基于互补理论的非连续变形分析方法
|
摘要
非连续变形分析(DDA)方法适用于解决工程中有较多不连续性界面的力学问题,如节理岩体工程稳定性分析。论文回顾了工程计算领域非连续性数值方法的发展历史,以及DDA方法研究现状。DDA方法处理接触的两种常用方法——罚函数法和拉格朗日乘子法,在实施过程中需要进行开-闭迭代来确保正确的接触方式。本文分析了现有接触处理方式的不足之处,引入数学领域前沿的互补理论和变分不等式理论,构造了CDDA和VIDDA,分别采用最热门的C-函数和自然投影函数将问题转化为非光滑方程组,对其解法进行了研究,编制了相应的计算程序并用丰富的数值算例验证了其有效性,就几个常见的工程问题进行了简单的应用研究。具体内容如下:
第二章详细介绍了现有DDA接触算法的数学原理,分析罚函数法和拉格朗日乘子法处理接触问题时存在的问题。
第三章首先介绍了有关互补理论方面的知识,添加接触力作为未知量,从块体的动量守恒变分方程出发重构了DDA的平衡方程,然后分析了每个接触必须满足的法向、切向条件,利用互补方程将其表达为接触方程,从而完成了基于互补理论的非连续变形分析模型——CDDA。
第四章利用最热门的C-函数和非光滑方程组算法来解CDDA模型,首先试验了在交线上不可微的min函数和相应的路径牛顿法(PNM),然后尝试了更优越的仅原点处不可微的FB函数并改进了相应的FB线搜索算法(FBLSA),采用大量的数值算例对两种算法进行验证。
第五章引入了变分不等式理论,建立了与CDDA模型等价的VIDDA模型,探讨了在接触表达方面变分不等式优良的扩展性,同样用路径牛顿法进行了求解,在用两个算例验证VIDDA之后,我们在本章末尾对三种算法的精度、速度、强健性进行了综合的比较。
第六章简单的将CDDA应用于解决边坡稳定性分析、坝基抗滑稳定性分析和预应力锚杆模拟等工程问题。
第七章为结论与展望。
The Discontinuous Deformation Analysis(DDA) method is suitable for solving geotechnical problems with many discontinuous interfaces inside the concerned domain,such as the stability analysis of fractured rock mass.The history of various discontinuous deformation analysis methods including DDA is stated.The penalty function method and the Lagrange multiplier method or its variants are generally utilized to solve contact problems in DDA.Each method has the merits and demerits and uses a process called the open-close iteration to realize the satisfaction of the contact conditions.To avoid the penalty factors and the open-close iteration,we reformulate the conventional DDA and build CDDA and VIDDA by introducing the complementary theory and the variational inequalty theory respectively.Then,CDDA and VIDDA are transfered to non-smooth equations by the C-function and the natural projection map.Various algorithms are ulitized to solve the equations and some practical examples originally designed by Shi are reanalyzed,which prove the recreated DDA methods are feasible.Finally,the CDDA and the VIDDA are applied in some common fields.The detailed contents are as follows:
In chapter 2,the mathematical theory of penalty function method and Lagrange multiplier method is stated,then we analysis the merits and demerits of each method and point out that the open-close iteration is uncertainly convergent.
In chapter 3,firstly we introduce some important concepts about complementary problems related to this dissertation.Secondly,we add the contact forces to basic unknowns,from the variational formulation of momentum conservation instead of the minimizing the potential function,we derive a system of equations for momentum conservation.Then we utilize C-functions to transform the inequalities reflecting contact conditions on all contact-pairs into the equivalent equations called the contact equations.Finally we combine the momentum conservation equations with the contact equations and thus obtain a system of nonlinear equations some of which are continuous but non-smooth.We call the proposed equations as the Complementary Discontinuous Deformation Analysis(CDDA).
In chapter 4 we choose the hot C-functions and non-smooth equations algorithms to slove CDDA.Firstly we test the simplest C-function,the min function,which is smooth over the plane except on a line is ulitized,and use the Path Newton Method to slove equations.Then we designate the C-function as the FB function that is smooth everywhere except at the original point,and improve the FB Line Search Algorithm for solveing the system of nonlinear equations.Some examples are analyzed,which prove the procedure is feasible.
In chapter 5 the variational inequalities theory is applied to this study.The DDA is reformulated as a box-constrained variational inequality problem.Based on the fact that the solution of variational inequality must be a fixed point of the natural projection map,we transfer this problem to the solution of non-smooth equations.We call the equations as the VIDDA.Then,the Path Newton Method(PNM) is used to solve the equations.Two examples are selected validate the procedure.Finally the precsion,efficiency and robustness of the three algorithms we proposed are compared.
Finally in chapter 6,the methods proposed in this dissertation are used to solve some geotechnical problems,such as slop stability,the stability of gravity dam against sliding and modeling pre-tension bolt.
Conclusions and prospects are put in Chapter 7.
第二章详细介绍了现有DDA接触算法的数学原理,分析罚函数法和拉格朗日乘子法处理接触问题时存在的问题。
第三章首先介绍了有关互补理论方面的知识,添加接触力作为未知量,从块体的动量守恒变分方程出发重构了DDA的平衡方程,然后分析了每个接触必须满足的法向、切向条件,利用互补方程将其表达为接触方程,从而完成了基于互补理论的非连续变形分析模型——CDDA。
第四章利用最热门的C-函数和非光滑方程组算法来解CDDA模型,首先试验了在交线上不可微的min函数和相应的路径牛顿法(PNM),然后尝试了更优越的仅原点处不可微的FB函数并改进了相应的FB线搜索算法(FBLSA),采用大量的数值算例对两种算法进行验证。
第五章引入了变分不等式理论,建立了与CDDA模型等价的VIDDA模型,探讨了在接触表达方面变分不等式优良的扩展性,同样用路径牛顿法进行了求解,在用两个算例验证VIDDA之后,我们在本章末尾对三种算法的精度、速度、强健性进行了综合的比较。
第六章简单的将CDDA应用于解决边坡稳定性分析、坝基抗滑稳定性分析和预应力锚杆模拟等工程问题。
第七章为结论与展望。
The Discontinuous Deformation Analysis(DDA) method is suitable for solving geotechnical problems with many discontinuous interfaces inside the concerned domain,such as the stability analysis of fractured rock mass.The history of various discontinuous deformation analysis methods including DDA is stated.The penalty function method and the Lagrange multiplier method or its variants are generally utilized to solve contact problems in DDA.Each method has the merits and demerits and uses a process called the open-close iteration to realize the satisfaction of the contact conditions.To avoid the penalty factors and the open-close iteration,we reformulate the conventional DDA and build CDDA and VIDDA by introducing the complementary theory and the variational inequalty theory respectively.Then,CDDA and VIDDA are transfered to non-smooth equations by the C-function and the natural projection map.Various algorithms are ulitized to solve the equations and some practical examples originally designed by Shi are reanalyzed,which prove the recreated DDA methods are feasible.Finally,the CDDA and the VIDDA are applied in some common fields.The detailed contents are as follows:
In chapter 2,the mathematical theory of penalty function method and Lagrange multiplier method is stated,then we analysis the merits and demerits of each method and point out that the open-close iteration is uncertainly convergent.
