Tsang K L. Mode III two-dimensional crack problem by two-level finite element method. International Journal Of Fracture, 2000,102(3): 345 - 358.
[132] Su R K, Leung A Y. Mixed mode cracks in Reissner plates. International Journal of Fracture, 2001, 107(3): 235-257.
[133] Su R K, Leung A Y. Three-dimensional mixed mode analysis of a cracked body by fractal finite element method. International Journal of Fracture, 2001,110(1): 1 - 20.
[134] Su R K, Sun H Y. Numerical solution of cracked thin plates subjected to bending, twisting and shear loads. International. International Journal Of Fracture, 2002, 117(4): 323 - 335.
[135] Tsang D K, Oyadiji S O, Leung A Y, et al. Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor. Engineering Fracture Mechanics, 2003, 70(15): 2199-2214.
[136] Su R K, Sun H Y. Numerical solutions of two-dimensional anisotropic crack problems. International Journal of Solids and Structures, 2003,40(18): 4615-4635.
[137] Xie J F, Sok S L, Leung A Y, et al. A parametric study on the fractal finite element method for two-dimensional crack problems. International Journal for Numerical Methods in Engineering, 2003, 58(4): 631-642.
[138] Su R K, Feng W J. Accurate determination of mode I and II leading coefficients of the Williams expansion by finite element analysis. Finite Elements in Analysis and Design, 2005, 41(11-12): 1175-1186.
[139] Tsang D K, Oyadiji S O, Leung A Y, et al. Two-dimensional fractal-like finite element method for thermoelastic crack analysis. International Journal of Solids and Structures, 2007,44(24): 7862-7876.
[140] Su R K, Fok S L. Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements. Engineering Fracture Mechanics, 2007, 74(10): 1649-1664.
[141] Reddy R M, Rao B N. Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method. Engineering Fracture Mechanics, 2008, 75(10): 2860-2906.
[142] Grigoriu M, Saif M, El-borgi S, et al. Mixed-mode fracture initiation and trajectory prediction under random stresses. International Journal Of Fracture, 1990,45: 19-34.
[143] Provan J W. Probabilistic fracture mechanics and reliability. Dordrecht: The Netherlands: Martinus Nijhoff Publishers, 1987.
[144] Besterfield G H, Lawrence M A, Belytschko T, et al. Brittle fracture reliability by probabilistic finite elements. ASCE Journal of Engineering Mechanics, 1990, 116: 642-659.
[145] Rahman S. Probabilistic fracture mechanics: J-estimation and finite element methods. Engineering Fracture Mechanics, 2001, 68(1): 107-125.
[146] Cruse T A. Numerical Evaluation of Elastic Stress Intensity Factors by the Boundary-Integral Equation Method. The surface Crack:Physical and Computational Solutions, New York, 1972:153-170.
[147] Snyder M D, Cruse T A. Boundary-integral equation analysis of cracked anisotropic plates. International Journal of Fracture, 1975, 11: 315-328.
[148] Ang W T. A boundary integral solution for the problem of multiple interacting cracks in an elastic material. International Journal Of Fracture, 1986, 31: 259-270.
[149] Ang W T, Clement D L. A boundary element method for determining the effect of holes on the stress distribution around a crack. International Journal for Numerical Methods in Engineering, 1986, 23(9): 1727-1737.
[150] Guimaraes S, Telles J C. On the numerical Green's function technique for cracks in Reissner's plates. Computer Methods in Applied Mechanics and Engineering, 2007, 196(21-24): 2478-2485.
[151] Mavrothanasis F I, Pavlou D G. Green's function for KI determination of axisymmetric elastic solids containing external circular crack. Engineering Fracture Mechanics, 2008, 75(8): 1891-1905.
[152] Blandford G E, Ingraffea A R, Liggett J A, et al. Two-dimensional stress intensity factor computations using the boundary elementmethod. International Journal for Numerical Methods in Engineering, 1981, 17: 387-404.
[153] Jia Z H, Shippy D J, Rizzo F J, et al. On the computation of two-dimensional stress intensity factors using the boundary element method. International Journal for Numerical Methods in Engineering, 1988, 26(12): 2739-2753.
[154] Polyzos D, Stamos A A, Beskos D E, et al. BEM computation of DSIF in cracked viscoelastic plates. Communications in Numerical Methods in Engineering, 1994, 10(1): 81-87.
[155] Ganguly S, Layton J B, Balakrishna C, et al. Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity. International Journal for Numerical Methods in Engineering, 2000, 48(5): 633-654.
[156] Martinez J, Dominguez J. On the use of quarter-point boundary elements for stress intensity factor computations. International Journal for Numerical Methods in Engineering, 1984, 20(10): 1941-1950.
[157] Green A E, Zerna W. Theoretical Elasticity. Oxford: Oxford(Clarendon), 1954.
[158] Portela A, Aliabadi M H, Rooke D P, et al. The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering, 1992, 33(6): 1269-1287.
[159] ASaez, Gallego R, Dominguez J, et al. Hypersingular quarter-point boundary elements for crack problems. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1681-1701.
[160] Chen W H, Chen T C. An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1739-1756.
[161] Sollero P, Aliabadi M H. Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Composite Structures, 1995, 31(3): 229-233.
[162] Matos P F, Moreira P M, Portela A, et al. Dual boundary element analysis of cracked plates: post-processing implementation of the singularity subtraction technique. Computers & Structures, 2004, 82(17-19): 1443-1449.
[163] Chau K T, Wang Y B. A new boundary integral formulation for plane elastic bodies containing cracks and holes. International Journal of Solids and Structures, 1999, 36(14): 2041-2074.
[164] Crouch S L. Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution. International Journal for Numerical Methods in Engineering, 1976, 10(2): 301-343.
[165] Crawford A M, Curran J H. Higher-order functional variation displacement discontinuity elements. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1982, 19(3): 143-148.
[166] Shou K J, Crouch S L. A higher order displacement discontinuity method for analysis of crack problems. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1995, 32(1): 49-55.
[167] Aliabadi M H. Boundary element formulations in fracture mechanics. Applied Mechanics Review, 1997,.
[168] Yan X Q. Stress intensity factors for interacting cracks and complex crack configurations in linear elastic media. Engineering Failure Analysis, 2007, 14(1): 179-195.
[169] Nisitani H. Solutions of notch problems by body force method. Stress analysis of notch problem, Alphen aan den Rijn,Netherlands, 1978:.
[170] Wolf J P, Song C M. Finite-Element Modelling of Unbounded Media. New York: Wiley, 1996.
[171] Song C M, Wolf J P. The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for unbounded media. Dynamic soil-structure interaction, current research in China and Swizerland, Beijiing, 1997:71-94.
[172] Song C M, Wolf J P. The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 1997, 147(3-4).
[173] Song C M, Wolf J P. Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method. Computers & Structures, 2002, 80(2): 183-197.
[174] Song C M. A matrix function solution for the scaled boundary finite-element equation in statics. Computer Methods in Applied Mechanics and Engineering, 2004, 193(23-26): 2325-2356.
[175] Song C M. Weighted block-orthogonal base functions for static analysis of unbounded domains. Proceedings of the 6th World Congress on Computational Mechanics, Beijing,China, 2004:615-620.
[176] Song C M. Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material corners. Engineering Fracture Mechanics, 2005, 72(10): 1498-1530.
[177] Chidgzey S R, Deeks A J. Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method. Engineering Fracture Mechanics, 2005, 72(13): 2019-2036.
[178] Song C M. Analysis of singular stress fields at multi-material corners under thermal loading. International Journal for Numerical Methods in Engineering, 2006,65(5): 620-652.
[179] Yang Z J, Deeks A J, Hao H, et al. Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach. Engineering Fracture Mechanics, 2007, 74(5): 669-687.
[180] Song C M, Vrcelj Z. Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-element method. Engineering Fracture Mechanics, 2008, 75(8): 1960-1980.
[181] Rao B N, Rahman S. A coupled meshless-finite element method for fracture analysis of cracks. International Journal of Pressure Vessels and Piping, 2001, 78(9): 647-657.
[182] Bao W Z, Han H, Huang Z Y, et al. Numerical simulations of fracture problems by coupling the FEM and the direct method of lines. Computer Methods in Applied Mechanics and Engineering, 2001, 190(37-38): 4831-4846.
[183]Aour B,Rahmani O,Nait-abdelaziz M,et al.A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics.International Journal of Solids and Structures,2007,44(7-8):2523-2539.
[184]Chidgzey S R,Trevelyan J,Deeks A J,et al.Coupling of the boundary element method and the scaled boundary finite element method for computations in fracture mechanics.Computers & Structures,2008,86(11-12):1198-1203.
[185]樊成.有县覆盖Kriging插值无网格法及其在岩体断裂中的应用研究:博士.大连:大连理工大学.2007.
[186]Mohammadi S.Extended finite element method for fracture analysis of structures.2008.
[187]Luco J E.Linear soil-structure interaction:a review.In Earthquake Ground Motion and its Effects on Structures,AMD,Datta SK(ed.),New Youk,1982:41-57.
[188]Kausel E.Local transmitting boundaries.Journal of Engineering Mechanics(ASCE),1988,114:1011-1027.
[189]Givoli D.Non-reflecting boundary conditions.Journal of Computational Physics,1991,94(1):1-29.
[190]Tsynkov S V.Numerical solution of problems on unbounded domains.A review.Applied Numerical Mathematics,1998,27(4):465-532.
[191]Astley R J.Infinite elements for wave problems:a review of current formulations and an assessment of accuracy.International Journal for Numerical Methods in Engineering,2000,49(7):951-976.
[192]Givoli D.High-order local non-reflecting boundary conditions:a review.Wave Motion,2004,39(4):319-326.
[193]Mohammad H B,A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry.International Journal for Numerical Methods in Engineering,2008,74(2):209-237.
[194]Chongmin S M.A boundary condition in Parle series for frequency-domain solution of wave propagation in unbounded domains.International Journal for Numerical Methods in Engineering,2007,69(11):2330-2358.
[195]WolfJ P.Dynamic Soil-Structure Interaction[M].Prentice-Hall:Englewood Cliffs,N J,1985.
[196]Wolf J P.Soil-Structure-Interaction Analysis in Time Domain[M].Prentice-Hall:Englewood Cliffs,NJ,1988.
[197]Hall W S,Oliveto G.Boundary Element Methods for Soil-Structure Interaction[M].Kluwer Academic Publishers:Dordrecht,2003.
[198]Givoli D.Numerical Methods for Problem in Infinite Domains[M].Elsevier:Amsterdam,1992.
[199]Lysmer J,Kuhlemeyer R L.Finite dynamic model for infinite media.Journal of Engineering the Mechanics Division,ASCE,1969,95(EM4):859-877.
[200]White W,Valliappan S,Lee I K,et al.Unified boundary for finite dynamic models.Journal of Engineering the Mechanics Division,ASCE,1977,103(EM5):949-964.
[201]T A.Compatible viscous boundary for discrete models.Journal of Engineering the Mechanics Division,ASCE,1978,104(EM5):1253-1266.
[202]Deeks A J,Randolph M F.Axisymmetric time-domain transmitting boundaries.Journal of Engineering Mechanics,ASCE,1994,120(1):25-42.
[203]Liu J B,Lu Y D.A direct method for analysis of dynamic soil-structure interaction based on interface idea.Dynamic Soil-Structure Interaction,current research in China and Swizerland,Beijing,1997:258-273.
[204]Smith W D.A nonreflecting plane boundary for wave propagation probems.Journal of Computational Physics,1974,15(4):492-503.
[205]Smith W D.The application of finite element analysis to body wave propagation problems.Geophysical Journal of the Royal Astronomical Society,1975,42(2):747-768.
[206]Cundall P A,Kunar R R,Carpenter P C,et al.Solution of infinite dynamic problems by finite modelling in the time domain.Proceedings of the 2nd international conference on applied numerical modelling,London,1979:339-351.
[207]Lindman E L.Free-Space boundary conditions for the time dependent wave equation.Journal of Computaional Physics,1975,18(1):66-78.
[208]Engquist B,Majda A.Absorbing boundary conditions for the numerical simulation of waves.Mathematics of Computation,1977,31(139):629-651.
[209]Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[210]廖振鹏,黄孔亮,杨柏坡,等.暂态波透射边界.中国科学A辑.1984,4(6):556-564.
[211]Liao Z P,Wong H L.A transmitting boundary for the numerical simulation of elastic wave propagation.Soil Dynamics and Earthquake Engineering,1984,3(4):174-183.
[212]胡志强.考虑坝一地基动力相互作用的有横缝拱坝地震响应分析:大连:大连理工大学,2003.