In chapter 3,firstly we introduce some important concepts about complementary problems related to this dissertation.Secondly,we add the contact forces to basic unknowns,from the variational formulation of momentum conservation instead of the minimizing the potential function,we derive a system of equations for momentum conservation.Then we utilize C-functions to transform the inequalities reflecting contact conditions on all contact-pairs into the equivalent equations called the contact equations.Finally we combine the momentum conservation equations with the contact equations and thus obtain a system of nonlinear equations some of which are continuous but non-smooth.We call the proposed equations as the Complementary Discontinuous Deformation Analysis(CDDA).
In chapter 4 we choose the hot C-functions and non-smooth equations algorithms to slove CDDA.Firstly we test the simplest C-function,the min function,which is smooth over the plane except on a line is ulitized,and use the Path Newton Method to slove equations.Then we designate the C-function as the FB function that is smooth everywhere except at the original point,and improve the FB Line Search Algorithm for solveing the system of nonlinear equations.Some examples are analyzed,which prove the procedure is feasible.
In chapter 5 the variational inequalities theory is applied to this study.The DDA is reformulated as a box-constrained variational inequality problem.Based on the fact that the solution of variational inequality must be a fixed point of the natural projection map,we transfer this problem to the solution of non-smooth equations.We call the equations as the VIDDA.Then,the Path Newton Method(PNM) is used to solve the equations.Two examples are selected validate the procedure.Finally the precsion,efficiency and robustness of the three algorithms we proposed are compared.
Finally in chapter 6,the methods proposed in this dissertation are used to solve some geotechnical problems,such as slop stability,the stability of gravity dam against sliding and modeling pre-tension bolt.
Conclusions and prospects are put in Chapter 7.
引文
1.K.Terzaghi.Theoretical Soil Mechanics John[M].Wiley&Sons,Inc.New York,1943.
2.沈珠江.关于计算岩土力学发展前景的几点看法,南京水利科学研究院,210029;清华大学水利水电工程系,100084.
3.R.E.Goodman,R.Taylor and T.L.Brekke.A Model for the Mechanics of Jointed Rock[J].Journal of the Soil Mechanics & Foundations Dvi.,ASCE 1968,94:637
4.M.G.Katona.A simple contact-friction interface element with application to buried culverts [J].Int J Num Anal Meth Geomech 1983,7:371-84
5.H.Zheng,D.F.Liu,C.F.Lee,Z.Q.Yue.A sophisticated node-pair model for interface problems[J].Computers and Geotechnics 2004,31:137-153
6.C.S.Desai,M.M.Zaman,J.G.Lightener,H.J.Siriwardane.Thin layer element for interfaces and joints[J].Int J Num Anal Meth Geomech 1984,8:19-43.
7.郑宏,葛修润,李焯芬.界面问题的混合有限元法[J].岩石力学与工程学报,2002,21(1):1-8.
8.B.C.Burman.Development of a numerical model for discontinua[J].Australian Geomechanics Journal,1974,G4(1):13-22.
9.T.Kawai.A new discrete analysis of nonlinear solid mechanics problems involving stability,plasticity and crack[J].Proceedings of the symposium on Applications of computer Methods in Engineering,Los Angeles,1977,Calif:1029-1038.
10.卓家寿,章青.不连续介质力学问题的界面元法[M].北京,科学出版社,2000.
11.P.A.Cundall.A computer model for simulating progressive,large-scale movements in blocky rock systems[J].Proceedings of the symposium of the International Society of Rock Mechanics,1971,Nancy,France,Vol(1):1-8.
12.王泳嘉,刑纪波.离散单元法及其在岩土力学中的应用[M].东北工学院出版社,1991.
13.R.E.Goodman,G.H.Shi,W.Boyle.Calculation of support for hard,jointed rock using the key block principle[A].In:Proceedings of the 23~(rd) US symposium of Rock Mechanics [C],1982:883-898
14.R.E.Goodman.Block theory and its application[J].Geo-technique,1995,3:383-423.
15.任青文.块体单元法及其在岩体稳定分析中的应用[J].河海大学学报,1995,23(1):1-7.
16.G.H.Shi.Discontinuous Deformation Analysis—A New Numerical Model for the Statics and Dynamics of Block Systems[D].Department of Civil Engineering University of California,Berkeley,1988,August.
17.石根华著,裴觉民译.数值流行方法与非连续变形分析[M].北京,清华大学出版社,1997.
18.M.M.MacLaughlin,D.M.Doolin.Review of validation of the discontinuous deformation analysis(DDA) method[J].INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS,2006,30(4):271-305
19.T.C.Ke,R.E.Goodman.Discontinuous deformation analysis and the artificial joint concept [J].Rock Mechanics(Nelson Lanbach Edited),Balkema,1994:599-606.
20.B.Amadei,C.T.Lin,S.Sture,J.Jung.Modeling fracture of rock masses with the DDA method[J].Rock Mechanics(Nelson Laubach Edited),Balkema,1994:583-590.
21.C.Lin,B.Amadei,J.Jung,J.Dwyer.Extensions of discontinuous deformation analysis for jointed rock masses[J].Int.J.Rock.Mech.Min.Sci.&Geotech.Abstr,1996,33(7):671-694.
22.刘军,李仲奎.非连续变形分析(DDA)中的块体单元形成,中国岩石力学与工程学会第七次学术大会论文集(M):334-338
23.C.Y.Wang,C.C.Chuang and J.Sheng.Time Integration Theories for the DDA Method with Finite Element Meshes[A].In:proc.15 Int.Forum on DDA[C].Berkeley,1996:263-287.
24.T.C.Chang.Nonlinear Dynamic Discontinuous Deformation Analysis with Finite Element Meshed Block Systems[D].University of California at Berkeley,1994.
25.G.Chen,Y.A.Ohnishi.Non-linear model for discontinuities in DDA[A],In:Proc.of the Third International Conference on Analysis of Discontinuous Deformation[C].Colorado,ARMA,1999:57-64.
26.S.C.Lee.Linear and Nonlinear modeling of viscous geo-materials with DDA[D].University of Colorado,2002.
27.姜清辉,周创兵,罗先启,郑宏.三维DDA与有限元的耦合分析方法及其应用[J].岩土工程学报,2006,28(8):998-1001.
28.J.C.Chern,C.Y.Koo,S.Chen.Development of Second Order Displacement Function for DDA and Manifold Method[A].In:Working Forum on the Manifold Method of Material Analysis[C],Vicksburg,1990:183-202
29.C.Y.Koo,J.C.Chem.The development of DDA with third order displacement function[A]. In:Proceedings of the First International Forum Discontinuous Deformation Analysis(DDA)and Simulations Discontinuous media[C],Berkeley,USA,1996:342-350.
30.C.Y.Koo,J.C.Chern.Modification of the DDA method for rigid block problems[J].Int J.of Rock Mech&Min.Sci,1998,35(6):683-693.