[213]Chen H Q.Application of transmitting boundaries to nonllinear dynamic analysis of arch dam-foundation-reservoir system.Dynamic soil-structure interaction,current research in China and Swizerland,Beijing,1997:115-124.
[214]Keys R G.Absorbing boundary conditions for acoustic media.Geophysics,1985,50(6).
[215]Higdon R L.Absorbing boundary conditions for acoustic and elastic waves in stratified media.Journal of Computational Physics,1992,101(2):386-418.
[216]Higdon R L.Absorbing boundary conditions difference approximations to the multi-dimensional wave equation.Mathematics of Computation,1986,47(176):437-459.
[217]Wolf J P,Song C.Doubly asymptotic multi-directional transmitting boundary for dynamic unbounded medium-structure-interaction analysis.Earthquake Engineering & Structural Dynamics,1995,24(2):175-188.
[218]Geers T L.Doubly asymptotic approximation for transient motions or submerged structures.Journal of the Acoustical Society of America,1978,64(5).
[219]Nicolas-vullierme B.A contribution to doubly asymptotic approximation:an operator top-down approach.Journal of Vibration and Acoustics,ASME,1991,I 13(3):409-515.
[220]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析.地震工程与工程振动.1996,(03).
[221]Ungless R F.An Infinite Element(Master Thesis):Master.Columbia:University of British Columbia,1973.
[222]Bettess P,Zienkiewicz O C.Diffraction and reflection of surface waves using finite and infinite elements.International Journal for Numerical Methods in Engineering,1977,11(8):1271-1290.
[223]Zienkiewicz O C,Bando K,Bettess P,et al.International Journal for Numerical Methods in Engineering,1985,21.(7).
[224]Zhang C H,Song C M.Boundary element technique in infinite and semi-infinite plane domain. Proceedings of the International Conference on Boundary element,Beijing,1986:.
[225]Zhang C H,Song C M,Wang G L,et al.3-D infinite boundary elements and simulation of monolithic dam foundations.Communications in Applied Numerical Methods,1989,5:389-400.
[226]Zhang C H,Song C M,Pekau O A,et al.Infinite boundary element for dynamic problems of 3-D half space.International Journal for Numerical Methods in Engineering,1991,31(3):447-462.
[227]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基.清华大学学报,1986,26(3):51-63.
[228]赵崇斌,张楚汉,张光斗.映射动力无穷元及其特性研究.地震工程与工程振动,1987,7(3):1-15.
[229]Zhang C H,Zhao C B.Coupling method of finite and infinite elements for strip foundation wave problems.Earthquake Engineering & Structural Dynamics,1987,15(7):839-851.
[230]Zhang C H,Zhao C B.Effects of canyon topography and geological conditions on strong ground motion,Earthquake Engineering & Structural Dynamics,1988,16(1):81-97.
[231]Astley R J.Wave envelope and infinite elements for acoustical radiation.International Journal for Numerical Methods in Fluids,1983,3(5):507-526.
[232]Burnett D S.A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion.Journal of the Acoustical Society of America,1994,96(5):2798-2816.
[233]Medina F,Penzien J.Infinite element for elstodynamics.Earthquake Engineering & Structureal Dynamics,t982,10(5):699-709.
[234]Khalili N,Valliappan S,Yazdi J T,et al.1D infinite element for dynamic problems in saturated porous media.Communications in Numerical Methods in Engineering,1997,13(9):727-738.
[235]Khalili N,Yazdi J T,Valliappan S,et al.Wave propagation analysis of two-phase saturated porous media using coupled finite-infinite element method.Soil Dynamics and Earthquake Engineering,1999,18(8):533-553.
[236]Kim D K,Yun C B.Time-domain soil-structure interaction analysis in two-dimensional medium based on analytical frequncy-dependent infinite elements.International Journal for Numerical Methods in Engineering,2000,47(7):124 l-1261.
[237]Yerli H T,Temel B,Kiral E,et al.Transient infinite elements for 2D soil-structure interaction analysis.Journal of Geotechnical and Geoenvironmental Engineering,1998,124(10):976-988.
[238]Yerli H T,Temel B,Kiral E,et al.Multi-wave transient and harmonic infinite elements for two-dimensional unbounded domain problems.Computers and Geotechnics,1999,24(3):185-206.
[239]Gerdes K.The conjugated vs.the unconjugated infinite element method for the helmhottz equation in exterior domains.Computer Methods in Applied Mechanics and Engineering,1998,152(1-2):125-145.
[240]Shirron J J,Babuska I.A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems.Computer Methods in Applied Mechanics and Engineering,1998,164(1-2):121-139.
[241]Astley R J.Infinite elements for wave problems:a review of current formulations and an assessment of accuracy.International Journal for Numerical Methods in Engineering,2000,49(7):951-976.
[242]Astley R J.Conditioning of infinite element schemes for wave problems.Communications in Numerical Methods in Engineering,2001,17(1):31-41.
[243]Gerdes K.A review of infinite element methods for exterior Helmholtz problems.Journal of Computational Acoustics,2000,8(1):43-62.
[244]水利部国际合作与科技司编著.当代水利科技前沿.北京:中国水利水电出版社,2005.
[245]Wolf J P.Approximate dynamic model of embedded foundation in time domain.Earthquake Engineering & Structural Dynamics,1986,14(5):683-703.
[246]Jean W Y,Ling T W,Penzien J,et al.System parameters of soil foundations for time domain dynamic analysis.Earthquake Engineering & Structural Dynamics,1990,19(4):541-553.
[247]Barros D,F C P...Luco J E,et al.Discrete model for vertical vibrations of surface and embedded foundation.Earthquake Engineering & Structural Dynamics,1990,19:289-303.
[248]栾茂田,林皋.地基动力阻抗的双自由度集总参数模型.大连理工大学学报,1996,(04).
[249]王复明.层状地基分析的样条半解析法及其应用:大连:大连理工大学,1987.
[250]Wang H B.Dynamic soil-structure interaction by combing FEM with trial fimction method and application to underground structure:Janpan:Okayama University,1994.
[251]Song C,Wolf J P.Dynamic stiffness of unbounded medium based on damping-solvent extraction.Earthquake Engineering & Structural Dynamics,1994,23(2):169-181.
[252]Basu U,Chopra A K.Numerical Evaluation of the Damping-Solvent Extraction Method in the Frequency Domain.Earthquake Engineering & Structural Dynamics,2002,31:1231-1250.
[253]李建波,陈健云,林皋.求解非均匀无限地基相互作用力的有限元时域阻尼抽取法.岩土工程学报,2004,26(3):263-267.
[254]李建波.结构一地基动力相互作用的时域数值分析方法研究:博士.大连:大连理工大学,2005.
[255]钟红,林皋,李建波.空间结构-地基动力相互作用数值分析时域算法研究.大连理工大学学报,2007,47(1):78-84.
[256]Zhong H,Lin G,Li J B,et al.An effecient time-domain damping solvent extraction algorithm and its application to arch darn-foundation interaction analysis.Communications in numerical methods in engineering,2007,in press.
[257]Abascal B,Domin.guez J.Vibrations of footings on zoned viscoelastic soils.Journal of Engineering Mechanics,1986,112(5)::433-447.
[258]Spyrakos C C,Beskos D E.Dynamic response of rigid strip foundations by time domain boundary element method.International Journal for Numerical Methods in Engineering,1986,23(8):1547-1565.
[259]Karabalis D L,Beskos D E.Dynamic response of 3-D rigid surface foundations by time domain boundary element method.Earthquake Engineering & Structural Dynamics,1984,12(1):73-93.
[260]Toki K,Sato T.Seismic response analyses of ground with irregular profiles by the boundary finite element method.Boundary elements,Berlin,1983:699-708.
[261]Tai G R,Shaw R P.Helmholtz equation eigenvalues and eigenmodes for arbitrary domains.Journal of the Acoustical Society of America,1974,56(3):796-804.
[262]Sanchez-sesma F J,Esquivel J A.Ground motion on alluvial valleys under incident plane SH waves.Bulletin of the Seismological Society of America,1979,69(4):1107-1120.
[263]Mossessian T K,Dravinski M.Scattering of elastic waves by three-dimensional surface topographies.Wave Motion,1989,11(6):579-592.
[264]Mossessian T K,Dravinski M.Amplification of elastic waves by a three dimensional valley,Part Ⅰ. Steady state response.Earthquake Engineering & Structural Dynamics,1990,19(5):667-680.
[265]Antes H,Trondle G.Analysis of stress waves by indirect BEM.Boundary Elements in Mechanical and Electrical Engineering,New York,1990:179-191.
[266]Beskos D E.Boundary element method in dynamic analysis.Applied Mechanics Reviews,1987,40(1):1-23.
[267]Beskos D E.Boundary element method in dynamic analysis:part Ⅱ(1986-1996).Applied Mechanics Reviews,1997,50(3):149-197.
[268]Nardini D,Brebbia C A.A new approach to free vibration analysis using boundary elements.Boundary Element Methods in Engineering,Berlin,1982:312-326.
[269]宋崇民,张楚汉.水坝抗震分析的动力边界元方法.地震工程与工程振动,1988,8(4):13-26.
[270]Loeffler C F,Mansur W J.Analysis of time integration schemes for boundary element applications to transient wave propagation problems.Boundary Element Techniques:Applicaiton in Stress Analysis and Heat Transfer,Southampton,1987:.
[271]陈虬,许廷兴.无限边界元动态分析的一种新列式.解析与数值结合法的理论及其工程应用,长沙,1989:279-284.
[272]Maier G,Diligenti M,Carini A,et al.Variational approach to boundary element elastodynamic analysis and extension to muttidomain problems.Computer Methods in Applied Mechanics and Engineering,1991,92(2):193-213.
[273]Sirtori S,Maier G,Novati G,et al.A Galerkin symmetric boundary-element method in elasticity:formulation and implementation.International Journal for Numerical Methods in Engineering,1992,35(2):255-282.
[274]Perez-gavilan J J,Aliabadi M H.A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems.Computer & Structures,2001,79(29-30):2621-2633.
[275]Frangi A,Maier G.Dynamic elastic-plastic analysis by a symmetric Galerkin boundary element method with time-independent kernels.Computer Methods In Applied Mechanics And Engineering,1999,171(3-4):281-308.
[276]Perez-gavilan J J,Aliabadi M H.A Galerkin boundary element formation with dual reciprocity for elastodynamics.International Journal for Numerical Methods in Engineering,2000,48(9):1331-1344.
[277]Bonnet M,Maier G,Polizzotto C,et al.Symmetric Galerkin boundary element methods.Applied Mechanics reviews,1998,51(11):669-704.
[278]冯康.论微分与积分方程以及有限与无限元.计算数学,1980,2(1):100-105.
[279]余德浩.自然边界元方法的数学理论.北京:科学出版社,1993.
[280]Spyrakos C C,Beskos D E.Dynamic response of flexible strip foundations by boundary and finite element methods.Soil Dynamics And Earthquake Engineering,1986,5(2):84-96.
[281]Touhei T,Ohmachi T.FE-BE method for dynamic analysis of dam-foundation-reservoir systems in the time domain.Earthquake Engineering & Structural Dynamics,1993,22(3):195-209.
[282]Underwood P,Geers T L.Doubly asymptotic,boundary-element analysis of dynamic soil-structure interaction.International Journal Of Solids And Structures,1981,17(7):687-697.
[283]Kobayashi S,Nishimura N,Mori K,et al.Applications of boundary element-finite element combined method to three-dimensional viscoelastodynamic problems.Boundary Elements,Oxford,1986:.
[284]杜其奎.波动方程的自然边界元与有限元耦合法.淮北煤师院学报,1999,20(2):1-10.
[285]贾祖朋,邬吉明,余德浩.三维Helmholtz方程外问题的自然边界元与有限元耦合法.计算数学,2001,23(3):357-368.
[286]Manolis G D.A comparative study on three boundary element method approaches to problems in elastodynamics.International Journal for Numerical Methods in Engineering,1983,19(1):73-91.
[287]Spyrakos C C,Antes H.Time domain boundary element method approaches in elastodynamics:A comparative study.Computers & Structures,1986,24(4):529-535.
[288]Gaul L,Schanz M.A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains.Computer Methods In Applied Mechanics And Engineering,1999,179(1-2):I 11-123.
[289]Kagawa Y,Yamabuchi T,Araki Y,et al.The infinite boundary element and its application to the unbounded Helmholtz problem.COMPEL-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering,1985,4(1):29-41o
[290]Zhang C H,Song C M,Pekau O A,et al.Infinite boundary elements for dynamic problems of 3-D half space.International Journal for Numerical Methods in Engineering,1991,31(3):447-462.