31.马永政,郑宏等.耦合无网格法的非连续变形分析法研究[J].岩石力学与工程学报,2007,26(增2):4195-4201。
32.马永政,郑宏等.应用自然邻接点插值法的块体非连续变形分析[J].岩土力学,2008,29(1):119-124。
33.Z.Y.Zhao,G.Jiong.Stress recovery procedure for discontinuous deformation analysis[J].Advance in Engneering Software,2009,40:52-57
34.G.H.Shi.Producing joint polygons,cutting joint blocks and finding key blocks for general free surface surfaces[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(11):2161-2170
35.陈文胜,郑宏等.岩石块体三维接触判断的侵入边法[J].岩石力学与工程学报,2004,23(4):565-571,.
36.J.Q.Wang,G.Lin.Static and dynamic stability analysis using 3D-DDA with incision body scheme[J].Earthquake Engineering and Engineering Vibration,2006,5(2):273-284,.
37.J.Liu,Q.D.Geng,X.J.Kong.A fast common plane identification algorithm for 3D contact problems[J].Computers and Geotechnics,2009,36:41-51
38.R.K.All,J.Ahmad,J.H.Wu.A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2008,35:746-759
39.S.A.R.Beyabanaki,R.G.Mikola,K.Hatami.Three-dimensional discontinuous deformation analysis(3-D DDA) using a new contact resolution algorithm[J].Computers and Geotechnics,2008,35:346-56
40.M.R.Yeung,Q.H.Jiang,N.Sun.A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2007,34:175-86
41.Y.M.Cheng.Advances and improvements in discontinuous deformation analysis[J].Computers and Geotechnics,1998,22(2):153-163
42.L.B.Hilbert,W.Yi,N.Cook,Y.Cai,G.P.Liang.A new discontinuous finite element method for interaction of many deformable bodies in geomechanics[A].In:Pro 8~(th) Int.Conf.on Computer Methods and Advances in Geomechanics[C],1994:831-836
43.Y.E.Cai,G.P.Liang,G.H.Shi,N.Cook.Studying impact problem by LDDA method,Discontinuous Deformation analysis(DDA) and Simulations of discontinuous media[M].TSI Press,1996.
44.蔡永恩,梁国平,殷有泉.多弹性体系统动力分析的LDDA方法[J].固体力学学报,2000,21(增刊):182-191,
45.张秀丽.断续节理岩体破坏过程的数值分析方法研究[D].中国科学院博士学位论文,2007.
46.马永政.非连续变形位移分析法位移模式改进及工程应用[D].中国科学院博士学位论文,2007.
47.郑宏,葛修润.改进的预处理共轭斜量法及其在工程有限元分析中的应用[J].应用数学和力学,1993,14(4):353-361.
48.M.Benzi,M.J.Gander,G.H.Golub.Optimization of the Hermitian and Skew-Hermitian splitting iteration for saddle point problems[A].BIT Numerical Mathematics,2003,43:881-900
49.郑宏,刘德富,黄哲聪.Lagrange方程组的直接解法[J].岩石力学与工程学报,2006,25(10):2079-2085.
50.郑宏,谭国焕,刘德富.近似对称矩阵的直接解法及其应用[J].岩土力学,2006,27(11):1180-1184
51.T.C.Ke,J.D.Bray.Modeling of particular media using discontinuous deformation analysis[J].JOURNAL OF ENGINEERING MECHANICS-ASCE,1995,121(11):1234-1243
52.P.A.Thomas,J.D.Bray,T.C.Ke.Discontinuous deformation analysis for soil mechanics[A].In:Proc.of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:454-462
53.O.Yuzo,M.Shigeru.Development of circular and elliptic disc elements for DDA[A].In:Proc.of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:44-52
54.P.A.Thomas,J.D.Bray.Capturing nonspherical shape of granular media with disk clusters[J].Journal of Geotechnical and Geoenvironmental Engoneering,1999,3:169-178
55.M.J.Jiang,H.S.Yu,D.Harris.A novel discrete model for granular material incorporating rolling resistance[J].Computers and Geotechnics,2005,32:340-357
56.张国新,李广信,郭瑞平.不连续变形分析与土的应力应变关系[J].清华大学学报(自然科学版),2000,40(8):102-105
57.T.C.Ke.The issue of rigid-body rotation in DDA[A].In:proc.First Int.Forum on DDA[C].Berkeley,1996:318-325.
58.M.M.Mary,S.Nicholas.Rigid-body rotations in DDA[A].In:proc.First Int.Forum on DDA [C].Berkeley,1996:620-636.
59.J.M.Pei.The effects of energy loss in block bumping on discontinuous deformation[A].In:Proc.of the First International Forum on Discontinuous De formation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:401-407.
60.王书法,朱维申.考虑空间影响的两种非连续变形分析方法[J].岩石力学与工程学报,2000,19(3):369-372
61.刘军,李仲奎.非连续变形分析(DDA)方法研究现状及发展趋势[J].岩石力学与工程学报,2004,23(5):839-845.
62.V.Kveldsvik,H.H.Einstein,B.Nilsen,L.H.Blikra.Numerical Analysis of the 650,000 m2Aknes Rock Slope based on Measured Displacements and Geotechnical Data.Rock Mech Rock Eng,Springer-Verlag,2008
63.G.C.Ma,A.Yashima,etal.Application of DDA to evaluate the mechanism of rock slope instabilityrock fall[A].In:3RD INTERNATIONAL SYMPOSIUM ON MODERN MINING & SAFETY TECHNOLOGY PROCEEDINGS,2008:67-78
64.J.H.Wu.Applying discontinuous deformation analysis to assess the constrained area of the unstable Chiu-fen-erh-shan landslide slope[A].In:INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS[C],2007,31(5):649-666
65.M.Moosavi,R.Grayeli.A model for cable bolt-rock mass interaction:Integration with discontinuous deformation analysis(DDA) algorithm[J].International Journal of Rock Mechanics & Mining Sciences,2006,43:661-670
66.R.Grayeli.Reinforcement design of blocky rock masses with cable bolts in Discontinuous Deformation Analysis(DDA) algorithm.ROCK MECHANICS:MEETING SOCIETY'S CHALLENGES AND DEMANDS,VOLS 1 AND 2-VOL:FUNDAMENTALS,NEW TECHNOLOGIES & NEW IDEAS;VOL 2:CASE HISTORIES,2007:1525-1531.
67.D.B.Mazor,Y.H.Hatzor,W.S.Dershowitz.Modeling mechanical layering effects on stability of underground openings in jointed sedimentary rocks[J].International Journal of Rock Mechanics & Mining Sciences,2009,46:262-271
68.M.Tsesarsky,Y.H.Hatzor.Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction-A parametric study using discontinuous deformation analysis(DDA)[J].Tunnelling and Underground Space Technology,2006,21:29-45
69.蔡永恩,罗纲等.不连续岩体-拱坝系统的动力过程数值模拟方法[J].岩土力学,2004,25(增2):361-365.
70.刘君,陈健云等.基于DDA和FEM耦合方法的碾压混凝土坝抗震安全性分析[J].大连理工大学学报,2003,43(6):793-798,
71.Z.A.Chen,B.H.Ling,W.M.Bai.3-D numerical simulation on influence of 1997 Mani earthquake occurrence to stability of tectonic blocks system in Qingzang and Chuandian zone using DDA plus FEM method[A].CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION,51(5):1422-1430
72.J.S.Sun,Q.H.Zhu,W.B.Lu.Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions[J].China Univ Mining & Technol,2007,17(4):0552-0556
73.R.Kamai,Y.H.Hatzor.Numerical analysis of block stone displacements in ancient masonry structures-A new method to estimate historic ground motions[J].INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS,2008,32(11):1321-1340
74.Y.Y.Jiao,X.L.Zhang,J.Zhao,Q.S.Liu.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics & Mining Sciences,2007,44:1070-1076
75.彼得.艾伯哈特,胡斌.现代接触动力学[M],南京,东南大学出版社,2003
76.B.Amadei,C.T.Lin,J.Dwyer.Recent extensions to the DDA method[A].Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations Of Discontinuous Media.Berkeley,CA,1996.
77.刘军,李仲奎.非连续变形分析方法中一些控制参数的设置[J].成都理工大学学报(自然 科学版),2004,31(5):522-526.
78.M.David,A.M.Doolin,N.Sitar.Displacement accuracy of Discontinuous Deformation Analysis method applied to sliding block[J].Journal of Engineering Mechanics,2002,12:1158-1168.
79.江巍,郑宏.非连续变形分析方法中人为参数的影响[J].岩土力学,2007,12:2603-2606.
80.郑宏.岩土力学中的几类非线性问题[博士论文D].中国科学院武汉岩土力学研究所,2000年10月.
81.F.Facchinei,J.S.Pang.Finite-dimensional variational inequalities and complementary problems[M].NewYork,Springer,2003.
82.韩继业,修乃华,戚厚铎.非线性互补理论及算法[M].上海,上海科学技术出版社,2006
83.C.E.Lemke,J.T.Howson.Equilibrium points of bimatrix games[J].SLAM Journal on Applied Mathematics,1964,12:413-423.
84.O.L.Mangasarian.Solution of symmetric linear complementarity problems by iterative methods[J].Journal of Optimization Theory and Appliications,1977,22:465-485.
85.S.C.Billups,K.G.Murty.Complementary problems[J].Journal of Computational and Applied Mathematics,2000,124:303-318.
86.修乃华,高自友.互补问题算法的新进展[J].数学进展,1999,28(3):193-210.
87.R.W.Cottle,J.S.Pang,R.E.Stone.The linear Complementary Problem[M].Academic Press,Boston,MA,1992
88.K.G.Murty.Linear Complementary,Linear and Nonlinear Programming[A],Heldermann Verlag,Berlin,1988,Free public access at http://www-personal.engin.umich.edu/～Murty /book/LCPbook/index.html
89.N.Karmarkar.A new polynomial-time algorithm for linear programming[M].Combinatorica,1984,4:373-395
90.S.J.Wright.Primal-dual interior-point methods[A].SLAM,Philadelphia,PA,1997.
91.M.Kojima,S.Mizuno,A.Yoshise.A polynomial-time algorithm for a class of linear complementarity problems[J].Mathematical Programming,1989,44:1-26
92.I.J.Lusting,R.E.Marsten,D.F.Shanno.Interior point methods for linear programming:computational state of the art[J].ORSA Journal on Computing,1994,6(1):1-14
93.A.Fischer.A special Newton-type optimization method[J].Optimization,1992,24:269-284.
94.O.L.Mangasarian.Equivalence of the complementarity problem to a system of nonlinear equations[J].SLAM Journal on Applied Mathematics,1976,31:89-92.
95.M.C.Ferris,C.Kanzow.Complementarity and related problems:A survey[A].In:P.M.Pardalos and M.G.C.Resende(eds.):Handbook on Applied Optimization[C].Oxford University Press,New York,2002:514-530.
96.李学文.三维摩擦接触问题的非光滑方程组方法研究[博士论文D],大连理工大学,2000年6月.
97.G.M.Korpelevich.The extragradient method for finding saddle points and other problems [M].Matecon,1976,12:747
98.B.S.He.A projection and contraction method for a class linear complementarity problems and its application in convex quadratic programming[J].Appl.Math.Optim,1992,25:247-262
99.M.V.Solodov,P.Tseng.Modified Projection-type Methods for Monotone Variational Inequalities[J].SLAM Joural on Control and Optimization,1996,34:1814-1830
100.孙德峰.广义非线性互补问题的投影梯度法[J].计算数学,1995,19:183-194
101.M.C.Ferris,C.Kanzow.Complementarity and related problems:A survey[A].In:P.M.Pardalos and M.G.C.Resende(eds.):Handbook on Applied Optimization[C],Oxford University Press,New York,2002:514-530
102.甯尤军,杨军.增广拉格朗日接触的DDA方法研究[J].计算力学学报,2009,12:2603-2606
103.M.R.Yeung.Application of Shi's discontinuous deformation analysis to the study of rock behavior[D].Berkeley:University of California,Berkeley,1991
104.H.Zheng,D.F.Liu.A new formulation of Signorini's type for seepage problems with free surface[J].International Journal for Numerical Methods in Engineering,2005,64(1):1-16.
105.左东启,王世夏,林益才.水工建筑物[M].南京:河海大学出版社,1995:85-164
106.李董辉.数值最优化[M].科学出版社,2005.
107.何素艳.互补问题算法研究及其在力学中的应用[博士论文D].大连理工大学,2003年7月.
108.尤明庆.岩石试样的强度及变形破坏过程.[M].北京,地质出版社,2000年
109.周思孟.复杂岩体若干岩石力学问题.[M].中国水利水电出版社.1998年6月.
110.陈祖煜.土质边坡稳定分析:原理.方法.程序[M].北京,中国水利水电出版社,2003
111.J.M.Duncan.State of the art:limit equilibrium and finite element analysis of slope[J].Journal of Geo-technical Engineering,ASCE,1996,122(7):577-596.
112.O.C.Zienkiewicz,C.Humpheson,R.W.Lewis.Associated and Non-Associated Visco-P lasticity and Plasticity in Soil Mechanics[J].Geo technique,1975,25(4):671-689.
113.宋二祥.土工结构安全系数的有限元计算[J].岩土工程学报,1997,19(2):127.
114.K.Ugai.A Method of Calculation of Total Factor of Safety of Slopes by Elasto-Plastic FEM [J].Soils and Foundations.JGS,Japanese,1989,29(2):190-195.
115,郑宏,李春光,李焯芬等.求解安全系数的有限元法[J].岩土工程学报,2002,24(5):626-628.
116.张鲁渝,郑颖人,赵尚毅等.有限元强度折减系数法-计算土坡稳定安全系数的精度研究[J].水利学报,2003,(1):21-27.