[291]Zhang C H,Pekau O A,Jin F,et al.Application of FE-BE-IBE coupling to dynamic interaction between alluvial soil and rock canyons.Earthquake Engineering & Structural Dynamics,1992,21(5):367-385.
[292]Wang C Y,Achenbach J D.Three-dimensional time-harmonic elastodynamic Green's functions for anisotropic solids.Proceedings of the Royal Society of London Series A-Mathematical & Physical Sciences,1995,449(1937):441-458.
[293]Wang C,Achenbach J D.Lamb's problem for solids of general anisotropy.Wave motion,1996,24(3):227-242.
[294]Wang C,Achenbach J D,Hirose S,et al.Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy.International Journal Of Solids And Structures,1996,33(26):3843-3864.
[295]Albuquerque E L,Sollero P,Aliabadi M H,et al.The boundary,element applied to time dependent problems in anisotropic materials.International Journal Of Solids And Structures,2002,39(5):1405-1422.
[296]Florez W F,Power H.DRM multidomain mass conservative interpolation approach for the BEM solution of the two-dimensional Navier-Stokes equations.Computers & Mathematics With Applications,2002,43(3-5):457-472.
[297]稽醒,臧跃龙,程玉民.边界元法进展及通用程序.上海:同济大学出版社,1997.
[298]Gao X,Davies T G.Boundary element programming in mechanics.Cambridge:Cambridge University Press,2002.
[299]Dasgupta G.A Finite Element Formulation for Unbounded Homogeneous Continua.Journal of Applied Mechanics-Transactions of the ASME,1982,49(1):136-140.
[300]Wolf J P,Weber B.On calculation the dynamic-stiffness matrix of the unbounded soil by cloning.International Symposium on Numerical Models in Geomechanics,Rotterdam,1982:486-494.
[301]John P W.Dynamic-stiffness matrix of unbounded soil by finite-element multi-cell cloning.Earthquake Engineering & Structural Dynamics,1994,23(3):233-250.
[302]Chongrnin S J.Unit-impulse response matrix of unbounded medium by finite-element based forecasting.International Journal for Numerical Methods in Engineering,1995,38(7):1073-1086.
[303]郭仲衡.相似等参单元.科学通报,1979,24(13):577-582.
[304]Zhang X,Wegner J L.Three-dimensional dynamic soil-structure interaction analysis in the time domain.Earthquake Engineering & Structural Dynamics,1999,28(12):1501-1524.
[305]Wegner J L,Zhang X,Free-vibration analysis of a three-dimensional soil-structure system.Earthquake Engineering & Structural Dynamics,2001,30(1):43-57.
[306]Ekevid T,Wiberg N.Wave propagation related to high-speed train:A scaled boundary FE-approach for unbounded domains.Computer Methods in Applied Mechanics and Engineering,2002,191(36):3947-3964.
[307]阎俊义.结构一地基相互作用的FE-SBFE时域耦合方法及其工程应用:博士.北京:清华大学,2004.
[308]杜建国.基于SBFEM的大坝-库水-地基动力相互作用分析:博士.大连:大连理工大学,2007.
[309]Lin G,Du J G,Hu Z Q,et al.Foundation Inhomogeneity on the Seismic Response.Proc.8th United States National Conference on Earthquake Engineering.2006:.
[310]Lin G,Du J G,Hu Z Q,et al.Earthquake Analyslncluding the Effects of Foundation Inhomogeneity.Frontiers of Architecture and Civil Engineering in China.2007:41-50.
[311]Bazyar M H,Song C.Transient analysis of wave propagation in non-homogeneous elastic unbounded domains by using the scaled boundary finite-element method[J].Earthquake Engineering and Structural Dynamics,2006,35:1787-1806.
[312]Deeks A J,Wolf J P.Semi-analytical elastostatic analysis of unbounded two-dimensional domains.International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(11):1031-1057.
[313]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading.International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(10):813-835.
[314]Doherty J P,Deeks A J.Semi-analytical far field model for three-dimensional finite-element analysis.International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(11):1121-1140.
[315]Song C,Wolf J P.The scaled boundary finite-element method:analytical solution in frequency domain.Computer Methods in Applied Mechanics and Engineering,1998,I64(I-2):249-264.
[316]Song C M,Wolf J P.Body loads in scaled boundary finite-element method.Computer Methods in Applied Mechanics and Engineering,1999,180(1-2):117-135.
[317]Wolf J P,Song C M.The scaled boundary finite-element method-a primer:derivations.Computers & Structures,2000,78(1-3):t91-210.
[318]Song C M,Wolf J P.The scaled boundary finite-element method-a primer:solution procedures.Computers & Structures,2000,78(1-3):211-225.
[319]Deeks A J,Wolf J P.A virtual work derivation of the scaled boundary finite-element method for elastostatics.Computational Mechanics,2002,28(6):489-504.
[320]Deeks A J,Wolf J P.Stress recovery and error estimation for the scaled boundary finite-element method.International Journal for Numerical Methods in Engineering,2002,54(4):557-583.
[321]Deeks A J,Wolf J P.An h-hierarchical adaptive procedure for the scaled boundary finite-element method.International Journal for Numerical Methods in Engineering,2002,54(4):585-605.
[322]Wolf J P.The scaled boundary finite element method[M].Chichester:John Wiley and Sons,2002.
[323]Song C M.Dynamic analysis of unbounded domains by a reduced set of base functions.Computer Methods in Applied Mechanics and Engineering,2006,195(33-36):4075-4094.
[324]杜建国,林皋.基于SBFEM的结构-地基动力相互作用时域算法的改进.水利学报,2007,38(1):8-14.
[325]Song C,Bazyar M H.A boundary condition in Pad6 series for frequency-domain solution of wave propagation in unbounded domains[J].International Journal for Numerical Methods in Engineering,2007,69:2330-2358.
[326]Bazyar M H,Song C.A continued-fraction based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry[J].International Journal for Numerical Methods in Engineering,2008,74(2):209-237.
[327]Vu T H,Decks A J.Use of higher-order shape functions in the scaled boundary finite element method.International Journal for Numerical Methods in Engineering,2006,65(10):1714-1733.
[328]Song C M,Bazyar M H.Development of a fundamental-solution-less boundary element method for exterior wave problems.Communications in Numerical Methods in Engineering,2008,24(4):257-279.
[329]Decks A J,Cheng L.Potential flow around obstacles using the scaled boundary finite-element method.International Journal for Numerical Methods in Fluids,2003,41(7):721-741.
[330]Rajan V S P,Raju K C J.Reformulation of the novel scaled boundary finite element method for electromagnetics.Proceedings of the 6th World Congress on Computational Methanics,Beijing,China,2004:.
[331]Fan S C,Li S M,Yu G Y,et al.Dynamic Fluid-Structure Interaction Analysis Using Boundary Finite Element Method-Finite Element Method.Journal of Applied Mechanics,2005,72(4).
[332]Lehmann L.Application of a coupled finite element/scaled boundary finite element procedure to acoustics.Proceedings of Coupled Problems[C],ECCOMAS,Santorini,Greece,2005:.
[333]滕斌,赵明,何广华.三维势流场的比例边界有限元求解方法.计算力学学报,2006,(03).
[334]Li B N,Cheng L,Decks A J,et al.A modified scaled boundary finite-element method for problems with parallel side-faces.Part I.Theoretical developments.Applied Ocean Research,2005,27(4-5):216-223.
[335]Li B N,Cheng L,Decks A J,et al.A modified scaled boundary finite-element method for problems with parallel side-faces.Part II.Application and evaluation.Applied Ocean Research,2005,27(4-5):224-234.
[336]Li B N,Cheng L,Decks A J,et al.A semi-analytical solution method for two-dimensional Helmholtz equation.Applied Ocean Research,2006,28(3):193-207.
[337]何广华,滕斌,李博宁.应用比例边界有限元法研究波浪与带狭缝三箱作用的共振现象.水动力学研究与进展(A辑),2006,(03).
[338]滕斌,何广华,李博宁.应用比例边界有限元法求解狭缝对双箱水动力的影响.海洋工程,2006,(02).
[339]Lin G,Du J G,Hu Z Q,et al.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption.Science in China Series E,2007,50(1).
[340]Irwin G R.Fracture Testing of High-Strength Sheet Materials Under Conditions Appropriate for Stress Analysis.In structural Mechanics:Proceedings of 1st Symposium on Naval Structural Mechanics, New York, 1960:557-591.
[341] Anderson T L. Fracture mechanics:fundamentals and applications. Boca Raton: CRC Press, 1991.
[342] Nash G L, Hilton P D. Stress intensity factors by enriched finite elements. Engineering Fracture Mechanics, 1978, 10(3): 485-496.
[343] Chen W H, Chang C S. Analysis of two dimensional fracture problems with multiple cracks under mixed boundary conditions. Engineering Fracture Mechanics, 1989, 34(4): 921-934.
[344] Chen W H, Chang C S. Analysis of two-dimensional mixed-mode crack problems by finite element alternating method. Computers & Structures, 1989, 33(6): 1451-1458.
[345] Lam K Y, Phua S P. Multiple crack interaction and its effect on stress intensity factor. Engineering Fracture Mechanics, 1991, 40(3): 585-592.
[346] Shu H M, Petit J, Bezine G, et al. Stress intensity factors for several groups of equal and parallel cracks in finite plates. Engineering Fracture Mechanics, 1994, 49(6): 933-941.
[347] Chen Y Z. Multiple crack problems for torsion thin-walled cylinder. International Journal of Pressure Vessels and Piping, 1999, 76(1): 49-53.
[348] Chen Y Z. Numerical solution for multiple crack problems of torsion bar. Computer Methods in Applied Mechanics and Engineering, 1999, 174(1-2): 203-209.
[349] Ventura D D, Smith R N. Some applications of singular fields in the solution of crack problems. International Journal for Numerical Methods in Engineering, 1998,42(5): 927-942. [350] Hwang C G, Wawrzynek P A, Ingraffea A R, et al. On the calculation of derivatives of stress intensity factors for multiple cracks. Engineering Fracture Mechanics, 2005, 72(8): 1171-1196. [351] Fotuhi A R, Faal R T, Fariborz S J, et al. In-plane analysis of a cracked orthotropic half-plane. International Journal of Solids and Structures, 2007, 44(5): 1608-1627.
[352] Marc A M, Krishan K C. Mechanical Behavior of Materials. New Jersy: Prentice-Hall, Inc, 1999.
[353] Menclk J. Strength and Fracture of Glass and Ceramics. New York: Elsevier Science, 1992.
[354] Wang R D. The stress intensity factors of a rectangular plate with collinear cracks under uniaxial tension. Engineering Fracture Mechanics, 1997, 56(3): 347-356.
[355] Tan C L, Lgao Y. Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks. Composite Structure, 1992, 20: 17-28.
[356] 涂传林. 裂缝面上受外荷载作用下的边界配置法及其应用.水利学报, 1983,7:9-16.
[357] Fett T, Munz D. Stress Intensity Factors and Weight Functions. Southampton: Computational Mechanics Publications, 1997.
[358] 丁遂栋. 断裂力学. 北京: 机械工业出版社, 1997.
[359] Yuuki R, Cho S B. Efficient boundary element analysis of stress intensity factors for interface cracks in dissimilar materials. Engineering Fracture Mechanics, 1989, 34: 179-188.
[360] Miyazaki N, Ikeda T, Soda T, et al. Stress intensity factor analysis of interface crack using boundary element method application of contour integral method. Engineering Fracture Mechanics, 1993, 45: 599-610.
[361] Zhang Z, Yao Z H, Du Q H, et al. Boundary element method for determining stress intensity factors of bimaterial interface crack. Theory and applications of boundary element methods. Proceedings of the Sixth China-Japan Symposium on BEM, Shanghai, 1994:315-320.
[362] Chen Y M. Numerical solutions of three dimensional dynamic crack problems and simulation of dynamic fracture phenomena by a "non-standard" finite difference method. Engineering Fracture Mechanics, 1978, 10(4): 699-708.
[363] Aoki S, Kishimoto K, Kondo H, et al. Elastodynamic analysis of crack by finite element method using singular element. 1978, 14(1): 59-67.
[364] Kishimoto K, Aoki S, Sakata M, et al. Dynamic stress intensity factors using J-integral and finite element method. Engineering Fracture Mechanics, 1980,13(2): 387-394.
[365] Murti V, Valliappan S. The use of quarter point element in dynamic crack analysis. Engineering Fracture Mechanics, 1986, 23(3): 585-614.
[366] Enderlein M, Ricoeur A, Kuna M, et al. Comparison of finite element techniques for 2D and 3D crack analysis under impact loading. International Journal of Solids and Structures, 2003, 40(13-14): 3425-3437.
[367] Rethore J, Gravouil A, Combescure A, et al. A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing. Computer Methods in Applied Mechanics and Engineering, 2004,193(42-44): 4493-4510.
[368] Song S H, Paulino G H. Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. International Journal of Solids and Structures, 2006,43(16): 4830-4866.
[369] Aliabadi M H. Dynamic Fracture Mechanics. Southampton, UK and Boston, USA.: Computational Mechanics Publications, 1995.
[370] Marrero M, Dominguez J. Time-domain BEM for three-dimensional fracture mechanics. Engineering Fracture Mechanics, 2004, 71(11): 1557-1575.
[371] Chirino F, Gallego R, Saez A, et al. A comparative study of three boundary element approaches to transient dynamic crack problems. Engineering Analysis with Boundary Elements, 1994, 13(1): 11-19.
[372] Dominguez J, Gallego R. Time domain boundary element method for dynamic stress intensity factor computations. International Journal For Numerical Methods In Engineering, 1992, 33(3): 635-647.
[373] Ariza M P, Dominguez J. General BE approach for three-dimensional dynamic fracture analysis. Engineering Analysis with Boundary Elements, 2002,26(8): 639-651.
[374] Fedelinski P, Aliabadi M H, Rooke D P, et al. The laplace transform DBEM for mixed-mode dynamic crack analysis. Computers & Structures, 1996, 59(6): 1021-1031.
[375] Fedelinski P. Boundary element method in dynamic analysis of structures with cracks. Engineering Analysis with Boundary Elements, 2004, 28(9): 1135-1147.
[376] Albuquerque E L, Sollero P, Aliabadi M H, et al. The boundary element method applied to time dependent problems in anisotropic materials. International Journal of Solids and Structures, 2002, 39(5): 1405-1422.
[377] Albuquerque E L. Sollero P, Fedelinski P, et al. Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems. Computers & Structures, 2003, 81(17): 1703-1713.
[378] Williams M L. The stress around a fault or crack in dissimilar media. Bulletin of the Seismological Society, 1959,49: 199-204.
[379] Sih C G, Paris P C, Irwin G R, et al. On cracks in rectilinearly anisotropic bodies. International Journal of Fracture, 1965, 3: 189 - 203.
[380]Zhu H,Tian T Y F Q.Composite materials dynamic fracture studies by generalized Shmuely difference.Engineering Fracture Mechanics,1996,54:869-877.
[381]Kobayashi A,Cherepy R D,Kinsel W,et al.T-elements:state of the art and future trends[J].Journal of Basic Engineering,Transactions of the ASME,Series D,1964,86:681-684.
[382]林皋,杜建国.基于SBFEM的坝一库水相互作用分析.大连理工大学学报,2005,45(5):723-729.
[383]Hall J F.An FFT algorithm for structural dynamics.Earthquake Engineering and Structural Dynamics,1982,10:797-811.
[2]凡耐理M,李进平,刘忠清.高拱坝对基础裂缝的敏感性研究.水利水电快报.1999,20(21):12-16.
[3]李瓒.石门拱坝的坝踵裂缝.水利学报.1999,11:61-65.
[4]Kaplan M F.Crack propagation and the fracture of concrete.ACI Journal,1961,58:591-610.
[5]潘家铮.重力坝设计.北京:水利水电出版社,1987.
[6]徐世娘.混凝土断裂机理:大连:大连理工大学,1988.
[7]徐世娘.混凝土断裂力学.大连:大连理工大学,1991.
[8]徐世娘,赵国藩.混凝_十结构裂缝扩展的双K断裂准则.土木工程学报.1992,25(2):32-38.
[9]徐世娘,赵国藩.混凝土断裂力学研究.大连:大连理工大学出版社,1991.
[10]Hillerborg A,Modeerand M,Petersson P E,et al.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.Cement and Concrete Research,1976,6(6):773-782.
[11]Bazant Z P.Crack band theory for fracture of concrete.Materials and Structures,1983,16(93):155-177.
[12]Swartz S E,Go C G.Validity of compliance calibration to cracked concrete beams in bending tests.Experimental Mechanics,1984,24(2):129-134.
[13]Swartz S E,Refai T M.Influence of size on opening mode fracture parameters for precracked concrete beams in bending.Proceedings of ESM-RILEM International conference on fracture of concrete and rock,Houston,Texas,1987:242-254.
[14]Jenq Y S,Shah S P.Two parameter fracture model for concrete,ASCE.Journal of Engineering Mechanics,1985,111(10):1227-1241.
[15]Bazant Z P,Kazemi M T.Size dependence of concrete fracture energy determined by Rilem work-of-fracture method.International Journal of Fracture,1991,51(2):121-138.
[16]Bazant Z P,Kazemi M T.Determination of fracture energy,process zone length and brittleness number from size effect,with application to rock and concrete.International Journal of Fracture,1990,44(2):111-131.
[17]Karihaloo B L.Fracture mechanics and structural concrete.New York:Copublished in the United States with John Wiley & Sons,1995.
[18]Bruhwiler E,Saomna V E.Water fracture interaction in concrete Part I:Fracture Properties.ACI Materials Journal,1995,92(3).
[19]Bruhwiler E,Saouma V E.Water fracture interaction in concrete Part II:Hydrostatic Pressure in Cracks.ACI Materials Journal,1995,92(4).
[20]Reinhardt H W,Sosoro M,Zhu X,et al.Cracked and repaired concrete subject to fluid penetration.Materials and Structures,1998,31:74-93.
[21]Slowik V,Saouma V E.Water pressure in propagating concrete cracks.Journal of Structural Engineering,2000,126(2):235-242.
[22]柏承新,赵代深.二次奇性边界元及其在重力坝坝踵断裂分析中的应用.土木工程学报,1988, (02):43-50.
[23]李庆斌,林皋,周鸿钧.异弹模界面裂缝的边界元分析及其应用.大连理工大学学报,1991,(02):1 99-204.
[24]刘光廷,王宗敏,周鸿钧.缝端奇异边界单元和界面裂缝的应力强度因子计算.清华大学学报(自然科学版),1996,(01):34-40.
[25]贾金生,李新宇,郑璀莹.特高重力坝考虑高压水劈裂影响的初步研究.水利学报.2006,(12):1509-1515
[26]Griffth A A.The phenomena of rupture and flow in solids.Philosophical Transactions Royal Society of London,1921,Series A221:163-168.
[27]Lawn B R.Fracture of Brittle Solids-Second Edition.Cambridge:Cambridge University,1993.
[28]Irwin G R.Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics,1957,24(4):361-364.
[29]20世纪理论和应用力学十大进展.力学进展,2001,31(03):322-326.
[30]柳春图,蒋持平.当前断裂力学发展的几个问题:固体力学发展趋势.黄克智,徐秉业.北京:北京理工大学出版社,1995322-326.
[31]Sih G C.Mechanics of fracture,Vol.1,Methods of analysis and solutions of crack problem.Leyden:Noordhoff International Publishing,1973.
[32]Rooke D P,Cartwright D J.Compendium of stress intensity factors.London:England:the Hillingdon,1976.
[33]中国航空研究院.应力强度因子手册.北京:科学出版社,1981.
[34]张行.断裂力学中应力强度因子的解法.北京:国防工业出版社,1992.
[35]Sih G C.Handbook of stress intensity factors.Bethlehem:Leheigh University,1973.
[36]Tada H,Paris P C,Irwin G R,et al.The stress analysis of cracks.Hellertown:Del Research Corp,1973.
[37]Murakami Y.Stress intensity factor handbook.New York:Pergamon Press,1987.
[38]余德浩.计算数学与科学工程计算及其在中国的若干发展.数学进展,2002,(01):1-6.
[39]Aliabadi M H,Rooke D P.Numerical Fracture Mechanics.Southampton/Boston:Kluwer Academic Pubsishers,1991.
[40]黎在良,王元汉,李廷芥.断裂力学中的边界数值方法.北京:地震出版社,1996.
[41]Zhu Z,Xie H,Ji S,et al.The mixed boundary problems for a mixed mode crack in a finite plate.Engineering Fracture Mechanics,1997,56(5):647-655.
[42]Fett T.Stress intensity factors and T-stress in edge-cracked rectangular plates under mixed boundary conditions.Engineering Fracture Mechanics,1998,60(5-6):625-630.
[43]Fett T,Bahr H.Mode I stress intensity factors and weight functions for short plates under different boundary conditions.Engineering Fracture Mechanics,1999,62(6):593-606.
[44]Fett T.Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions.Engineering Fracture Mechanics,2001,68(9):1119-1136.
[45]Fett T.Stress intensity factors and T-stress for single and double-edge-cracked circular disks under mixed boundary conditions.Engineering Fracture Mechanics,2002,69(1):69-83.
[46]Liebowitz H,Sandhu J S,Lee J D,et al.Computational fracture mechanics:Research and application. Engineering Fracture Mechanics,1995,50(5-6):653-670.
[47]Chen Y M.Numerical computation of dynamic stress intensity factors,by a Lagrangian finite-difference method(the HEMP code).Engineering Fracture Mechanics,1975,7(4):653-660.
[48]Lin X,Ballmann J.Re-consideration of Chen's problem by finite difference method.Engineering Fracture Mechanics,1993,44(5):735-739.
[49]Altus E.The finite difference technique for solving crack problems.Engineering Fracture Mechanics,1984,19(5):947-957.
[50]Liebowitz H,Moyer E T.Finite Element Methods in Fracture Mechanics.Computers & Structures,1989,31(1):1-9.
[51]Mowbray D F.A note on the finite element method in linear fracture mechanics.Engineering Fracture Mechanics,1970,2(2):173-176.
[52]Chan S K,Tuba I S,Wilson W K,et al.On the finite element method in linear fracture mechanics.Engineering Fracture Mechanics,1970,2(1):1-17.
[53]Banks-sills L.Application of the finite element method to linear elastic fracture mechanics.Applied Mechanics Reviews,1991,44(10):447-461.
[54]Henshell R D,Shaw K G.Crack tip finite elements are unnecessary.International Journal for Numerical Methods in Engineering,1975,9:495-507.
[55]Barsoum R S.On the use of isoparametric finite elements in linear fracture mechanics.International Journal for Numerical Methods in Engineering,1976,10:25-37.
[56]Barsoum R S.Trangular quarter-point elements as elastic and perfectly-plastic crack tip elements.International Journal for Numerical Methods in Engineering,1977,11:85-98.
[57]Owen D R,Fawkes A J.Engineering Fracture Mechanics:Numerical Methods and Application.Swansea,U.K.:Pineridge Press Ltd,1982.
[58]姚敬之.有限元法中的过渡单元.固体力学学报,1985,(04):541-548.
[59]姚敬之.奇应变拟协调元.河海大学学报(自然科学版),1988,(04):72-83.
[60]姚敬之.关于奇应变拟协调元的一点注记.河海大学学报:自然科学版,1991,19(4):127-129.
[61]陈万吉,陈伦元,杨健.拟协调奇异元.固体力学学报,1984,(03):351-366.
[62]李英治,柳春图.Reissner型平板弯曲断裂问题分析.力学学报,1983,(04):366-375.
[63]李英治,柳春图.用应力杂交法计算Reissner型板复合型弯曲应力强度因子.航空学报,1986,(06):553-558.
[64]李英治,李敏华,柳春图.含表面裂纹三维体裂纹尖端应力应变场及应力强度因子计算.中国科学A辑,1988,(08):828-842.
[65]冯金辉,柳春图.含裂纹有限结构的局部.整体分析.应用力学学报,1999,(02):145-150.
[66]Tracey D M.Finite elements,for determination of crack tip elastic stress intensity factors.Engineering Fracture Mechanics,1971,3(3):255-265.
[67]Tracey D M,Cook T S.Analysis of power type singularities using finite elements.International Journal Numerical Method in Engineering,1977,11:1225-1233.
[68]Pu S L,Hussain M A,Lorensen W E,et al.The collapsed cubic isoparametric element as a singular element for crack problems.International Journal Numerical Method in Engineering,1978,12:1727-1742.
[69]Lin K Y,Tong P.Singular finite elements for the fracture analysis of V-notched plate.International Journal Numerical Method in Engineering,1980,15:1343-1354.
[70]Givoli D,Rivkin L.The DtN finite element method for elastic domains with cracks and reentrant comers.COMPUTERS & Structures,1993,49:633-642.
[71]王志超,张理苏.一种新的准谐调有限元列式方法及在断裂力学中的应用.力学学报,1990,22(4):457-462.