117.D.V.Griffiths,P.A.Lane.Slope Stability Analysis by Finite Elements[J].Geo technique,1999,49(3):387-403.
118.E.M.Dawson,W.H.Roth,A.Drescher.Slope Stability Analysis by Strength Reduction[J].Geotechnique,1999,49(6):835-840.
119.T.Matsui,K.C.San.Finite Element Slope Stability Analysis by Shear Strength Reduction Technique[J].Soils and foundations,JSSM FE,1992,32(1):59-70.
120.连镇营.基坑工程三维有限元数值分析中若干问题的研究[博士论文D].大连理工大学,2001.
121.郑颖人,赵尚毅,宋雅坤.有限元强度折减法研究进展[J].后勤工程学院学报,2005,3:1-6.
122.E.Hoek,J.W.Bray,卢世宗译.岩石边坡工程[M].北京,冶金工业出版社,1983
123.孙东亚,彭一江,王兴珍.DDA数值方法在岩质边坡倾倒破坏分析中的应用[J].岩石力学与工程学报,2002,21(1):39-42.
124.张国新,武晓峰.裂隙渗流对岩石边坡稳定的影响——渗流、变形耦合作用的DDA法[J].岩石力学与工程学报,2003,22(8):1269-1275.
125.M.MacLaughlin,N.Sitar,D.Doolin,T.Abbot.Investigation of slope-stability kinematics using discontinuous deformation analysis[J].International Journal of Rock Mechanics &Mining Sciences,2001,38:753-762.
126.沈振中,大西有三.基于非连续变形分析的水库岩体边坡稳定分析方法[J].水利学报,2004,3:117-122.
127.J.M.Pei,Z.H.Lu.An application of DDA to a jointed rock slope[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:395-401.
128.T.C.Ke.Application of DDA to stability analysis of rock masses[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:334-342.
129.X.C.Dong,A.Q.Wu,F.Ren.A preliminary application of discontinuous deformation analysis to the three gorges project on Yangtze River China[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:310-318.
130.S.L.Zhao,M.R.Salami,M.S.Rahman.Discontinuous deformation analysis simulation of rock slope failure processes[A].In:Proc of 9th International Conference on Computer Methods and Advances in Geomechanics[C].Rotterdam,A.A.Balkema,1997:473-477.
131.G.Q.Chen,Ohnishi.Slope stability analysis using discontinuous deformation analysis method[A].In:Rock Mecganics for Industry[C].[s.I.]:[s.n.],1999,I:535-541.
132.Y.H.Hatzor.Dynamic rock slope stability analysis at masada national monument using block theory and DDA[A].In:Rock Mechanics for Industry[C].[s.I.]:[s.n.],I999,I:63-70.
133.周少怀,杨家岭.DDA数值方法及工程应用[J].岩土力学,2000,21(2):123-125.
134.郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用[J].岩石力学与工程学报,2004,23(19):3381-3388
135.郑颖人,赵尚毅.用有限元法求边坡稳定安全系数[J].公路交通技术,2002,1:7-9
136.郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析[J].中国工程科学,2002,4(10):57-61
137.H.Zheng,D.F.Liu,C.G.Li.Slope stability analysis based on elasto-plastic finite element method[J].International Journal for Numerical Methods in Engineering,2005,64(14):1871-1888
138.黄盛俭,刘君,孔宪京.强度折减DDA法及其在边坡稳定分析中的应用[J].岩石力学与工程学报,2008,27(增1):2799-2806.
139.江巍.非连续变形分析方法中的几个问题[硕士论文D].三峡大学,2006年6月.
140.混凝土重力坝设计规范(SL 319-2005).中华人民共和国水利部,2005
141.日本财团法人大坝技术中心:多目的大坝的建设.(株)技报堂出版,1987
142.Y.I.Kim,B.Amadei,E.Pan.Modeling the effect of geology on uplift in concrete gravity dam foundations with the discontinuous deformation analysis[A].In:Rock Mechanics for Industry[C].[s.I.]:[s.n.],1999,I:527-534
143.张国新,金峰.重力坝抗滑稳定分析中DDA与有限元方法的比较[J].水力发电学报,2004,23(1):10-14
144.姜清辉,丰定祥.三维非连续变形分析方法中的锚杆模拟[J].岩土力学,2001,22(2):176-178
145.张秀丽,焦玉勇,刘泉声.非连续变形分析(DDA)方法中的预应力锚杆模拟[J].地下空间与工程学报,2008,4(1):38-41
2.沈珠江.关于计算岩土力学发展前景的几点看法,南京水利科学研究院,210029;清华大学水利水电工程系,100084.
3.R.E.Goodman,R.Taylor and T.L.Brekke.A Model for the Mechanics of Jointed Rock[J].Journal of the Soil Mechanics & Foundations Dvi.,ASCE 1968,94:637
4.M.G.Katona.A simple contact-friction interface element with application to buried culverts [J].Int J Num Anal Meth Geomech 1983,7:371-84
5.H.Zheng,D.F.Liu,C.F.Lee,Z.Q.Yue.A sophisticated node-pair model for interface problems[J].Computers and Geotechnics 2004,31:137-153
6.C.S.Desai,M.M.Zaman,J.G.Lightener,H.J.Siriwardane.Thin layer element for interfaces and joints[J].Int J Num Anal Meth Geomech 1984,8:19-43.
7.郑宏,葛修润,李焯芬.界面问题的混合有限元法[J].岩石力学与工程学报,2002,21(1):1-8.
8.B.C.Burman.Development of a numerical model for discontinua[J].Australian Geomechanics Journal,1974,G4(1):13-22.
9.T.Kawai.A new discrete analysis of nonlinear solid mechanics problems involving stability,plasticity and crack[J].Proceedings of the symposium on Applications of computer Methods in Engineering,Los Angeles,1977,Calif:1029-1038.
10.卓家寿,章青.不连续介质力学问题的界面元法[M].北京,科学出版社,2000.
11.P.A.Cundall.A computer model for simulating progressive,large-scale movements in blocky rock systems[J].Proceedings of the symposium of the International Society of Rock Mechanics,1971,Nancy,France,Vol(1):1-8.
12.王泳嘉,刑纪波.离散单元法及其在岩土力学中的应用[M].东北工学院出版社,1991.
13.R.E.Goodman,G.H.Shi,W.Boyle.Calculation of support for hard,jointed rock using the key block principle[A].In:Proceedings of the 23~(rd) US symposium of Rock Mechanics [C],1982:883-898
14.R.E.Goodman.Block theory and its application[J].Geo-technique,1995,3:383-423.
15.任青文.块体单元法及其在岩体稳定分析中的应用[J].河海大学学报,1995,23(1):1-7.
16.G.H.Shi.Discontinuous Deformation Analysis—A New Numerical Model for the Statics and Dynamics of Block Systems[D].Department of Civil Engineering University of California,Berkeley,1988,August.
17.石根华著,裴觉民译.数值流行方法与非连续变形分析[M].北京,清华大学出版社,1997.