[72]钟万勰,张洪武.平面断裂解析元的列式.机械强度,1995,17(3):1-6.
[73]Meguid S A,Tan M,Zh Z H,et al.Analysis of cracks perpenticular to biomaterial interfaces using a novel FE.International Journal Of Fracture,1995,.
[74]Rahulkumar P,Saigal S,Yunus S,et al.SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS.International Journal for Numerical Methods ir Engineering,1997,40(6):1091-1114.
[75]Munaswamy K,Pullela R.Computation of stress intensity factors for through cracks in plates using p-version finite element method.Communications in Numerical Methods in Engineering,2007.
[76]Xiao Q Z,Karihaloo B L,Williams F W,et al.Application of penalty-equilibrium hybrid stress element method to crack problems.Engineering Fracture Mechanics,1999,63(1):1-22.
[77]Wu C C,Cheung Y K.On optimization approaches of hybrid stress elements.Finite Elements ir Analysis and Design,1995,21(1-2):111-128.
[78]Yamada Y,Okumura H.Finite element analysis of stress and strain singularity eigenstate in inhomogeneous media or composite materials.Hybrid and Mixed Finite Methods,New York,1983:325-343.
[79]平学成,陈梦成.楔形体尖端近似场的非协调有限元特征法.华东交通大学学报,2001,(04):6-11.
[80]梁平英,陈梦成.一种新的计算各向异性材料裂纹尖端应力强度因子杂交元法.计算力学学报,2007,(02):209-214.
[81]张武,林胜良.多参量断裂力学广义杂交/混合裂纹有限元法.应用力学学报,2004,(01):62-67.
[82]Noor A K,Babuska I.Quality assessment and control of finite element solutions.Finite Elements in Analysis and Design,1987,3(1):1-26.
[83]lyer N R,Appa R T.A review of error analysis and adaptive refinement methodologies in finite element applications.Part I:Error analysis.Journal of Structural Engineering,1992,19:77-94.
[84]lyer N R,Appa R T.A review of error analysis and adaptive refinement methodologies in finite element applications.Part II:Adaptive refinements.Journal of Structural Engineering,1992,19:125-137.
[85]Babuka I,Rheinboldt W C.A-posteriori error estimates for the finite element method.International Journal for Numerical Methods in Engineering,1978,12(10):1597-1615.
[86]Zienkiewicz O C,Zhu J Z.A simple error estimator and adaptive procedure for practical engineerng analysis.International Journal for Numerical Methods in Engineering,1987,24(2):337-357.
[87]Zienkiewicz O C,Zhu J Z.The superconvergent patch recovery and a posteriori error estimators.Part Ⅰ:The recovery technique;PartII:Error estimates and adaptivity.International Journal For Numerical Methods In Engineering,1992,33:1331-1382.
[88]Wiberg N E,Abdulwahab F.Patch recovery based on superconvergent derivatives and equilibrium. International Journal for Numerical Methods in Engineering, 1993, 36(16): 2703-2724.
[89] Wiberg N E, Abdulwahab F. Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. International Journal for Numerical Methods in Engineering, 1994, 37(20): 3417-3440.
[90] Wiberg N E, Li X D, Abdulwahab F, et al. Adaptive finite element procedures in elasticity and plasticity. Engineering Computations, 1996, 12: 120 - 141.
[91] Wiberg N E, Li X D. Adaptive finite element procedures for linear and non-linear dynamics. International Journal for Numerical Methods in Engineering, 1999, 46(10): 1781-1802.
[92] Blacker T, Belytschko T. Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 1994, 37(3): 517-536.
[93] Schleupen A, Ramm E. Local and global error estimations in linear structural dynamics. Computers & Structures, 2000, 76(6): 741-756.
[94] Zienkiewicz O C, Taylor R L. The finite element method, vol. I: The basis, vol. II: Solid mechanics. Oxford: Butterworth-Hienemann Ltd, 2000.
[95] Ainsworth M, Oden J T. Posteriori Error Estimation in Finite Element Analysis. New York: Wiley-Interscience, 2000.
[96] Palani G S, Iyer N R, Dattaguru B, et al. New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems. Engineering Fracture Mechanics, 2006, 73(6): 802-819.
[97] Min J B, Bass J M, Spradley L W, et al. Adaptive finite element methods for two-dimensional problems in computational fracture mechanics. Computers & Structures, 1994, 50(3): 433-445.
[98] Koenke C, Harte R, Kratzig W B, et al. On adaptive remeshing techniques for crack simulation problems. Engineering Computations, 1998, 15: 74-88.
[99] Murthy K, Mukhopadhyay M. Unification of stress intensity factor (SIF) extraction methods with an h-adaptive finite element scheme. Communications in Numerical Methods in Engineering, 2001, 17(7): 509-520.
[100] Lim I L, Johnston I W, Choi S K, et al. Comparison between various displacement-based stress intensity factor computation techniques. International Journal of Fracture, 1992, 58: 193 - 120.
[101] Meshii T, Watanabe K. Stress intensity factor error index for finite element analysis with singular elements. Engineering Fracture Mechanics, 2002, 70(5): 657-669.
[102] Palani G S, Dattaguru B, Iyer N R, et al. Numerically integrated modified virtual crack closure integral technique for 2-D crack problems. Structural Engineering and Mechanics, 2004, 18(6): 731-744.
[103] Gallimard L, Panetier J. Error estimation of stress intensity factors for mixed-mode cracks. International Journal for Numerical Methods in Engineering, 2006, 68(3): 299-316.
[104] Stern M, Becker E B, Dunham R S, et al. A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture, 1976, 12(3): 359 - 368.
[105] Giner E, Fhenmayor F J, Tarancon J E, et al. An improvement of the EDI method in linear elastic fracture mechanics by means of a posteriori and an error estimator in G. International Journal for Numerical Methods in Engineering, 2004, 59(4): 533-558.
[106] Xuan Z C, Par N, Peraire J, et al. Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity. Computer Methods in Applied Mechanics and Engineering, 2006, 195(4-6): 430-443.
[107]Oden J T,Demkowiez L,Strouboulis T,et al.Adaptive methods for problems in solid and fluid mechanics.Accuracy estimates and adaptive refinements in finite element computations,Chichester,1986:249-280.
[108]Ogen G,Schiff B.Constrained finite elements for singular boundary value problems.Journal of Computational Physics,1983,51(1):65-82.
[109]Yosibash Z,Schiff B.A superelement for two-dimensional singular boundary value problems in linear elasticity.International Journal of Fracture,1993,62(4):325-340.
[110]Yosibash Z,Schiff B.Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities.Finite Elements in Analysis and Design,1997,26(4):315-335.
[111]Go C G,Lin C I,Lin Y S,et al.Formulation of a super-element for the dynamic problem of a cracked plate.Communications in Numerical Methods in Engineering,1998,14(12):1143-1154.
[112]Song C M.A super-element for crack analysis in the time domain.International Journal for Numerical Methods in Engineering,2004,61(8):1332-1357.
[113]Thatcher R W.Singularities in the solution of Laplace's equation in two dimensions.Journal of the Institute of Mathematics and Its AoDlications,1975,16:303-319.
[114]应隆安.计算应力强度因子的无限相似单元法.中国科学A辑,1977,(06):517-535.
[115]Houde H.The numerical solutions of interface problems by infinite element method.Numerische Mathematik,1982,39:39-50.
[116]应隆安.无限元方法.北京:北京大学出版社,1992.
[117]Ying L.Infinite Element Methods.Beijing/Braunschweig:Peking University Press/Vieweg Publishing,1995.
[118]李有堂.平面断裂问题的相似单元理论及其应用研究:博士.兰州:兰州大学,1997.
[119]Liu D S,Chiou D Y.A coupled IEM/FEM approach for solving elastic problems with multiple cracks.International Journal of Solids and Structures,2003,40(8):1973-1993.
[120]Panagiotopoulos P D.Fractal geometry in solids and structures.International Journal of Solids and Structures,1992,29(17):2159-2175.
[121]Panagiotopoulos P D,Panagouli O K,Mistakidis E S,et al.Fractal geometry and fractal material behavior in Solids and Structures.Archive of Applied Mechanics,1993,63(1):1-24.
[122]Leung A Y,Wong S C.Two-level finite element method for plane cracks.Communications in Applied Numerical Methods,1989,5(4):263-274.
[123]Leung A Y,Su R K.Mode I crack problems by fractal two level finite element methods.Engineering Fracture Mechanics,1994,48(6):847-856.
[124]Leung A Y,Su R K.Mixed-mode two-dimensional crack problem by fractal two level finite element method.Engineering Fracture Mechanics,1995,51(6):889-895.
[125]Leung A Y,Su R K.Body-force linear elastic stress intensity factor calculation using fractal two level finite element method.Engineering Fracture Mechanics,1995,51(6):879-888.
[126]Leung A Y,Su R K.Fractal two-level finite element method for 2-D cracks.Microcomputers in Civil Engineering,1996,11:249-257.
[127]Williams M L.Stress singularities resulting from various boundary conditions in angular comers of plates in extensions.Journal of Applied Mechanics,1957,24:109-114.
[128] Leung A Y, Su R K. Fractal two-level finite element method for free vibration of cracked beams. Journal of Shock and Vibration, 1998, 5(1): 61 - 68.
[129] Leung A Y, Su R K. Eigenfunction expansion for penny-shaped and circumferential cracks. International Journal of Fracture, 1998, 89(3): 205-222.
[130] Leung A Y, Su R K. Two-level finite element study of axisymmetric cracks. International Journal Of Fracture, 1998, 89(2).
[131] Leung A Y, Tsang K L. Mode III two-dimensional crack problem by two-level finite element method. International Journal Of Fracture, 2000,102(3): 345 - 358.
[132] Su R K, Leung A Y. Mixed mode cracks in Reissner plates. International Journal of Fracture, 2001, 107(3): 235-257.
[133] Su R K, Leung A Y. Three-dimensional mixed mode analysis of a cracked body by fractal finite element method. International Journal of Fracture, 2001,110(1): 1 - 20.
[134] Su R K, Sun H Y. Numerical solution of cracked thin plates subjected to bending, twisting and shear loads. International. International Journal Of Fracture, 2002, 117(4): 323 - 335.
[135] Tsang D K, Oyadiji S O, Leung A Y, et al. Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor. Engineering Fracture Mechanics, 2003, 70(15): 2199-2214.
[136] Su R K, Sun H Y. Numerical solutions of two-dimensional anisotropic crack problems. International Journal of Solids and Structures, 2003,40(18): 4615-4635.
[137] Xie J F, Sok S L, Leung A Y, et al. A parametric study on the fractal finite element method for two-dimensional crack problems. International Journal for Numerical Methods in Engineering, 2003, 58(4): 631-642.
[138] Su R K, Feng W J. Accurate determination of mode I and II leading coefficients of the Williams expansion by finite element analysis. Finite Elements in Analysis and Design, 2005, 41(11-12): 1175-1186.
[139] Tsang D K, Oyadiji S O, Leung A Y, et al. Two-dimensional fractal-like finite element method for thermoelastic crack analysis. International Journal of Solids and Structures, 2007,44(24): 7862-7876.
[140] Su R K, Fok S L. Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements. Engineering Fracture Mechanics, 2007, 74(10): 1649-1664.
[141] Reddy R M, Rao B N. Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method. Engineering Fracture Mechanics, 2008, 75(10): 2860-2906.
[142] Grigoriu M, Saif M, El-borgi S, et al. Mixed-mode fracture initiation and trajectory prediction under random stresses. International Journal Of Fracture, 1990,45: 19-34.
[143] Provan J W. Probabilistic fracture mechanics and reliability. Dordrecht: The Netherlands: Martinus Nijhoff Publishers, 1987.
[144] Besterfield G H, Lawrence M A, Belytschko T, et al. Brittle fracture reliability by probabilistic finite elements. ASCE Journal of Engineering Mechanics, 1990, 116: 642-659.
[145] Rahman S. Probabilistic fracture mechanics: J-estimation and finite element methods. Engineering Fracture Mechanics, 2001, 68(1): 107-125.
[146] Cruse T A. Numerical Evaluation of Elastic Stress Intensity Factors by the Boundary-Integral Equation Method. The surface Crack:Physical and Computational Solutions, New York, 1972:153-170.
[147] Snyder M D, Cruse T A. Boundary-integral equation analysis of cracked anisotropic plates. International Journal of Fracture, 1975, 11: 315-328.
[148] Ang W T. A boundary integral solution for the problem of multiple interacting cracks in an elastic material. International Journal Of Fracture, 1986, 31: 259-270.
[149] Ang W T, Clement D L. A boundary element method for determining the effect of holes on the stress distribution around a crack. International Journal for Numerical Methods in Engineering, 1986, 23(9): 1727-1737.
[150] Guimaraes S, Telles J C. On the numerical Green's function technique for cracks in Reissner's plates. Computer Methods in Applied Mechanics and Engineering, 2007, 196(21-24): 2478-2485.
[151] Mavrothanasis F I, Pavlou D G. Green's function for KI determination of axisymmetric elastic solids containing external circular crack. Engineering Fracture Mechanics, 2008, 75(8): 1891-1905.
[152] Blandford G E, Ingraffea A R, Liggett J A, et al. Two-dimensional stress intensity factor computations using the boundary elementmethod. International Journal for Numerical Methods in Engineering, 1981, 17: 387-404.
[153] Jia Z H, Shippy D J, Rizzo F J, et al. On the computation of two-dimensional stress intensity factors using the boundary element method. International Journal for Numerical Methods in Engineering, 1988, 26(12): 2739-2753.
[154] Polyzos D, Stamos A A, Beskos D E, et al. BEM computation of DSIF in cracked viscoelastic plates. Communications in Numerical Methods in Engineering, 1994, 10(1): 81-87.
[155] Ganguly S, Layton J B, Balakrishna C, et al. Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity. International Journal for Numerical Methods in Engineering, 2000, 48(5): 633-654.
[156] Martinez J, Dominguez J. On the use of quarter-point boundary elements for stress intensity factor computations. International Journal for Numerical Methods in Engineering, 1984, 20(10): 1941-1950.
[157] Green A E, Zerna W. Theoretical Elasticity. Oxford: Oxford(Clarendon), 1954.
[158] Portela A, Aliabadi M H, Rooke D P, et al. The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering, 1992, 33(6): 1269-1287.
[159] ASaez, Gallego R, Dominguez J, et al. Hypersingular quarter-point boundary elements for crack problems. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1681-1701.
[160] Chen W H, Chen T C. An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1739-1756.
[161] Sollero P, Aliabadi M H. Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Composite Structures, 1995, 31(3): 229-233.
[162] Matos P F, Moreira P M, Portela A, et al. Dual boundary element analysis of cracked plates: post-processing implementation of the singularity subtraction technique. Computers & Structures, 2004, 82(17-19): 1443-1449.
[163] Chau K T, Wang Y B. A new boundary integral formulation for plane elastic bodies containing cracks and holes. International Journal of Solids and Structures, 1999, 36(14): 2041-2074.
[164] Crouch S L. Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution. International Journal for Numerical Methods in Engineering, 1976, 10(2): 301-343.
[165] Crawford A M, Curran J H. Higher-order functional variation displacement discontinuity elements. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1982, 19(3): 143-148.
[166] Shou K J, Crouch S L. A higher order displacement discontinuity method for analysis of crack problems. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1995, 32(1): 49-55.
[167] Aliabadi M H. Boundary element formulations in fracture mechanics. Applied Mechanics Review, 1997,.
[168] Yan X Q. Stress intensity factors for interacting cracks and complex crack configurations in linear elastic media. Engineering Failure Analysis, 2007, 14(1): 179-195.
[169] Nisitani H. Solutions of notch problems by body force method. Stress analysis of notch problem, Alphen aan den Rijn,Netherlands, 1978:.
[170] Wolf J P, Song C M. Finite-Element Modelling of Unbounded Media. New York: Wiley, 1996.
[171] Song C M, Wolf J P. The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for unbounded media. Dynamic soil-structure interaction, current research in China and Swizerland, Beijiing, 1997:71-94.
[172] Song C M, Wolf J P. The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 1997, 147(3-4).
[173] Song C M, Wolf J P. Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method. Computers & Structures, 2002, 80(2): 183-197.
[174] Song C M. A matrix function solution for the scaled boundary finite-element equation in statics. Computer Methods in Applied Mechanics and Engineering, 2004, 193(23-26): 2325-2356.
[175] Song C M. Weighted block-orthogonal base functions for static analysis of unbounded domains. Proceedings of the 6th World Congress on Computational Mechanics, Beijing,China, 2004:615-620.
[176] Song C M. Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material corners. Engineering Fracture Mechanics, 2005, 72(10): 1498-1530.
[177] Chidgzey S R, Deeks A J. Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method. Engineering Fracture Mechanics, 2005, 72(13): 2019-2036.
[178] Song C M. Analysis of singular stress fields at multi-material corners under thermal loading. International Journal for Numerical Methods in Engineering, 2006,65(5): 620-652.
[179] Yang Z J, Deeks A J, Hao H, et al. Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach. Engineering Fracture Mechanics, 2007, 74(5): 669-687.
[180] Song C M, Vrcelj Z. Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-element method. Engineering Fracture Mechanics, 2008, 75(8): 1960-1980.
[181] Rao B N, Rahman S. A coupled meshless-finite element method for fracture analysis of cracks. International Journal of Pressure Vessels and Piping, 2001, 78(9): 647-657.
[182] Bao W Z, Han H, Huang Z Y, et al. Numerical simulations of fracture problems by coupling the FEM and the direct method of lines. Computer Methods in Applied Mechanics and Engineering, 2001, 190(37-38): 4831-4846.
[183]Aour B,Rahmani O,Nait-abdelaziz M,et al.A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics.International Journal of Solids and Structures,2007,44(7-8):2523-2539.
[184]Chidgzey S R,Trevelyan J,Deeks A J,et al.Coupling of the boundary element method and the scaled boundary finite element method for computations in fracture mechanics.Computers & Structures,2008,86(11-12):1198-1203.
[185]樊成.有县覆盖Kriging插值无网格法及其在岩体断裂中的应用研究:博士.大连:大连理工大学.2007.
[186]Mohammadi S.Extended finite element method for fracture analysis of structures.2008.
[187]Luco J E.Linear soil-structure interaction:a review.In Earthquake Ground Motion and its Effects on Structures,AMD,Datta SK(ed.),New Youk,1982:41-57.
[188]Kausel E.Local transmitting boundaries.Journal of Engineering Mechanics(ASCE),1988,114:1011-1027.
[189]Givoli D.Non-reflecting boundary conditions.Journal of Computational Physics,1991,94(1):1-29.
[190]Tsynkov S V.Numerical solution of problems on unbounded domains.A review.Applied Numerical Mathematics,1998,27(4):465-532.
[191]Astley R J.Infinite elements for wave problems:a review of current formulations and an assessment of accuracy.International Journal for Numerical Methods in Engineering,2000,49(7):951-976.
[192]Givoli D.High-order local non-reflecting boundary conditions:a review.Wave Motion,2004,39(4):319-326.
[193]Mohammad H B,A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry.International Journal for Numerical Methods in Engineering,2008,74(2):209-237.
[194]Chongmin S M.A boundary condition in Parle series for frequency-domain solution of wave propagation in unbounded domains.International Journal for Numerical Methods in Engineering,2007,69(11):2330-2358.
[195]WolfJ P.Dynamic Soil-Structure Interaction[M].Prentice-Hall:Englewood Cliffs,N J,1985.
[196]Wolf J P.Soil-Structure-Interaction Analysis in Time Domain[M].Prentice-Hall:Englewood Cliffs,NJ,1988.
[197]Hall W S,Oliveto G.Boundary Element Methods for Soil-Structure Interaction[M].Kluwer Academic Publishers:Dordrecht,2003.
[198]Givoli D.Numerical Methods for Problem in Infinite Domains[M].Elsevier:Amsterdam,1992.
[199]Lysmer J,Kuhlemeyer R L.Finite dynamic model for infinite media.Journal of Engineering the Mechanics Division,ASCE,1969,95(EM4):859-877.
[200]White W,Valliappan S,Lee I K,et al.Unified boundary for finite dynamic models.Journal of Engineering the Mechanics Division,ASCE,1977,103(EM5):949-964.
[201]T A.Compatible viscous boundary for discrete models.Journal of Engineering the Mechanics Division,ASCE,1978,104(EM5):1253-1266.
[202]Deeks A J,Randolph M F.Axisymmetric time-domain transmitting boundaries.Journal of Engineering Mechanics,ASCE,1994,120(1):25-42.
[203]Liu J B,Lu Y D.A direct method for analysis of dynamic soil-structure interaction based on interface idea.Dynamic Soil-Structure Interaction,current research in China and Swizerland,Beijing,1997:258-273.
[204]Smith W D.A nonreflecting plane boundary for wave propagation probems.Journal of Computational Physics,1974,15(4):492-503.
[205]Smith W D.The application of finite element analysis to body wave propagation problems.Geophysical Journal of the Royal Astronomical Society,1975,42(2):747-768.
[206]Cundall P A,Kunar R R,Carpenter P C,et al.Solution of infinite dynamic problems by finite modelling in the time domain.Proceedings of the 2nd international conference on applied numerical modelling,London,1979:339-351.
[207]Lindman E L.Free-Space boundary conditions for the time dependent wave equation.Journal of Computaional Physics,1975,18(1):66-78.
[208]Engquist B,Majda A.Absorbing boundary conditions for the numerical simulation of waves.Mathematics of Computation,1977,31(139):629-651.
[209]Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67(6):1529-1540.
[210]廖振鹏,黄孔亮,杨柏坡,等.暂态波透射边界.中国科学A辑.1984,4(6):556-564.
[211]Liao Z P,Wong H L.A transmitting boundary for the numerical simulation of elastic wave propagation.Soil Dynamics and Earthquake Engineering,1984,3(4):174-183.
[212]胡志强.考虑坝一地基动力相互作用的有横缝拱坝地震响应分析:大连:大连理工大学,2003.
[213]Chen H Q.Application of transmitting boundaries to nonllinear dynamic analysis of arch dam-foundation-reservoir system.Dynamic soil-structure interaction,current research in China and Swizerland,Beijing,1997:115-124.
[214]Keys R G.Absorbing boundary conditions for acoustic media.Geophysics,1985,50(6).
[215]Higdon R L.Absorbing boundary conditions for acoustic and elastic waves in stratified media.Journal of Computational Physics,1992,101(2):386-418.
[216]Higdon R L.Absorbing boundary conditions difference approximations to the multi-dimensional wave equation.Mathematics of Computation,1986,47(176):437-459.
[217]Wolf J P,Song C.Doubly asymptotic multi-directional transmitting boundary for dynamic unbounded medium-structure-interaction analysis.Earthquake Engineering & Structural Dynamics,1995,24(2):175-188.
[218]Geers T L.Doubly asymptotic approximation for transient motions or submerged structures.Journal of the Acoustical Society of America,1978,64(5).
[219]Nicolas-vullierme B.A contribution to doubly asymptotic approximation:an operator top-down approach.Journal of Vibration and Acoustics,ASME,1991,I 13(3):409-515.
[220]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析.地震工程与工程振动.1996,(03).
[221]Ungless R F.An Infinite Element(Master Thesis):Master.Columbia:University of British Columbia,1973.
[222]Bettess P,Zienkiewicz O C.Diffraction and reflection of surface waves using finite and infinite elements.International Journal for Numerical Methods in Engineering,1977,11(8):1271-1290.
[223]Zienkiewicz O C,Bando K,Bettess P,et al.International Journal for Numerical Methods in Engineering,1985,21.(7).
[224]Zhang C H,Song C M.Boundary element technique in infinite and semi-infinite plane domain. Proceedings of the International Conference on Boundary element,Beijing,1986:.
[225]Zhang C H,Song C M,Wang G L,et al.3-D infinite boundary elements and simulation of monolithic dam foundations.Communications in Applied Numerical Methods,1989,5:389-400.
[226]Zhang C H,Song C M,Pekau O A,et al.Infinite boundary element for dynamic problems of 3-D half space.International Journal for Numerical Methods in Engineering,1991,31(3):447-462.
[227]赵崇斌,张楚汉,张光斗.用无穷元模拟半无限平面弹性地基.清华大学学报,1986,26(3):51-63.
[228]赵崇斌,张楚汉,张光斗.映射动力无穷元及其特性研究.地震工程与工程振动,1987,7(3):1-15.
[229]Zhang C H,Zhao C B.Coupling method of finite and infinite elements for strip foundation wave problems.Earthquake Engineering & Structural Dynamics,1987,15(7):839-851.
[230]Zhang C H,Zhao C B.Effects of canyon topography and geological conditions on strong ground motion,Earthquake Engineering & Structural Dynamics,1988,16(1):81-97.
[231]Astley R J.Wave envelope and infinite elements for acoustical radiation.International Journal for Numerical Methods in Fluids,1983,3(5):507-526.
[232]Burnett D S.A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion.Journal of the Acoustical Society of America,1994,96(5):2798-2816.
[233]Medina F,Penzien J.Infinite element for elstodynamics.Earthquake Engineering & Structureal Dynamics,t982,10(5):699-709.
[234]Khalili N,Valliappan S,Yazdi J T,et al.1D infinite element for dynamic problems in saturated porous media.Communications in Numerical Methods in Engineering,1997,13(9):727-738.
[235]Khalili N,Yazdi J T,Valliappan S,et al.Wave propagation analysis of two-phase saturated porous media using coupled finite-infinite element method.Soil Dynamics and Earthquake Engineering,1999,18(8):533-553.
[236]Kim D K,Yun C B.Time-domain soil-structure interaction analysis in two-dimensional medium based on analytical frequncy-dependent infinite elements.International Journal for Numerical Methods in Engineering,2000,47(7):124 l-1261.
[237]Yerli H T,Temel B,Kiral E,et al.Transient infinite elements for 2D soil-structure interaction analysis.Journal of Geotechnical and Geoenvironmental Engineering,1998,124(10):976-988.
[238]Yerli H T,Temel B,Kiral E,et al.Multi-wave transient and harmonic infinite elements for two-dimensional unbounded domain problems.Computers and Geotechnics,1999,24(3):185-206.
[239]Gerdes K.The conjugated vs.the unconjugated infinite element method for the helmhottz equation in exterior domains.Computer Methods in Applied Mechanics and Engineering,1998,152(1-2):125-145.
[240]Shirron J J,Babuska I.A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems.Computer Methods in Applied Mechanics and Engineering,1998,164(1-2):121-139.
[241]Astley R J.Infinite elements for wave problems:a review of current formulations and an assessment of accuracy.International Journal for Numerical Methods in Engineering,2000,49(7):951-976.
[242]Astley R J.Conditioning of infinite element schemes for wave problems.Communications in Numerical Methods in Engineering,2001,17(1):31-41.
[243]Gerdes K.A review of infinite element methods for exterior Helmholtz problems.Journal of Computational Acoustics,2000,8(1):43-62.
[244]水利部国际合作与科技司编著.当代水利科技前沿.北京:中国水利水电出版社,2005.
[245]Wolf J P.Approximate dynamic model of embedded foundation in time domain.Earthquake Engineering & Structural Dynamics,1986,14(5):683-703.
[246]Jean W Y,Ling T W,Penzien J,et al.System parameters of soil foundations for time domain dynamic analysis.Earthquake Engineering & Structural Dynamics,1990,19(4):541-553.
[247]Barros D,F C P...Luco J E,et al.Discrete model for vertical vibrations of surface and embedded foundation.Earthquake Engineering & Structural Dynamics,1990,19:289-303.
[248]栾茂田,林皋.地基动力阻抗的双自由度集总参数模型.大连理工大学学报,1996,(04).
[249]王复明.层状地基分析的样条半解析法及其应用:大连:大连理工大学,1987.
[250]Wang H B.Dynamic soil-structure interaction by combing FEM with trial fimction method and application to underground structure:Janpan:Okayama University,1994.
[251]Song C,Wolf J P.Dynamic stiffness of unbounded medium based on damping-solvent extraction.Earthquake Engineering & Structural Dynamics,1994,23(2):169-181.
[252]Basu U,Chopra A K.Numerical Evaluation of the Damping-Solvent Extraction Method in the Frequency Domain.Earthquake Engineering & Structural Dynamics,2002,31:1231-1250.
[253]李建波,陈健云,林皋.求解非均匀无限地基相互作用力的有限元时域阻尼抽取法.岩土工程学报,2004,26(3):263-267.
[254]李建波.结构一地基动力相互作用的时域数值分析方法研究:博士.大连:大连理工大学,2005.
[255]钟红,林皋,李建波.空间结构-地基动力相互作用数值分析时域算法研究.大连理工大学学报,2007,47(1):78-84.
[256]Zhong H,Lin G,Li J B,et al.An effecient time-domain damping solvent extraction algorithm and its application to arch darn-foundation interaction analysis.Communications in numerical methods in engineering,2007,in press.
[257]Abascal B,Domin.guez J.Vibrations of footings on zoned viscoelastic soils.Journal of Engineering Mechanics,1986,112(5)::433-447.
[258]Spyrakos C C,Beskos D E.Dynamic response of rigid strip foundations by time domain boundary element method.International Journal for Numerical Methods in Engineering,1986,23(8):1547-1565.
[259]Karabalis D L,Beskos D E.Dynamic response of 3-D rigid surface foundations by time domain boundary element method.Earthquake Engineering & Structural Dynamics,1984,12(1):73-93.
[260]Toki K,Sato T.Seismic response analyses of ground with irregular profiles by the boundary finite element method.Boundary elements,Berlin,1983:699-708.
[261]Tai G R,Shaw R P.Helmholtz equation eigenvalues and eigenmodes for arbitrary domains.Journal of the Acoustical Society of America,1974,56(3):796-804.
[262]Sanchez-sesma F J,Esquivel J A.Ground motion on alluvial valleys under incident plane SH waves.Bulletin of the Seismological Society of America,1979,69(4):1107-1120.
[263]Mossessian T K,Dravinski M.Scattering of elastic waves by three-dimensional surface topographies.Wave Motion,1989,11(6):579-592.
[264]Mossessian T K,Dravinski M.Amplification of elastic waves by a three dimensional valley,Part Ⅰ. Steady state response.Earthquake Engineering & Structural Dynamics,1990,19(5):667-680.
[265]Antes H,Trondle G.Analysis of stress waves by indirect BEM.Boundary Elements in Mechanical and Electrical Engineering,New York,1990:179-191.
[266]Beskos D E.Boundary element method in dynamic analysis.Applied Mechanics Reviews,1987,40(1):1-23.
[267]Beskos D E.Boundary element method in dynamic analysis:part Ⅱ(1986-1996).Applied Mechanics Reviews,1997,50(3):149-197.
[268]Nardini D,Brebbia C A.A new approach to free vibration analysis using boundary elements.Boundary Element Methods in Engineering,Berlin,1982:312-326.
[269]宋崇民,张楚汉.水坝抗震分析的动力边界元方法.地震工程与工程振动,1988,8(4):13-26.
[270]Loeffler C F,Mansur W J.Analysis of time integration schemes for boundary element applications to transient wave propagation problems.Boundary Element Techniques:Applicaiton in Stress Analysis and Heat Transfer,Southampton,1987:.
[271]陈虬,许廷兴.无限边界元动态分析的一种新列式.解析与数值结合法的理论及其工程应用,长沙,1989:279-284.
[272]Maier G,Diligenti M,Carini A,et al.Variational approach to boundary element elastodynamic analysis and extension to muttidomain problems.Computer Methods in Applied Mechanics and Engineering,1991,92(2):193-213.
[273]Sirtori S,Maier G,Novati G,et al.A Galerkin symmetric boundary-element method in elasticity:formulation and implementation.International Journal for Numerical Methods in Engineering,1992,35(2):255-282.
[274]Perez-gavilan J J,Aliabadi M H.A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems.Computer & Structures,2001,79(29-30):2621-2633.
[275]Frangi A,Maier G.Dynamic elastic-plastic analysis by a symmetric Galerkin boundary element method with time-independent kernels.Computer Methods In Applied Mechanics And Engineering,1999,171(3-4):281-308.
[276]Perez-gavilan J J,Aliabadi M H.A Galerkin boundary element formation with dual reciprocity for elastodynamics.International Journal for Numerical Methods in Engineering,2000,48(9):1331-1344.
[277]Bonnet M,Maier G,Polizzotto C,et al.Symmetric Galerkin boundary element methods.Applied Mechanics reviews,1998,51(11):669-704.
[278]冯康.论微分与积分方程以及有限与无限元.计算数学,1980,2(1):100-105.
[279]余德浩.自然边界元方法的数学理论.北京:科学出版社,1993.
[280]Spyrakos C C,Beskos D E.Dynamic response of flexible strip foundations by boundary and finite element methods.Soil Dynamics And Earthquake Engineering,1986,5(2):84-96.
[281]Touhei T,Ohmachi T.FE-BE method for dynamic analysis of dam-foundation-reservoir systems in the time domain.Earthquake Engineering & Structural Dynamics,1993,22(3):195-209.
[282]Underwood P,Geers T L.Doubly asymptotic,boundary-element analysis of dynamic soil-structure interaction.International Journal Of Solids And Structures,1981,17(7):687-697.
[283]Kobayashi S,Nishimura N,Mori K,et al.Applications of boundary element-finite element combined method to three-dimensional viscoelastodynamic problems.Boundary Elements,Oxford,1986:.
[284]杜其奎.波动方程的自然边界元与有限元耦合法.淮北煤师院学报,1999,20(2):1-10.
[285]贾祖朋,邬吉明,余德浩.三维Helmholtz方程外问题的自然边界元与有限元耦合法.计算数学,2001,23(3):357-368.
[286]Manolis G D.A comparative study on three boundary element method approaches to problems in elastodynamics.International Journal for Numerical Methods in Engineering,1983,19(1):73-91.
[287]Spyrakos C C,Antes H.Time domain boundary element method approaches in elastodynamics:A comparative study.Computers & Structures,1986,24(4):529-535.
[288]Gaul L,Schanz M.A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains.Computer Methods In Applied Mechanics And Engineering,1999,179(1-2):I 11-123.
[289]Kagawa Y,Yamabuchi T,Araki Y,et al.The infinite boundary element and its application to the unbounded Helmholtz problem.COMPEL-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering,1985,4(1):29-41o
[290]Zhang C H,Song C M,Pekau O A,et al.Infinite boundary elements for dynamic problems of 3-D half space.International Journal for Numerical Methods in Engineering,1991,31(3):447-462.
[291]Zhang C H,Pekau O A,Jin F,et al.Application of FE-BE-IBE coupling to dynamic interaction between alluvial soil and rock canyons.Earthquake Engineering & Structural Dynamics,1992,21(5):367-385.
[292]Wang C Y,Achenbach J D.Three-dimensional time-harmonic elastodynamic Green's functions for anisotropic solids.Proceedings of the Royal Society of London Series A-Mathematical & Physical Sciences,1995,449(1937):441-458.
[293]Wang C,Achenbach J D.Lamb's problem for solids of general anisotropy.Wave motion,1996,24(3):227-242.
[294]Wang C,Achenbach J D,Hirose S,et al.Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy.International Journal Of Solids And Structures,1996,33(26):3843-3864.
[295]Albuquerque E L,Sollero P,Aliabadi M H,et al.The boundary,element applied to time dependent problems in anisotropic materials.International Journal Of Solids And Structures,2002,39(5):1405-1422.
[296]Florez W F,Power H.DRM multidomain mass conservative interpolation approach for the BEM solution of the two-dimensional Navier-Stokes equations.Computers & Mathematics With Applications,2002,43(3-5):457-472.
[297]稽醒,臧跃龙,程玉民.边界元法进展及通用程序.上海:同济大学出版社,1997.
[298]Gao X,Davies T G.Boundary element programming in mechanics.Cambridge:Cambridge University Press,2002.
[299]Dasgupta G.A Finite Element Formulation for Unbounded Homogeneous Continua.Journal of Applied Mechanics-Transactions of the ASME,1982,49(1):136-140.
[300]Wolf J P,Weber B.On calculation the dynamic-stiffness matrix of the unbounded soil by cloning.International Symposium on Numerical Models in Geomechanics,Rotterdam,1982:486-494.
[301]John P W.Dynamic-stiffness matrix of unbounded soil by finite-element multi-cell cloning.Earthquake Engineering & Structural Dynamics,1994,23(3):233-250.
[302]Chongrnin S J.Unit-impulse response matrix of unbounded medium by finite-element based forecasting.International Journal for Numerical Methods in Engineering,1995,38(7):1073-1086.
[303]郭仲衡.相似等参单元.科学通报,1979,24(13):577-582.
[304]Zhang X,Wegner J L.Three-dimensional dynamic soil-structure interaction analysis in the time domain.Earthquake Engineering & Structural Dynamics,1999,28(12):1501-1524.
[305]Wegner J L,Zhang X,Free-vibration analysis of a three-dimensional soil-structure system.Earthquake Engineering & Structural Dynamics,2001,30(1):43-57.
[306]Ekevid T,Wiberg N.Wave propagation related to high-speed train:A scaled boundary FE-approach for unbounded domains.Computer Methods in Applied Mechanics and Engineering,2002,191(36):3947-3964.
[307]阎俊义.结构一地基相互作用的FE-SBFE时域耦合方法及其工程应用:博士.北京:清华大学,2004.
[308]杜建国.基于SBFEM的大坝-库水-地基动力相互作用分析:博士.大连:大连理工大学,2007.
[309]Lin G,Du J G,Hu Z Q,et al.Foundation Inhomogeneity on the Seismic Response.Proc.8th United States National Conference on Earthquake Engineering.2006:.
[310]Lin G,Du J G,Hu Z Q,et al.Earthquake Analyslncluding the Effects of Foundation Inhomogeneity.Frontiers of Architecture and Civil Engineering in China.2007:41-50.
[311]Bazyar M H,Song C.Transient analysis of wave propagation in non-homogeneous elastic unbounded domains by using the scaled boundary finite-element method[J].Earthquake Engineering and Structural Dynamics,2006,35:1787-1806.
[312]Deeks A J,Wolf J P.Semi-analytical elastostatic analysis of unbounded two-dimensional domains.International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(11):1031-1057.
[313]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading.International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(10):813-835.
[314]Doherty J P,Deeks A J.Semi-analytical far field model for three-dimensional finite-element analysis.International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(11):1121-1140.
[315]Song C,Wolf J P.The scaled boundary finite-element method:analytical solution in frequency domain.Computer Methods in Applied Mechanics and Engineering,1998,I64(I-2):249-264.
[316]Song C M,Wolf J P.Body loads in scaled boundary finite-element method.Computer Methods in Applied Mechanics and Engineering,1999,180(1-2):117-135.
[317]Wolf J P,Song C M.The scaled boundary finite-element method-a primer:derivations.Computers & Structures,2000,78(1-3):t91-210.
[318]Song C M,Wolf J P.The scaled boundary finite-element method-a primer:solution procedures.Computers & Structures,2000,78(1-3):211-225.
[319]Deeks A J,Wolf J P.A virtual work derivation of the scaled boundary finite-element method for elastostatics.Computational Mechanics,2002,28(6):489-504.
[320]Deeks A J,Wolf J P.Stress recovery and error estimation for the scaled boundary finite-element method.International Journal for Numerical Methods in Engineering,2002,54(4):557-583.
[321]Deeks A J,Wolf J P.An h-hierarchical adaptive procedure for the scaled boundary finite-element method.International Journal for Numerical Methods in Engineering,2002,54(4):585-605.
[322]Wolf J P.The scaled boundary finite element method[M].Chichester:John Wiley and Sons,2002.
[323]Song C M.Dynamic analysis of unbounded domains by a reduced set of base functions.Computer Methods in Applied Mechanics and Engineering,2006,195(33-36):4075-4094.
[324]杜建国,林皋.基于SBFEM的结构-地基动力相互作用时域算法的改进.水利学报,2007,38(1):8-14.
[325]Song C,Bazyar M H.A boundary condition in Pad6 series for frequency-domain solution of wave propagation in unbounded domains[J].International Journal for Numerical Methods in Engineering,2007,69:2330-2358.
[326]Bazyar M H,Song C.A continued-fraction based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry[J].International Journal for Numerical Methods in Engineering,2008,74(2):209-237.
[327]Vu T H,Decks A J.Use of higher-order shape functions in the scaled boundary finite element method.International Journal for Numerical Methods in Engineering,2006,65(10):1714-1733.
[328]Song C M,Bazyar M H.Development of a fundamental-solution-less boundary element method for exterior wave problems.Communications in Numerical Methods in Engineering,2008,24(4):257-279.
[329]Decks A J,Cheng L.Potential flow around obstacles using the scaled boundary finite-element method.International Journal for Numerical Methods in Fluids,2003,41(7):721-741.
[330]Rajan V S P,Raju K C J.Reformulation of the novel scaled boundary finite element method for electromagnetics.Proceedings of the 6th World Congress on Computational Methanics,Beijing,China,2004:.
[331]Fan S C,Li S M,Yu G Y,et al.Dynamic Fluid-Structure Interaction Analysis Using Boundary Finite Element Method-Finite Element Method.Journal of Applied Mechanics,2005,72(4).
[332]Lehmann L.Application of a coupled finite element/scaled boundary finite element procedure to acoustics.Proceedings of Coupled Problems[C],ECCOMAS,Santorini,Greece,2005:.
[333]滕斌,赵明,何广华.三维势流场的比例边界有限元求解方法.计算力学学报,2006,(03).
[334]Li B N,Cheng L,Decks A J,et al.A modified scaled boundary finite-element method for problems with parallel side-faces.Part I.Theoretical developments.Applied Ocean Research,2005,27(4-5):216-223.
[335]Li B N,Cheng L,Decks A J,et al.A modified scaled boundary finite-element method for problems with parallel side-faces.Part II.Application and evaluation.Applied Ocean Research,2005,27(4-5):224-234.
[336]Li B N,Cheng L,Decks A J,et al.A semi-analytical solution method for two-dimensional Helmholtz equation.Applied Ocean Research,2006,28(3):193-207.
[337]何广华,滕斌,李博宁.应用比例边界有限元法研究波浪与带狭缝三箱作用的共振现象.水动力学研究与进展(A辑),2006,(03).
[338]滕斌,何广华,李博宁.应用比例边界有限元法求解狭缝对双箱水动力的影响.海洋工程,2006,(02).
[339]Lin G,Du J G,Hu Z Q,et al.Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption.Science in China Series E,2007,50(1).
[340]Irwin G R.Fracture Testing of High-Strength Sheet Materials Under Conditions Appropriate for Stress Analysis.In structural Mechanics:Proceedings of 1st Symposium on Naval Structural Mechanics, New York, 1960:557-591.
[341] Anderson T L. Fracture mechanics:fundamentals and applications. Boca Raton: CRC Press, 1991.
[342] Nash G L, Hilton P D. Stress intensity factors by enriched finite elements. Engineering Fracture Mechanics, 1978, 10(3): 485-496.
[343] Chen W H, Chang C S. Analysis of two dimensional fracture problems with multiple cracks under mixed boundary conditions. Engineering Fracture Mechanics, 1989, 34(4): 921-934.
[344] Chen W H, Chang C S. Analysis of two-dimensional mixed-mode crack problems by finite element alternating method. Computers & Structures, 1989, 33(6): 1451-1458.
[345] Lam K Y, Phua S P. Multiple crack interaction and its effect on stress intensity factor. Engineering Fracture Mechanics, 1991, 40(3): 585-592.
[346] Shu H M, Petit J, Bezine G, et al. Stress intensity factors for several groups of equal and parallel cracks in finite plates. Engineering Fracture Mechanics, 1994, 49(6): 933-941.
[347] Chen Y Z. Multiple crack problems for torsion thin-walled cylinder. International Journal of Pressure Vessels and Piping, 1999, 76(1): 49-53.
[348] Chen Y Z. Numerical solution for multiple crack problems of torsion bar. Computer Methods in Applied Mechanics and Engineering, 1999, 174(1-2): 203-209.
[349] Ventura D D, Smith R N. Some applications of singular fields in the solution of crack problems. International Journal for Numerical Methods in Engineering, 1998,42(5): 927-942. [350] Hwang C G, Wawrzynek P A, Ingraffea A R, et al. On the calculation of derivatives of stress intensity factors for multiple cracks. Engineering Fracture Mechanics, 2005, 72(8): 1171-1196. [351] Fotuhi A R, Faal R T, Fariborz S J, et al. In-plane analysis of a cracked orthotropic half-plane. International Journal of Solids and Structures, 2007, 44(5): 1608-1627.
[352] Marc A M, Krishan K C. Mechanical Behavior of Materials. New Jersy: Prentice-Hall, Inc, 1999.
[353] Menclk J. Strength and Fracture of Glass and Ceramics. New York: Elsevier Science, 1992.
[354] Wang R D. The stress intensity factors of a rectangular plate with collinear cracks under uniaxial tension. Engineering Fracture Mechanics, 1997, 56(3): 347-356.
[355] Tan C L, Lgao Y. Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks. Composite Structure, 1992, 20: 17-28.
[356] 涂传林. 裂缝面上受外荷载作用下的边界配置法及其应用.水利学报, 1983,7:9-16.
[357] Fett T, Munz D. Stress Intensity Factors and Weight Functions. Southampton: Computational Mechanics Publications, 1997.
[358] 丁遂栋. 断裂力学. 北京: 机械工业出版社, 1997.
[359] Yuuki R, Cho S B. Efficient boundary element analysis of stress intensity factors for interface cracks in dissimilar materials. Engineering Fracture Mechanics, 1989, 34: 179-188.
[360] Miyazaki N, Ikeda T, Soda T, et al. Stress intensity factor analysis of interface crack using boundary element method application of contour integral method. Engineering Fracture Mechanics, 1993, 45: 599-610.
[361] Zhang Z, Yao Z H, Du Q H, et al. Boundary element method for determining stress intensity factors of bimaterial interface crack. Theory and applications of boundary element methods. Proceedings of the Sixth China-Japan Symposium on BEM, Shanghai, 1994:315-320.
[362] Chen Y M. Numerical solutions of three dimensional dynamic crack problems and simulation of dynamic fracture phenomena by a "non-standard" finite difference method. Engineering Fracture Mechanics, 1978, 10(4): 699-708.
[363] Aoki S, Kishimoto K, Kondo H, et al. Elastodynamic analysis of crack by finite element method using singular element. 1978, 14(1): 59-67.
[364] Kishimoto K, Aoki S, Sakata M, et al. Dynamic stress intensity factors using J-integral and finite element method. Engineering Fracture Mechanics, 1980,13(2): 387-394.
[365] Murti V, Valliappan S. The use of quarter point element in dynamic crack analysis. Engineering Fracture Mechanics, 1986, 23(3): 585-614.
[366] Enderlein M, Ricoeur A, Kuna M, et al. Comparison of finite element techniques for 2D and 3D crack analysis under impact loading. International Journal of Solids and Structures, 2003, 40(13-14): 3425-3437.
[367] Rethore J, Gravouil A, Combescure A, et al. A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing. Computer Methods in Applied Mechanics and Engineering, 2004,193(42-44): 4493-4510.
[368] Song S H, Paulino G H. Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. International Journal of Solids and Structures, 2006,43(16): 4830-4866.
[369] Aliabadi M H. Dynamic Fracture Mechanics. Southampton, UK and Boston, USA.: Computational Mechanics Publications, 1995.
[370] Marrero M, Dominguez J. Time-domain BEM for three-dimensional fracture mechanics. Engineering Fracture Mechanics, 2004, 71(11): 1557-1575.
[371] Chirino F, Gallego R, Saez A, et al. A comparative study of three boundary element approaches to transient dynamic crack problems. Engineering Analysis with Boundary Elements, 1994, 13(1): 11-19.
[372] Dominguez J, Gallego R. Time domain boundary element method for dynamic stress intensity factor computations. International Journal For Numerical Methods In Engineering, 1992, 33(3): 635-647.
[373] Ariza M P, Dominguez J. General BE approach for three-dimensional dynamic fracture analysis. Engineering Analysis with Boundary Elements, 2002,26(8): 639-651.
[374] Fedelinski P, Aliabadi M H, Rooke D P, et al. The laplace transform DBEM for mixed-mode dynamic crack analysis. Computers & Structures, 1996, 59(6): 1021-1031.
[375] Fedelinski P. Boundary element method in dynamic analysis of structures with cracks. Engineering Analysis with Boundary Elements, 2004, 28(9): 1135-1147.
[376] Albuquerque E L, Sollero P, Aliabadi M H, et al. The boundary element method applied to time dependent problems in anisotropic materials. International Journal of Solids and Structures, 2002, 39(5): 1405-1422.
[377] Albuquerque E L. Sollero P, Fedelinski P, et al. Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems. Computers & Structures, 2003, 81(17): 1703-1713.
[378] Williams M L. The stress around a fault or crack in dissimilar media. Bulletin of the Seismological Society, 1959,49: 199-204.
[379] Sih C G, Paris P C, Irwin G R, et al. On cracks in rectilinearly anisotropic bodies. International Journal of Fracture, 1965, 3: 189 - 203.
[380]Zhu H,Tian T Y F Q.Composite materials dynamic fracture studies by generalized Shmuely difference.Engineering Fracture Mechanics,1996,54:869-877.
[381]Kobayashi A,Cherepy R D,Kinsel W,et al.T-elements:state of the art and future trends[J].Journal of Basic Engineering,Transactions of the ASME,Series D,1964,86:681-684.
[382]林皋,杜建国.基于SBFEM的坝一库水相互作用分析.大连理工大学学报,2005,45(5):723-729.
[383]Hall J F.An FFT algorithm for structural dynamics.Earthquake Engineering and Structural Dynamics,1982,10:797-811.