18.M.M.MacLaughlin,D.M.Doolin.Review of validation of the discontinuous deformation analysis(DDA) method[J].INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS,2006,30(4):271-305
19.T.C.Ke,R.E.Goodman.Discontinuous deformation analysis and the artificial joint concept [J].Rock Mechanics(Nelson Lanbach Edited),Balkema,1994:599-606.
20.B.Amadei,C.T.Lin,S.Sture,J.Jung.Modeling fracture of rock masses with the DDA method[J].Rock Mechanics(Nelson Laubach Edited),Balkema,1994:583-590.
21.C.Lin,B.Amadei,J.Jung,J.Dwyer.Extensions of discontinuous deformation analysis for jointed rock masses[J].Int.J.Rock.Mech.Min.Sci.&Geotech.Abstr,1996,33(7):671-694.
22.刘军,李仲奎.非连续变形分析(DDA)中的块体单元形成,中国岩石力学与工程学会第七次学术大会论文集(M):334-338
23.C.Y.Wang,C.C.Chuang and J.Sheng.Time Integration Theories for the DDA Method with Finite Element Meshes[A].In:proc.15 Int.Forum on DDA[C].Berkeley,1996:263-287.
24.T.C.Chang.Nonlinear Dynamic Discontinuous Deformation Analysis with Finite Element Meshed Block Systems[D].University of California at Berkeley,1994.
25.G.Chen,Y.A.Ohnishi.Non-linear model for discontinuities in DDA[A],In:Proc.of the Third International Conference on Analysis of Discontinuous Deformation[C].Colorado,ARMA,1999:57-64.
26.S.C.Lee.Linear and Nonlinear modeling of viscous geo-materials with DDA[D].University of Colorado,2002.
27.姜清辉,周创兵,罗先启,郑宏.三维DDA与有限元的耦合分析方法及其应用[J].岩土工程学报,2006,28(8):998-1001.
28.J.C.Chern,C.Y.Koo,S.Chen.Development of Second Order Displacement Function for DDA and Manifold Method[A].In:Working Forum on the Manifold Method of Material Analysis[C],Vicksburg,1990:183-202
29.C.Y.Koo,J.C.Chem.The development of DDA with third order displacement function[A]. In:Proceedings of the First International Forum Discontinuous Deformation Analysis(DDA)and Simulations Discontinuous media[C],Berkeley,USA,1996:342-350.
30.C.Y.Koo,J.C.Chern.Modification of the DDA method for rigid block problems[J].Int J.of Rock Mech&Min.Sci,1998,35(6):683-693.
31.马永政,郑宏等.耦合无网格法的非连续变形分析法研究[J].岩石力学与工程学报,2007,26(增2):4195-4201。
32.马永政,郑宏等.应用自然邻接点插值法的块体非连续变形分析[J].岩土力学,2008,29(1):119-124。
33.Z.Y.Zhao,G.Jiong.Stress recovery procedure for discontinuous deformation analysis[J].Advance in Engneering Software,2009,40:52-57
34.G.H.Shi.Producing joint polygons,cutting joint blocks and finding key blocks for general free surface surfaces[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(11):2161-2170
35.陈文胜,郑宏等.岩石块体三维接触判断的侵入边法[J].岩石力学与工程学报,2004,23(4):565-571,.
36.J.Q.Wang,G.Lin.Static and dynamic stability analysis using 3D-DDA with incision body scheme[J].Earthquake Engineering and Engineering Vibration,2006,5(2):273-284,.
37.J.Liu,Q.D.Geng,X.J.Kong.A fast common plane identification algorithm for 3D contact problems[J].Computers and Geotechnics,2009,36:41-51
38.R.K.All,J.Ahmad,J.H.Wu.A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2008,35:746-759
39.S.A.R.Beyabanaki,R.G.Mikola,K.Hatami.Three-dimensional discontinuous deformation analysis(3-D DDA) using a new contact resolution algorithm[J].Computers and Geotechnics,2008,35:346-56
40.M.R.Yeung,Q.H.Jiang,N.Sun.A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis[J].Computers and Geotechnics,2007,34:175-86
41.Y.M.Cheng.Advances and improvements in discontinuous deformation analysis[J].Computers and Geotechnics,1998,22(2):153-163
42.L.B.Hilbert,W.Yi,N.Cook,Y.Cai,G.P.Liang.A new discontinuous finite element method for interaction of many deformable bodies in geomechanics[A].In:Pro 8~(th) Int.Conf.on Computer Methods and Advances in Geomechanics[C],1994:831-836
43.Y.E.Cai,G.P.Liang,G.H.Shi,N.Cook.Studying impact problem by LDDA method,Discontinuous Deformation analysis(DDA) and Simulations of discontinuous media[M].TSI Press,1996.
44.蔡永恩,梁国平,殷有泉.多弹性体系统动力分析的LDDA方法[J].固体力学学报,2000,21(增刊):182-191,
45.张秀丽.断续节理岩体破坏过程的数值分析方法研究[D].中国科学院博士学位论文,2007.
46.马永政.非连续变形位移分析法位移模式改进及工程应用[D].中国科学院博士学位论文,2007.
47.郑宏,葛修润.改进的预处理共轭斜量法及其在工程有限元分析中的应用[J].应用数学和力学,1993,14(4):353-361.
48.M.Benzi,M.J.Gander,G.H.Golub.Optimization of the Hermitian and Skew-Hermitian splitting iteration for saddle point problems[A].BIT Numerical Mathematics,2003,43:881-900
49.郑宏,刘德富,黄哲聪.Lagrange方程组的直接解法[J].岩石力学与工程学报,2006,25(10):2079-2085.
50.郑宏,谭国焕,刘德富.近似对称矩阵的直接解法及其应用[J].岩土力学,2006,27(11):1180-1184
51.T.C.Ke,J.D.Bray.Modeling of particular media using discontinuous deformation analysis[J].JOURNAL OF ENGINEERING MECHANICS-ASCE,1995,121(11):1234-1243
52.P.A.Thomas,J.D.Bray,T.C.Ke.Discontinuous deformation analysis for soil mechanics[A].In:Proc.of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:454-462
53.O.Yuzo,M.Shigeru.Development of circular and elliptic disc elements for DDA[A].In:Proc.of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:44-52
54.P.A.Thomas,J.D.Bray.Capturing nonspherical shape of granular media with disk clusters[J].Journal of Geotechnical and Geoenvironmental Engoneering,1999,3:169-178
55.M.J.Jiang,H.S.Yu,D.Harris.A novel discrete model for granular material incorporating rolling resistance[J].Computers and Geotechnics,2005,32:340-357
56.张国新,李广信,郭瑞平.不连续变形分析与土的应力应变关系[J].清华大学学报(自然科学版),2000,40(8):102-105
57.T.C.Ke.The issue of rigid-body rotation in DDA[A].In:proc.First Int.Forum on DDA[C].Berkeley,1996:318-325.
58.M.M.Mary,S.Nicholas.Rigid-body rotations in DDA[A].In:proc.First Int.Forum on DDA [C].Berkeley,1996:620-636.
59.J.M.Pei.The effects of energy loss in block bumping on discontinuous deformation[A].In:Proc.of the First International Forum on Discontinuous De formation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque:TSI Press,1996:401-407.
60.王书法,朱维申.考虑空间影响的两种非连续变形分析方法[J].岩石力学与工程学报,2000,19(3):369-372
61.刘军,李仲奎.非连续变形分析(DDA)方法研究现状及发展趋势[J].岩石力学与工程学报,2004,23(5):839-845.
62.V.Kveldsvik,H.H.Einstein,B.Nilsen,L.H.Blikra.Numerical Analysis of the 650,000 m2Aknes Rock Slope based on Measured Displacements and Geotechnical Data.Rock Mech Rock Eng,Springer-Verlag,2008
63.G.C.Ma,A.Yashima,etal.Application of DDA to evaluate the mechanism of rock slope instabilityrock fall[A].In:3RD INTERNATIONAL SYMPOSIUM ON MODERN MINING & SAFETY TECHNOLOGY PROCEEDINGS,2008:67-78
64.J.H.Wu.Applying discontinuous deformation analysis to assess the constrained area of the unstable Chiu-fen-erh-shan landslide slope[A].In:INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS[C],2007,31(5):649-666
65.M.Moosavi,R.Grayeli.A model for cable bolt-rock mass interaction:Integration with discontinuous deformation analysis(DDA) algorithm[J].International Journal of Rock Mechanics & Mining Sciences,2006,43:661-670
66.R.Grayeli.Reinforcement design of blocky rock masses with cable bolts in Discontinuous Deformation Analysis(DDA) algorithm.ROCK MECHANICS:MEETING SOCIETY'S CHALLENGES AND DEMANDS,VOLS 1 AND 2-VOL:FUNDAMENTALS,NEW TECHNOLOGIES & NEW IDEAS;VOL 2:CASE HISTORIES,2007:1525-1531.
67.D.B.Mazor,Y.H.Hatzor,W.S.Dershowitz.Modeling mechanical layering effects on stability of underground openings in jointed sedimentary rocks[J].International Journal of Rock Mechanics & Mining Sciences,2009,46:262-271
68.M.Tsesarsky,Y.H.Hatzor.Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction-A parametric study using discontinuous deformation analysis(DDA)[J].Tunnelling and Underground Space Technology,2006,21:29-45
69.蔡永恩,罗纲等.不连续岩体-拱坝系统的动力过程数值模拟方法[J].岩土力学,2004,25(增2):361-365.
70.刘君,陈健云等.基于DDA和FEM耦合方法的碾压混凝土坝抗震安全性分析[J].大连理工大学学报,2003,43(6):793-798,
71.Z.A.Chen,B.H.Ling,W.M.Bai.3-D numerical simulation on influence of 1997 Mani earthquake occurrence to stability of tectonic blocks system in Qingzang and Chuandian zone using DDA plus FEM method[A].CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION,51(5):1422-1430
72.J.S.Sun,Q.H.Zhu,W.B.Lu.Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions[J].China Univ Mining & Technol,2007,17(4):0552-0556
73.R.Kamai,Y.H.Hatzor.Numerical analysis of block stone displacements in ancient masonry structures-A new method to estimate historic ground motions[J].INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS,2008,32(11):1321-1340
74.Y.Y.Jiao,X.L.Zhang,J.Zhao,Q.S.Liu.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics & Mining Sciences,2007,44:1070-1076
75.彼得.艾伯哈特,胡斌.现代接触动力学[M],南京,东南大学出版社,2003
76.B.Amadei,C.T.Lin,J.Dwyer.Recent extensions to the DDA method[A].Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations Of Discontinuous Media.Berkeley,CA,1996.
77.刘军,李仲奎.非连续变形分析方法中一些控制参数的设置[J].成都理工大学学报(自然 科学版),2004,31(5):522-526.
78.M.David,A.M.Doolin,N.Sitar.Displacement accuracy of Discontinuous Deformation Analysis method applied to sliding block[J].Journal of Engineering Mechanics,2002,12:1158-1168.
79.江巍,郑宏.非连续变形分析方法中人为参数的影响[J].岩土力学,2007,12:2603-2606.
80.郑宏.岩土力学中的几类非线性问题[博士论文D].中国科学院武汉岩土力学研究所,2000年10月.
81.F.Facchinei,J.S.Pang.Finite-dimensional variational inequalities and complementary problems[M].NewYork,Springer,2003.
82.韩继业,修乃华,戚厚铎.非线性互补理论及算法[M].上海,上海科学技术出版社,2006
83.C.E.Lemke,J.T.Howson.Equilibrium points of bimatrix games[J].SLAM Journal on Applied Mathematics,1964,12:413-423.
84.O.L.Mangasarian.Solution of symmetric linear complementarity problems by iterative methods[J].Journal of Optimization Theory and Appliications,1977,22:465-485.
85.S.C.Billups,K.G.Murty.Complementary problems[J].Journal of Computational and Applied Mathematics,2000,124:303-318.
86.修乃华,高自友.互补问题算法的新进展[J].数学进展,1999,28(3):193-210.
87.R.W.Cottle,J.S.Pang,R.E.Stone.The linear Complementary Problem[M].Academic Press,Boston,MA,1992
88.K.G.Murty.Linear Complementary,Linear and Nonlinear Programming[A],Heldermann Verlag,Berlin,1988,Free public access at http://www-personal.engin.umich.edu/～Murty /book/LCPbook/index.html
89.N.Karmarkar.A new polynomial-time algorithm for linear programming[M].Combinatorica,1984,4:373-395
90.S.J.Wright.Primal-dual interior-point methods[A].SLAM,Philadelphia,PA,1997.
91.M.Kojima,S.Mizuno,A.Yoshise.A polynomial-time algorithm for a class of linear complementarity problems[J].Mathematical Programming,1989,44:1-26
92.I.J.Lusting,R.E.Marsten,D.F.Shanno.Interior point methods for linear programming:computational state of the art[J].ORSA Journal on Computing,1994,6(1):1-14
93.A.Fischer.A special Newton-type optimization method[J].Optimization,1992,24:269-284.
94.O.L.Mangasarian.Equivalence of the complementarity problem to a system of nonlinear equations[J].SLAM Journal on Applied Mathematics,1976,31:89-92.
95.M.C.Ferris,C.Kanzow.Complementarity and related problems:A survey[A].In:P.M.Pardalos and M.G.C.Resende(eds.):Handbook on Applied Optimization[C].Oxford University Press,New York,2002:514-530.
96.李学文.三维摩擦接触问题的非光滑方程组方法研究[博士论文D],大连理工大学,2000年6月.
97.G.M.Korpelevich.The extragradient method for finding saddle points and other problems [M].Matecon,1976,12:747
98.B.S.He.A projection and contraction method for a class linear complementarity problems and its application in convex quadratic programming[J].Appl.Math.Optim,1992,25:247-262
99.M.V.Solodov,P.Tseng.Modified Projection-type Methods for Monotone Variational Inequalities[J].SLAM Joural on Control and Optimization,1996,34:1814-1830
100.孙德峰.广义非线性互补问题的投影梯度法[J].计算数学,1995,19:183-194
101.M.C.Ferris,C.Kanzow.Complementarity and related problems:A survey[A].In:P.M.Pardalos and M.G.C.Resende(eds.):Handbook on Applied Optimization[C],Oxford University Press,New York,2002:514-530
102.甯尤军,杨军.增广拉格朗日接触的DDA方法研究[J].计算力学学报,2009,12:2603-2606
103.M.R.Yeung.Application of Shi's discontinuous deformation analysis to the study of rock behavior[D].Berkeley:University of California,Berkeley,1991
104.H.Zheng,D.F.Liu.A new formulation of Signorini's type for seepage problems with free surface[J].International Journal for Numerical Methods in Engineering,2005,64(1):1-16.
105.左东启,王世夏,林益才.水工建筑物[M].南京:河海大学出版社,1995:85-164
106.李董辉.数值最优化[M].科学出版社,2005.
107.何素艳.互补问题算法研究及其在力学中的应用[博士论文D].大连理工大学,2003年7月.
108.尤明庆.岩石试样的强度及变形破坏过程.[M].北京,地质出版社,2000年
109.周思孟.复杂岩体若干岩石力学问题.[M].中国水利水电出版社.1998年6月.
110.陈祖煜.土质边坡稳定分析:原理.方法.程序[M].北京,中国水利水电出版社,2003
111.J.M.Duncan.State of the art:limit equilibrium and finite element analysis of slope[J].Journal of Geo-technical Engineering,ASCE,1996,122(7):577-596.
112.O.C.Zienkiewicz,C.Humpheson,R.W.Lewis.Associated and Non-Associated Visco-P lasticity and Plasticity in Soil Mechanics[J].Geo technique,1975,25(4):671-689.
113.宋二祥.土工结构安全系数的有限元计算[J].岩土工程学报,1997,19(2):127.
114.K.Ugai.A Method of Calculation of Total Factor of Safety of Slopes by Elasto-Plastic FEM [J].Soils and Foundations.JGS,Japanese,1989,29(2):190-195.
115,郑宏,李春光,李焯芬等.求解安全系数的有限元法[J].岩土工程学报,2002,24(5):626-628.
116.张鲁渝,郑颖人,赵尚毅等.有限元强度折减系数法-计算土坡稳定安全系数的精度研究[J].水利学报,2003,(1):21-27.
117.D.V.Griffiths,P.A.Lane.Slope Stability Analysis by Finite Elements[J].Geo technique,1999,49(3):387-403.
118.E.M.Dawson,W.H.Roth,A.Drescher.Slope Stability Analysis by Strength Reduction[J].Geotechnique,1999,49(6):835-840.
119.T.Matsui,K.C.San.Finite Element Slope Stability Analysis by Shear Strength Reduction Technique[J].Soils and foundations,JSSM FE,1992,32(1):59-70.
120.连镇营.基坑工程三维有限元数值分析中若干问题的研究[博士论文D].大连理工大学,2001.
121.郑颖人,赵尚毅,宋雅坤.有限元强度折减法研究进展[J].后勤工程学院学报,2005,3:1-6.
122.E.Hoek,J.W.Bray,卢世宗译.岩石边坡工程[M].北京,冶金工业出版社,1983
123.孙东亚,彭一江,王兴珍.DDA数值方法在岩质边坡倾倒破坏分析中的应用[J].岩石力学与工程学报,2002,21(1):39-42.
124.张国新,武晓峰.裂隙渗流对岩石边坡稳定的影响——渗流、变形耦合作用的DDA法[J].岩石力学与工程学报,2003,22(8):1269-1275.
125.M.MacLaughlin,N.Sitar,D.Doolin,T.Abbot.Investigation of slope-stability kinematics using discontinuous deformation analysis[J].International Journal of Rock Mechanics &Mining Sciences,2001,38:753-762.
126.沈振中,大西有三.基于非连续变形分析的水库岩体边坡稳定分析方法[J].水利学报,2004,3:117-122.
127.J.M.Pei,Z.H.Lu.An application of DDA to a jointed rock slope[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:395-401.
128.T.C.Ke.Application of DDA to stability analysis of rock masses[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:334-342.
129.X.C.Dong,A.Q.Wu,F.Ren.A preliminary application of discontinuous deformation analysis to the three gorges project on Yangtze River China[A].In:Proc of the First International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media[C].Albuquerque,TSI Press,1996:310-318.
130.S.L.Zhao,M.R.Salami,M.S.Rahman.Discontinuous deformation analysis simulation of rock slope failure processes[A].In:Proc of 9th International Conference on Computer Methods and Advances in Geomechanics[C].Rotterdam,A.A.Balkema,1997:473-477.
131.G.Q.Chen,Ohnishi.Slope stability analysis using discontinuous deformation analysis method[A].In:Rock Mecganics for Industry[C].[s.I.]:[s.n.],1999,I:535-541.
132.Y.H.Hatzor.Dynamic rock slope stability analysis at masada national monument using block theory and DDA[A].In:Rock Mechanics for Industry[C].[s.I.]:[s.n.],I999,I:63-70.
133.周少怀,杨家岭.DDA数值方法及工程应用[J].岩土力学,2000,21(2):123-125.
134.郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用[J].岩石力学与工程学报,2004,23(19):3381-3388
135.郑颖人,赵尚毅.用有限元法求边坡稳定安全系数[J].公路交通技术,2002,1:7-9
136.郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析[J].中国工程科学,2002,4(10):57-61
137.H.Zheng,D.F.Liu,C.G.Li.Slope stability analysis based on elasto-plastic finite element method[J].International Journal for Numerical Methods in Engineering,2005,64(14):1871-1888
138.黄盛俭,刘君,孔宪京.强度折减DDA法及其在边坡稳定分析中的应用[J].岩石力学与工程学报,2008,27(增1):2799-2806.
139.江巍.非连续变形分析方法中的几个问题[硕士论文D].三峡大学,2006年6月.
140.混凝土重力坝设计规范(SL 319-2005).中华人民共和国水利部,2005
141.日本财团法人大坝技术中心:多目的大坝的建设.(株)技报堂出版,1987
142.Y.I.Kim,B.Amadei,E.Pan.Modeling the effect of geology on uplift in concrete gravity dam foundations with the discontinuous deformation analysis[A].In:Rock Mechanics for Industry[C].[s.I.]:[s.n.],1999,I:527-534
143.张国新,金峰.重力坝抗滑稳定分析中DDA与有限元方法的比较[J].水力发电学报,2004,23(1):10-14
144.姜清辉,丰定祥.三维非连续变形分析方法中的锚杆模拟[J].岩土力学,2001,22(2):176-178
145.张秀丽,焦玉勇,刘泉声.非连续变形分析(DDA)方法中的预应力锚杆模拟[J].地下空间与工程学报,2008,4(1):38-41
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |