沥青混合料非连续力学计算模型的研究
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摘要
近年来,车辙、水损坏和开裂为代表的早期损坏现象由于严重影响到沥青路面的使用性能而备受关注。研究表明,这些早期损坏总是在局部区域首先发生,然后扩展到其他区域的。为了减少和避免早期损害的发生,获得局部区域的应力状态是非常必要的。虽然试验方法可以准确的得出结果,但由于测量手段的局限性和影响因素的多样性,很难得到各种组合情况下的应力分布;而连续力学方法由于不考虑沥青混合料的不连续状态,也很难得到细观下沥青胶浆的应力分柿。非连续计算方法正是为了弥补这些方法的不足而提出的。
非连续计算方法主要有离散单元法、DDA法以及数值流形法。文中分析了每种方法的基本原理和优缺点,同时考虑到沥青混合料空隙发达、多种材料耦合、颗粒松散、以及大变形等特点,通过比较认为:数值流形法能够满足这种计算的需要。不过基于规则网格的数值流形法由于受到网格的限制,在处理材料交界面处的位移协调以及特大变形时还面临很多困难。为了改进这种方法,文中采用Galerkin型无网格法与数值流形法相结合来求解沥青混合料的力学问题,得到了很好的效果。
文中首先详细讨论了非连续计算面临的三个关键性技术:计算模型的生成、接触的判断与施加,以及数据的存储格式和求解方案。
鉴于无网格和流形法的计算特点,文中提出了“级配-基球-预压”的沥青混合料非连续模型生成方法。并讨论了颗粒级配的控制、颗粒的嵌挤压密、多面体模型的投放、以及沥青胶浆的生成等问题。
对于接触点的搜索,计算证明:采用分格检索和公共平面结合的方法可以大大提高搜索的效率。另外,为了将无网法融合到数值流形法中,重新推导了数值流形法中接触子阵的形式,并实现了不同计算节点采用不同影响节点的计算格式。
通过分析非连续计算的刚度矩阵特点,认为采用动态的数据压缩格式有利于提高刚度子阵的装配效率和减少数据的存储量。同时,经过计算表明,当方程的阶数不是特别高时,采用直接求解方法可以保证计算的精度和速度,当阶数很高时,建议采用带预处理的迭代方法。
其次,文中重点探讨了无网格流形法的建立和实现方法,其中包括近似方案的构造、离散格式的形成、本质边界的处理和各种子阵的计算格式等问题。针对上述形成的沥青混合料非连续模型,给出了材料交界面位移协调、沥青胶浆的连接、影响节点的搜索以及接触块体的构造等内容的处理方法。同时,通过与有限元的对比,还讨论了无网格流形方法的精度问题。
文章最后对无网格流形法在沥青混合料细观应力分布和空隙水压力影响等方面的应用做了探讨。为了和连续力学方法方法对比,还介绍了采用有限元方法进行相应计算的方法。虽然文中的算例较为简单,但还是能得出很多有意义的结论:
(1)沥青混合料的应力分布是与骨料和沥青胶浆的模量的比率密切相关的。比值越大,骨料的应力越集中,而比值越小,骨料和沥青的应力分布越均匀。因此可以通过调整模量比值促使骨料和沥青胶浆共同协调受力,以最大程度地发挥它们各自的极限强度。模量比值的减小虽然可以使颗粒内受力均匀,但往往会导致颗粒与颗粒间的应力的不均匀分布。
(2)欧拉方程耦合计算方法中,水是作为固体的附加质量参与到受力体系中来的,它的存在导致了沥青混合料颗粒内部应力的降低,但它几乎不影响骨料与沥青的应力分配比例。
Some early damage phenomenons such as rutting, moisture damage and cracking, which are seriously corrupting pavement service performance, have been drawn significant attentions in recent year. Researches show that these early damages tend to occur in local region, and then spread to other regions. In order to reduce or avoid this kind of damage, the stress condition of local region should be made clear first of all. Although the stress can be measured by experiment accurately, its distribution under multi-component load is difficult to obtain with the limited measurement instruments. Since the continuous mechanics method ignores the discontinuation status of asphalt mixture, the meso-level stress distribution is hardly gotten. The discontinuous computation method is considered advanced to cover the shortage above.
Discrete Element Method, Discontinuous Deformation Analysis and Numerical Manifold Method can all be used in discontinuum mechanics numeration. The fundamental principles, advantages and disadvantages are studied in this paper. Through taking into account the characteristic of asphalt mixture (high porosity, loosening particles, coupled of multi materials with large deformation and so on), Numerical Manifold Method provids a good way to satisfy the purpose of computation after detailed comparisons. However, the Numerical Manifold Method is still limited in processing the coordination of displacement and large deformation because of the dependence of mesh. A combination with Mesh-free Galerkin Method is advanced to solve the mechanics problems of asphalt mixture. And remarkable improvement has been gained through this method.
Firstly, three key technologies of discontinuous computation method: the generation of computation model, the identification and application of contact, storing and processing format of data are detailed discussed.
The generation method of asphalt mixture discontinuum mechanics model named Gradation-Sphere-Precompaction is developed based on the calculation features of Mesh-free Method and Numerical Manifold Method. The controlling of particle graduation, the break-in and pressure of particles, the location of polyhedral model and the generation of asphalt mastic and other issues are outlined.
The adoption of Lattice Search and Common Plane method is proved to greatly improve the efficiency in searching contact points. In addition, the sub-contact-matrix in Numerical Manifold Method is reconstituted to merge the Mesh-free method. The scheme is realized for different node with different support nodes.
By analysis of discontinuous stiffness matrix, it is concluded that dynamic data compression format is benefit in improving assemble efficiency of the stiffness matrix and reducing the data storage. At the same time, the calculation proves that direct solution procedure guarantees both the precision and speed of computation when the rank of stiffness matrix is not particularly high, and pretreatment iteration method is recommended when the rank is relatively high.
Secondly, the realization of Mesh-free Manifold method is focused in this paper. The problems of construction of approximate program, formation of discrete format, transaction of essence boundary and computation format of sub-matrix are indicated. According to the asphalt mixture discontinuous model, the deposit method of material boundary displacement coordinate, the link of asphalt mastic, the search of affection point and the formation of contact blocks and so on are also established. Meanwhile, the precision of this method is also discussed by comparison with finite element method.
Finally, the application of Mesh-free Manifold method subjecting the deformation and infuluce of water pressure on asphalt mixture is presented. In order to comparison with the continuous mechanics method result, the corresponding calculation with finite element method is also introduced. Though simple cased is used here, some meaningful conclusions are found as follows:
a) The stress distribution of asphalt mixture is closely related to the modulus ratio of stone and asphalt mastic. The stress concentration on stone is found in high ratio, while the stress profile has evenly distribution in low ratio. As a result, to maximize their ultimate strength respectively, the coordinate mechanical status of stone and asphalt mastic could be obtained by adjustment of modulus ratio. The decrease of modules leads to stress distribution balanced inside the particles, but unbalanced between the particles.
b) In analysis of Solid-liquid interaction by Euler Equation, the presence of water results in stress decreasing of asphalt mixture internal particles as an additional mass of solid in the mechanic system. But it hardly affects the stress distribution ratio of stone and asphalt.
非连续计算方法主要有离散单元法、DDA法以及数值流形法。文中分析了每种方法的基本原理和优缺点,同时考虑到沥青混合料空隙发达、多种材料耦合、颗粒松散、以及大变形等特点,通过比较认为:数值流形法能够满足这种计算的需要。不过基于规则网格的数值流形法由于受到网格的限制,在处理材料交界面处的位移协调以及特大变形时还面临很多困难。为了改进这种方法,文中采用Galerkin型无网格法与数值流形法相结合来求解沥青混合料的力学问题,得到了很好的效果。
文中首先详细讨论了非连续计算面临的三个关键性技术:计算模型的生成、接触的判断与施加,以及数据的存储格式和求解方案。
鉴于无网格和流形法的计算特点,文中提出了“级配-基球-预压”的沥青混合料非连续模型生成方法。并讨论了颗粒级配的控制、颗粒的嵌挤压密、多面体模型的投放、以及沥青胶浆的生成等问题。
对于接触点的搜索,计算证明:采用分格检索和公共平面结合的方法可以大大提高搜索的效率。另外,为了将无网法融合到数值流形法中,重新推导了数值流形法中接触子阵的形式,并实现了不同计算节点采用不同影响节点的计算格式。
通过分析非连续计算的刚度矩阵特点,认为采用动态的数据压缩格式有利于提高刚度子阵的装配效率和减少数据的存储量。同时,经过计算表明,当方程的阶数不是特别高时,采用直接求解方法可以保证计算的精度和速度,当阶数很高时,建议采用带预处理的迭代方法。
其次,文中重点探讨了无网格流形法的建立和实现方法,其中包括近似方案的构造、离散格式的形成、本质边界的处理和各种子阵的计算格式等问题。针对上述形成的沥青混合料非连续模型,给出了材料交界面位移协调、沥青胶浆的连接、影响节点的搜索以及接触块体的构造等内容的处理方法。同时,通过与有限元的对比,还讨论了无网格流形方法的精度问题。
文章最后对无网格流形法在沥青混合料细观应力分布和空隙水压力影响等方面的应用做了探讨。为了和连续力学方法方法对比,还介绍了采用有限元方法进行相应计算的方法。虽然文中的算例较为简单,但还是能得出很多有意义的结论:
(1)沥青混合料的应力分布是与骨料和沥青胶浆的模量的比率密切相关的。比值越大,骨料的应力越集中,而比值越小,骨料和沥青的应力分布越均匀。因此可以通过调整模量比值促使骨料和沥青胶浆共同协调受力,以最大程度地发挥它们各自的极限强度。模量比值的减小虽然可以使颗粒内受力均匀,但往往会导致颗粒与颗粒间的应力的不均匀分布。
(2)欧拉方程耦合计算方法中,水是作为固体的附加质量参与到受力体系中来的,它的存在导致了沥青混合料颗粒内部应力的降低,但它几乎不影响骨料与沥青的应力分配比例。
Some early damage phenomenons such as rutting, moisture damage and cracking, which are seriously corrupting pavement service performance, have been drawn significant attentions in recent year. Researches show that these early damages tend to occur in local region, and then spread to other regions. In order to reduce or avoid this kind of damage, the stress condition of local region should be made clear first of all. Although the stress can be measured by experiment accurately, its distribution under multi-component load is difficult to obtain with the limited measurement instruments. Since the continuous mechanics method ignores the discontinuation status of asphalt mixture, the meso-level stress distribution is hardly gotten. The discontinuous computation method is considered advanced to cover the shortage above.
Discrete Element Method, Discontinuous Deformation Analysis and Numerical Manifold Method can all be used in discontinuum mechanics numeration. The fundamental principles, advantages and disadvantages are studied in this paper. Through taking into account the characteristic of asphalt mixture (high porosity, loosening particles, coupled of multi materials with large deformation and so on), Numerical Manifold Method provids a good way to satisfy the purpose of computation after detailed comparisons. However, the Numerical Manifold Method is still limited in processing the coordination of displacement and large deformation because of the dependence of mesh. A combination with Mesh-free Galerkin Method is advanced to solve the mechanics problems of asphalt mixture. And remarkable improvement has been gained through this method.
Firstly, three key technologies of discontinuous computation method: the generation of computation model, the identification and application of contact, storing and processing format of data are detailed discussed.
The generation method of asphalt mixture discontinuum mechanics model named Gradation-Sphere-Precompaction is developed based on the calculation features of Mesh-free Method and Numerical Manifold Method. The controlling of particle graduation, the break-in and pressure of particles, the location of polyhedral model and the generation of asphalt mastic and other issues are outlined.
The adoption of Lattice Search and Common Plane method is proved to greatly improve the efficiency in searching contact points. In addition, the sub-contact-matrix in Numerical Manifold Method is reconstituted to merge the Mesh-free method. The scheme is realized for different node with different support nodes.
By analysis of discontinuous stiffness matrix, it is concluded that dynamic data compression format is benefit in improving assemble efficiency of the stiffness matrix and reducing the data storage. At the same time, the calculation proves that direct solution procedure guarantees both the precision and speed of computation when the rank of stiffness matrix is not particularly high, and pretreatment iteration method is recommended when the rank is relatively high.
Secondly, the realization of Mesh-free Manifold method is focused in this paper. The problems of construction of approximate program, formation of discrete format, transaction of essence boundary and computation format of sub-matrix are indicated. According to the asphalt mixture discontinuous model, the deposit method of material boundary displacement coordinate, the link of asphalt mastic, the search of affection point and the formation of contact blocks and so on are also established. Meanwhile, the precision of this method is also discussed by comparison with finite element method.
Finally, the application of Mesh-free Manifold method subjecting the deformation and infuluce of water pressure on asphalt mixture is presented. In order to comparison with the continuous mechanics method result, the corresponding calculation with finite element method is also introduced. Though simple cased is used here, some meaningful conclusions are found as follows:
a) The stress distribution of asphalt mixture is closely related to the modulus ratio of stone and asphalt mastic. The stress concentration on stone is found in high ratio, while the stress profile has evenly distribution in low ratio. As a result, to maximize their ultimate strength respectively, the coordinate mechanical status of stone and asphalt mastic could be obtained by adjustment of modulus ratio. The decrease of modules leads to stress distribution balanced inside the particles, but unbalanced between the particles.
b) In analysis of Solid-liquid interaction by Euler Equation, the presence of water results in stress decreasing of asphalt mixture internal particles as an additional mass of solid in the mechanic system. But it hardly affects the stress distribution ratio of stone and asphalt.
引文
[1]交通部.2007年公路水路交通行业发展统计公报.2008.
[2]邓学钧,黄卫,黄晓明.路面结构计算和设计电算方法.南京:东南大学出版社,1997.
[3]Cundall P A.A computer model for simulating progressive large scale movements in blocky system.Proceedings of the symposium of the International Society of Rock Mechanics,Nancy,France,1971:8-12.
[4]胡霞光.沥青混合料微观力学分析综述.长安大学学报:自然科学版.2005,25(2):6-10.
[5]田莉,刘玉,王秉纲.沥青混合料三维离散元模型及其重构技术.长安大学学报:自然科学版.2007,27(4):23-27.
[6]肖昭然,胡霞光,刘玉.沥青混合料细观结构离散元分析.公路.2007,(4):145-148.
[7]田莉,刘玉,胡霞光等.模拟沥青混合料集料的多面体颗粒随机生成算法及程序.中国公路学报.2007,20(3):5-10.
[8]盛晓军,鲁华征,陈星光.沥青结合料离散元模型.交通标准化.2006,(2):57-60.
[9]黄晚清.SMA粗集料骨架结构的细观力学模型研究:(博士学位论文).成都:西南交通大学,2007.
[10]Chang K G.Micromechanical simulation of hot mix asphalt:(Ph.D dissertation).Newark:New Jersey Institute of Technology,1995.
[11]Chang K G,Meegoda J N.Micromechanical simulation of hot mix asphalt.Journal of Engineering Mechanics.1997,123(5):495-503.
[12]You Z.Development of a Micromechanical Modeling Approach to Predict Asphalt Mixture Stiffness Using Discrete Element Method:(Ph.D dissertation).University of Illinois at Urbana-Champaign,2003.
[13]You Z,Buttlar W G.Discrete Element Modeling to Predict the Modulus of Asphalt Concrete Mixtures.Journal of Materials in CiviI Engineering(ASCE).2004,16(2):140-146.
[14]You Z,Buttlar W G.Application of Discrete Element Modeling Techniques to Predict the Complex Modulus of Asphalt-Aggregate Hollow Cylinders Subjected to Internal Pressure.Journal of the Transportation Research Board National Research Council.2005,1929:218-226.
[15]You Z,Buttlar W G.Micromechanical Modeling Approach to Predict Compressive Complex Moduli of Asphalt Mixture Using Distinct Element Method.Journal of the Transportation Research Board National Research Council,Washington DC.2006,1970:73-83.
[16]You Zhanping,Buttlar W G,Dai Qingli.Aggregate Effect on Asphalt Mixture Properties by Modeling Particle-to-Particle Interaction.Proceedings of Sessions of the 15th U.S.National Congress of Theoretical and Applied Mechanics,Boulder,Colorado,USA, 2006:14-21.
[17]Christoffersion J.,Mehrabadi M.M.,Nemat—nasser S.A micro-mechanical description of granular material behavior.J.Appl.Mech.1981,48:339-344.
[18]Rothenberg L.,Selvadurai A.P.S.Micro-mechanical definition of the cauchy stress tensor of particulate media.Mechanics of Structured Media,Amserdam,1981:469-486.
[19]Chang S.C.Moduli of granular materials with viscoelastic binders.Proceeding of ASME Mechanics and Materials Conference,Baltimore,MD,1996.
[20]Shi Gen-hua.Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block system:(ph.D Thesis).University of California,Berkeley,1988.
[21]周少怀,杨家岭.DDA数值方法及工程应用研究.岩土力学.2000,21(2):123-125.
[22]黄可明,郑鸣芳.块体系统不连续变形分析(DDA)方法评述.水利科技.2004,(1):44-46.
[23]刘军,李仲奎.非连续变形分析(DDA)方法研究现状及发展趋势.岩石力学与工程学报.2004,23(5):839-845.
[24]江巍,郑宏,王彦海.非连续变形分析(DDA)方法理论研究发展现状.黑龙江水专学报.2005,32(4):83-85.
[25]石根华著,裴觉民译.数值流形方法与非连续变形分析.北京:清华大学出版社,1997.
[26]Cundall P A,Strack O D L.A discrete numerical model for granular assembles.Geotechnique.1979,29(1):47-65.
[27]Drescher A,De Jissein De Jong.Photo elastic veification of a granular material.Journal of the Mechanics and Physics of Solids.1972,20:337-351.
[28]李红艳.离散元干-湿颗粒模型研究及应用:(博士学位论文).北京:中国农业大学,2004.
[29]Cundall P A.Computer simulations of dense sphere assemblies.Micromechanics of Granular Materials,Amsterdam,1988:113-123.
[30]Cundall P A.Formulation of a three-dimensional distinct element model-Part Ⅰ:A scheme to detect and represent contacts in a system composed of many polyhedral blocks.International Journal Of Rock Mechanics in Mining Sciences & Geo-mechanics Abstract.1988,25(3):107-116.
[31]Hart R,Cundall P A,Lemos J.Formulation of a three-dimensional distinct element model-Part Ⅱ:Mechanics calculations for motion and interaction of a system composed of many polyhedral blocks.International Journal Of Rock Mechanics in Mining Sciences & Geo-mechanics Abstract.1988,25(3):117-125.
[32]Rothenburg L,Bathurst R J.Micromechanical features of granular assemblies with planar elliptical particles.Geotechnique.1992,42(1):79-95.
[33]Ng T T.Numerical simulation of granular soil using elliptical particles.Computer and Geotechnics.1994,16:153-169.
[34]Ting J M,Khwaja M,Meachum L,et al.An ellipse based discrete element model for granular materials.International Journal for Numerical and Analytical Methods in Geomechanics.1993,17:603-623.
[35]Ng T T.Fabric study of granular materials after compaction.Journal of Engineering Mechanics.1999,125(12):1390-1394.
[36]Lin X,Ng T T.A three-dimensional discrete element model using arrays of ellipsoids.Geotechnique.1997,47(2):319-329.
[37]Williams J R1,O'conner R.A linear complexity intersection algorithm for DEM simulations of arbitrary geometries.Engineering Computations.1995,12:185-201.
[38]Hogue,C.Shape representation and contact detection for discrete elements simulations of arbitrary geometries.Engineering Computations.1998,15(3):374-390.
[39]Favier J F,Kremmer M,Raji A O.Shape representation of axi-symmetrical,non-spherical particles in discrete element simulation using multi-element model particles.Engineering Computations.1999,16(4):467-480.
[40]Thorton C,Barnes D J.Computer simulated deformation of compact granular assemblies.Acta Mechanic.1986,64(1-2):45-61.
[41]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用.沈阳:东北工学院出版社,1991.
[42]麻凤海,范学理,王泳嘉.岩层移动动态过程的离散单元法分析.煤炭学报.1996,21(4):388-392.
[43]焦玉勇,葛修润.三维离散单元法及其在滑坡分析中的应用.岩土工程学报.2000,22(1):101-104.
[44]焦玉勇,张秀丽,刘泉声等.用非连续变形分析方法模拟岩石裂纹扩展.岩石力学与工程学报.2007,26(4):682-691.
[45]焦玉勇,葛修润.三维离散元法地下水及锚杆的模拟.岩石力学与工程学报.1999,18(1):6-11.
[46]张锐,李建桥等.离散单元法在土壤机械特性动态仿真中的应用进展.农业工程学报.2003,19(1):16-19.
[47]徐泳,李艳洁,李红艳.离散元法在农业机械化中应用评述.农机化研究.2004,(5):26-30.
[48]董劲男.基于面向对象技术的离散元法分析设计软件开发研究:(硕士学位论文).长春:吉林大学,2005.
[49]Yu A,Bridgwater J,Burbidge A.On the modeling of the packing of fine particles.Powder Technology.1997,92:185-194.
[50]Xu B,Yu A.Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics.Chemical Engineering Science.1997,52:2786-2809.
[51]Xu B,Yu A,Chew S J.Simulation of the gas-solid flow in a bed with lateral gas blasting.Powder Technology.2000,109:13-26.
[52]刘安源,刘石,姜凡.鼓泡流化床流动特性的欧拉—离散单元方法模拟.燃烧科学与技术. 2003,9(2):148-152.
[53]黎明,谢灼利等.应用离散单元法对二维流化床内流态进行数值模拟研究.北京化工大学学报:自然科学版.2002,29(2):6-10.
[54]俞良群,杨建斌.筒仓内部压力及流场的数值模拟与实验验证.烟台大学学报:自然科学与工程版.1999,12(4):255-262.
[55]徐泳,Kafui K.D.用颗粒离散元法模拟料仓卸料过程.农业工程学报.1999,15(3):65-69.
[56]周德义,马成林.散粒农业物料孔口出流成拱的离散单元仿真.农业工程学报.1996,12(2):186-189.
[57]武锦涛,陈纪忠,阳永荣.模拟颗粒流动的离散元方法及其应用.现代化工.2003,23(4):56-58.
[58]Walton O R.Numerical simulation of inclined chute flows of monodisperse inelastic,frictional spheres.Mechanics of Materials.1993,16:239-247.
[59]Hanes D M,Walton O R.Simulations and physical measurements of glass spheres flowing down a bumpy incline.Powder Technology.2000,109((1-3)):133-144.
[60]Karion A,Hunt M L.Wall stresses in granular Couette flows of mono-sized particles and binary mixtures.Powder Technology.2000,109(1-3):145-163.
[61]Mustoe G G W,Miyata M.Material flow analysis of noncircular-shaped granular media using discrete element methods.Journal of Engineering Mechanics.2001,127(10):1017-1026.
[62]Cleary P W.DEM simulation of industrial particle flows:case studies of dragline excavators,mixing in tumblers and centrifugal mills.Powder Technology.2000,26(2):89-111.
[63]Lorig L J,Brady B H G,Cundall P A.Hybrid discrete element-boundary element analysis of jointed rock.International Journal Rock Mechanics in Mining Science & Geomechanics Abstract.1986,23(4):303-312.
[64]金峰,贾伟伟等.离散元—边界元动力耦合模型.水利学报.2001,(1):23-27.
[65]金峰,王光纶.离散元—边界元动力耦合模型在地下结构动力分析中的应用.水利学报.2001,(2):24-28.
[66]Horner D A,Carrillo A R,Peters J F.High resolution soil vehicle interaction modeling.Mechanics Of Structures And Machines.1998,26(3):305-318.
[67]Homer O A,Peters J F,Carrillo A R.Large scale discrete element modeling of vehicle-soil interaction.Journal of Engineering Mechanics.2001,127(10):1027-1032.
[68]Han K,Peric D,Owen D R J.A combined finite/discrete element simulation of shot peening processes.Part Ⅰ:studies on 20 interaction laws.Engineering Computations.2000,17(5):593-619.
[69]Han K,Peric D,Owen D R J.A combined finite/discrete element simulation of shot peening processes. Part II: 3D interaction laws. Engineering Computations. 2000, 17(65): 680-702.
[70] Owen D R J, Feng Y T. Parallelised finite / discrete element simulation of multi-fracturing solids and discrete systems. Engineering Computations. 2001, 18(3): 557-576.
[71] Buttar W G, You Z P. Discrete element modeling of asphalt concrete: Transportation Research Record. 2001.
[72] 王端宜,张肖宁等. 用虚拟试验方法评价沥青混合料的级配类型. 华南理工大学学报:自然科学版. 2003, 31(2): 48-51.
[73] Johnson K. L. Contact Mechanics. Cambridge: Cambridge University Press, 1989.
[74] Gladwell G. M. L. Contact Probelems in the Classical Theory of Elasticity. Alphen and den Rijn, Sijthoff and Noordhoff, 1980.
[75] Zhu H., Chang C. S., Rish Iii J. M. Normal and tangential compliance for conforming binder contact. I: Elastic binder. Int. J. Solids Stuct. 1996, 33: 4337-4349.
[76] Zhu H., Chang C. S., Rish Iii J. M. Normal and tangential compliance for conforming binder contact. II: visco-elastic binder. Int. J. Solids Stuct. 1996, 33: 4351-4363.
[77] Zhu H., Chang C. S., Rish Iii J. M. Rolling compliance for elastic and viscoelastic conforming binder contact. Int. J. Solids Struct. 1997, 34: 4073-4086.
[78] Zhu Han. A contact mechanism based theory of Maxwell matrix composites. Int. J. Solids Struct. 2001, 38: 4477-4488.
[79] Itasca. PFC2D 2. 00 Particle Flow Code in Two Dimensions. Minneapolis Minnesota., 1998.
[80] Chern J C, Koo C Y, Chen S. Development of Second Order Displacement Function for DDA and Manifold Method. Working Forum on the Manifold Method of Material Analysis, Vicksburg, 1990:183-202.
[81] Koo C Y, Chern J C. The development of DDA with third order displacement function. Proceedings of the First International Forum Discontinuous Deformation Analysis (DDA) and Simulations Discontinuous media, Berkeley, U. S. A, 1996:342-350.
[82] Ma Max Y, Zaman Musharraf, Zhou J H. Discontinuous deformation Analysis using the third order displacement function. Proceedings of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous media, Berkeley, U. S. A, 1996:383-394.
[83] Shi G H. Block System Modeling By Discontinuous Deformation Analysis. Southampton, UK and Boston, USA: Computational Mechanics Publications, 1993.
[84] Bernard Amadei, Chihsen Lin, Jerry Dwyer. Recent Extensions to the DDA Method. proc. 1st Int. Forum on DDA, Berkeley, U.S.A. 1996:1-30.
[85] Hilbert L B Jr, Yi W, Cook N G W. A new discontinuous finite element method for interaction of many deformable bodies ingeomechanics. Pro 8'h Int. Conf. meth adv, Geomech.,1994.
[86]Cai Yongen,Liang Cuo-pin,Shi Geng-hua,et al.Studing impact problem by LDDA method:Discontinuous Deformation analysis(DDA) and Simulations of discontinuous media.TSI Press,1996.
[87]Liang Guo-pin,Wang Cheng-guo.LDDA on the high speed catenary-pantograph system dynamics:Discontinuous Deformation analysis(DDA) and simulations of discontinuous media.TSI press,1996.
[88]Wang Chung-yue,Chuang Ching-chiang,Sheng Jopan.Time Integration Theories for the DDA Method with Finite Element Meshes.proc.1st Int.Forum on DDA,Berkeley,U.S.A,1996:263-287.
[89]Dong Xuecheng,Wu Aiqing,Ren Fang.A Preliminary Application of Discontinuous Deformation Analysis(DDA) to the Three Gorges Project on Yangtze River,China.proc.1st Int.Forum on DDA,Berkeley,U.S.A.,1996:310-317.
[90]Ke Te-chih.Application of DDA to Stability Analysis of Rock Masses.proc.1st Int.Forum on DDA,Berkeley,U.S.A,1996:334-341.
[91]裴觉民,石根华.岩石滑坡体的块体动态稳定和非连续变形分析.水利学报.1993,(3):28-34.
[92]吴洪词.用改进的DDA法模拟岩体的破裂.岩石力学与工程学报.1997,15(增):556-558.
[93]Chris Pearce,Nenad Bicanic,Appapillai Thavalingham,Zhi Hong Liao.On the DDA Framework for Modelling Concrete Fracture.3rd.Int.Conf.on DDA,Colorado,USA,1999.
[94]Yuzo Ohnishi,Shigeru Miki.Development of Circular and Elliptic Disc Elements for DDA.proc.1st Int.Forum on DDA,Berkeley,USA,1996:44-51.
[95]Patricia A Thomas,Jonathan D Bray,Fe-chih Ke.Discontinuous Reformation Analysis for soil mechanics,proc.1st Int.Forum on DDA,Berkeley,USA,1996:454-462.
[96]Guangqi Chen,Shigeru Miki,Yuzo Ohnishi.Development of the interactive visualization system for DDA.Proceedings of The 9th Int.Conf,on computer Methods and Advances in Geomechanics,Wuhan,China,1997:495-500.
[97]Zhang Yonghui,Cheng Yungming.The extension and application of DDA method.岩土工程学报.1998,20(2):109-111.
[98]吴益民.节理岩体三维不连续变形分析方法研究及应用:(博士学位论文).武汉:武汉大学,2003.
[99]Shi Gen-hua.Applications of Discontinuous Deformation Analysis and Manifold Method.3rd Int.Conf.on DDA,Colorado,USA,1999:3-15.
[100]王如路,陈乃明,刘宝深.三维块体不连续变形分析理论简析.岩石力学与工程学报.1996,15(3):219-224.
[101]姜清辉.三维非连续变形分析方法的研究:(博士学位论文).武汉:中国科学院武汉岩土力 学研究所,2000.
[102]Lin Jeen-shang.Continuous and Discontinuous Analysis using the Manifold Method.Proceedings of the First International Conference on Analysis of Discontinuous deformation,Taipei,1995.
[103]Hideomi Ohtsubo,et al.Utilization of Finite Covers in the Manifold Method for Accuracy Control.Proceedings of the 2rd international Conference on Analysis of Discontinuous Deformation,Kyoto,1997.
[104]蔡永吕,张湘伟.流形方法的矩形覆盖系统及其全自动生成算法.重庆大学学报:自然科学版.2001,24(1):42-46.
[105]蔡永吕,朱合华,夏才初.流形方法覆盖系统自动生成算法.同济大学学报:自然科学版.2004,32(5):585-590.
[106]骆少明,姜冬茹等.金属成形过程的数值流形模拟方法研究.机械工程学报.2002,38(8):105-109.
[107]骆少明,蔡永吕等.数值流形方法中的网格重分技术及其应用.重庆大学学报:自然科学版.2001,24(4):34-37.
[108]王水林,葛修润.四个物理覆盖构成一个单元的流形方法及应用.岩石力学与工程学报.1999,18(3):312-316.
[109]田荣,Ugai K.高阶流形方法及其应用.工程力学.2001,18(2):21-26.
[110]Lu Ming.High-Order Manifold Methed With Simplex Integration.Proceedings of ICADD-5,2002.
[111]张国新,彭静.二阶流形元法与结构变形分析.力学学报.2002,34(2):261-269.
[112]Zhang Guoxin,Zhu Bofang,Lu Zhengchao.Cracking Simulation of the Wuqiangxi Ship Lock by Manifold Method.The 6th International conference on analysis of discontinuous deformation,Trondheim,Norway.,2003.
[113]Zhang G X,Sugiura Y,Hasegawa H.Crack propagation and thermal fracture analysis by manifold method.Proceedings of the second international conference on analysis of discontinuous deformation,Kyoto Japan,1997:282-297.
[114]章光,王水林.数值流形方法及其应用介绍.岩土工程界.2000,3(12):44-46.
[115]Sasaki T,Morikawa S,Ishii D,et al.Elastic-plastic analysis of jointed rock models by manifold method.In:Proc.of the 2nd International Conference on Analysis of Discontinuous Deformation,Kyoto,Japan,1997:309-316.
[116]王书法,朱维中等.岩体弹塑性分析的数值流形方法.岩石力学与工程学报.2002,21(6):900-904.
[117]曹文贵,速宝王.岩体锚固支护的数值流形方法模拟及其应用.岩土工程学报.2001,23(5):581-583.
[118]王书法,朱维中等.加锚岩体变形分析的数值流形方法.岩石力学与工程学报.2002,21(8):1120-1123.
[119]王芝银,李云鹏.数值流形方法中的几点改进.岩土工程学报.1998,20(6):33-36.
[120]王芝银,李刚.岩体力学中的增量数值流形方法及其应用.西安矿业学院学报.1998,18(A09):23-27.
[121]朱以文,曾又林.岩石大变形分析的增量流形方法.岩石力学与工程学报.1999,18(1):1-5.
[122]Ke Te-chih,Tang Jyh-haw.Modeling of solid-fluid interaction using the manifold method.In:Proceedings of 2nd North American Rock Mechanics Symposium,Montreal,Quebec,Canada,1996:1815-1822.
[123]王水林.数值流形方法介绍及其应用.岩土工程界.2000,3(12):44-46.
[124]Yuzo Ohnishi,Makoto Tanaka,Tomofumi Koyama.Manifold method in saturated-unsaturated groundwater flow analysis.In:3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice,Vail,Colorado,USA,1999:1213-1228.
[125]林绍忠.单纯形积分的递推公式.长江科学院院报.2005,22(3):32-34.
[126]Lin Dezhang,Mo Haihong.Manifold method of material analysis.In:Working Forum on the Manifold of Material Analysis,Jenner,California,USA,1995:147-164.
[127]周维垣,杨若琼.流形元法及其在工程中的应用.岩石力学与工程学报.1996,15(3):211-218.
[128]周维垣,黄岩松,林鹏.三维无单元伽辽金法及其在拱坝分析中的应用.水利学报.2005,36(6):644-649.
[129]胡云进,周维垣,寇晓东.三维无单元法及其应用.岩石力学与工程学报.2004,23(7):1136-1140.
[130]田荣.连续与非连续变形分析的有限覆盖无单元方法及其应用研究:(博士学位论文).大连:大连理工大学,2000.
[131]张国新,王光纶等.基于流形的结构体破坏分析.岩石力学与工程学报.2001,20(3):281-287.
[132]祁勇峰.数值流形法在三维弹性连续体静力分析中的应用研究:(硕士学位论文).武汉:长江科学院,2005.
[133]梁国平,何江衡.广义有限元方法——一类新的逼近空间.力学进展.1995,25(4):562-565.
[134]王玉杰,张大克.广义有限元法的两个超收敛定理.工科数学.2000,16(2):27-29.
[135]彭自强,李小凯,葛修润.广义有限元法对动态裂纹扩展的数值模拟.岩石力学与工程学报.2004,23(18):3132-3137.
[136]栾茂田,田荣.广义节点有限元法.计算力学学报.2000,17(2):192-200.
[137]曹国金,姜弘道.无单元法研究和应用现状及动态.力学进展.2002,32(4):526-534.
[138]Genki Yagawa,Tomonari Furukawa.Recent Developments of Free Mesh Method.Int.J.Numer.Mech.Engng.2000,47:1419-1443.
[139] Belytschko T, Krongauz Y, Organ D. Meshless methods: an overview and recent developments. Computer Methods In Applied Mechanics And Engineering. 1996, 139:3-47.
[140] 张雄,宋康祖,陆明万. 无网格法研究进展及其应用. 计算力学学报. 2003, 20(6):730-742.
[141] Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astron Journal. 1977, 8: 1013-1024.
[142] Monaghan J J. An introduction to SPH. Comp Phys Comm. 1988, 48: 89-96.
[143] Liu W K, Jun S L, Shaofau A, et al. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering. 1995, 38: 1655-1679.
[144] Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse Approximation and diffuse elements. Computational Mechanics. 1992, 10: 307-318.
[145] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin Methods. International Journal for Numerical Methods in Engineering. 1994, 37: 229-256.
[146] Arluri S N, Zhu T. A New Meshless Local Pretrov-Galerkin Approach in Computational Mechanics. Computational Mechanics. 1998, 22(2): 117-127.
[147] Zhu T, Zhang J, Arluri S N. A Meshless Local Boundary Integral Equation Method for Solving Nonlinear Problems. Computational Mechanics. 1998, 22(3): 174-186.
[148] Melen J M, Babuska I. The Partition of Unity Finite Element Method: Basic Theory and Application. Comp. Methods in Appl. Mech. and Engng. 1996, 139: 289-314.
[149] Sukumar N, Moran B Belytschko T. The Natural Element Method in Solid Mechanics. Int. J. Numer. Methods Engng. 1998, 43: 839-887.
[150] Natarajan Sukumar. The Natural Element Method in Solid Mechanics: (ph. D Dissertation). Northwestern University, 1998.
[151] Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Comput Mech. 1999, 23: 219-230.
[152] Belytschko T, Krongauz Y, Organ D Et Al. Smoothing and acclerated computations in the element free Galerkin method. J. Comput. Appl. Math. 1996, 74: 111-126.
[153] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. Int J Numer Methods Engrg. 1998, 41: 1215-1233.
[154] Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. Int J Numer Methods Engrg. 1996, 29: 923-938.
[155] Belytschko T, Lu Y Y, Gu L. Crack propagation by element-free Galerkin methods. Engrg Frac Mech. 1995, 51: 295-315.
[156] Liu G R, Gu Y T. Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Comput Mech. 2000, 26: 166-173.
[157] Belytschko T, Organ D, Krongauz Y. A coupled finite element-element free Galerkin method.Comput Mech.1995,17:186-195.
[158]Zhang X,Liu X H,Song K Z Et Al.Least-square collocation meshless method.Int J Numer Methods Engrg.2001,51(9):1089-1100.
[159]张雄,胡炜,潘小飞等.加权最小二乘无网格法.中国计算力学大会2001论文集,广州,2001:333-338.
[160]石金龙.计算机辅助设计与工程分析中的数值流形方法:(硕士学位论文).长沙:国防科学技术大学,2004.
[161]Jia Lu,Liu Chengxue.Introduction of Element-Free Gaierkin Method(EFGM) and Its Preliminary Application in Asphalt Pavement Mechanical Analysis.Transportation Research Board(TRB) 87th Annual Meeting,Washington DC,2008.
[162]Bathurst R J,Rothenburg L.Micromechanical aspects of isotropic granular assemblies with linear contact interactions..J.Appl.Mech.Am.Soc.Mech.Engrs.1988,55:17-23.
[163]Lin X,Ng T T.Contact detection algorithms for three-dimensional ellipsoids in discrete element modeling.International Journal for Numerical and Analytical Methods in Geomechanics.1995,(19):653-659.
[164]Thomas P.Discontinuous deformation analysis of particulate media:(Ph.D disseration).Univ.of California,Berkeley,1977.
[165]Feng Y T,Han K,Owen D R J.Filling domains with disks:An advancing front approach.Inter.J.Numer.Methods in Engineering.2003,56(5):699-731.
[166]O'sullivan C,Bray J D,Riemer M F.Influence of particle shape and surface friction variability on response of rod-shaped particulate media.ASCE J.Engineering Mechanics.2002,128(11):1182-1192.
[167]Ferrez J A.Dynamic triangulations for efficient 3-D simulation of granular materials:(Ph.D disseration),Lausanne,:Ecole Polytechnique Federal de Lausanne,2001.
[168]Bagi K.From order to chaos:The mechanical behavior of regular and irregular assemblies.Proceedings QuaDPM'03 Workshop,BUTE Budapest,2003:33-42.
[169]Cui L,O'sullivan C.Analysis of a triangulation based approach for specimen generation for discrete element simulations.Granular Matter.2003,5:135-145.
[170]张登良.沥青与沥青混合料.北京:人民交通出版社,1993.
[171]沈金安.沥青及沥青混合料路用性能·.北京:人民交通出版社,2001.
[172]Vemuri B C,Chen L,Vu-quou L,et al.Efficient and accurate collision detection for granular flow simulation.Graphical Models and Image Processing.1998,60:403-422.
[173]Asmar B N,Langston P A.Validation tests on a distinct element model of vibrating cohesive particle systems.Computers and Chemical Engineering.2002,26:785-802.
[174]Vu-quoc L,Zhang X,Walton O R.A 3-D discrete-element method for dry granular flows of ellipsoidal particles.Comput.Methods Appl.Mech.Engrg.2000,187:483-528.
[175]姜清辉,杨文柱,吴益民等.三维非连续变形分析方法中摩擦接触问题的研究.岩石力学与工程学报.2002,21(增2):2418-2421.
[176]郑榕明,张勇慧.基于六面体覆盖的三维数值流形方法的理论探讨与应用.岩石力学与工程学报.2004,23(10):1745-1754.
[177]姜清辉,张煜.三维离散块体边-边接触模拟.岩土力学.2006,27(8):1369-1373.
[178]郑金华.稀疏矩阵的存储结构和乘法运算.湘潭大学自然科学学报.1994,16(2):133-136.
[179]张永杰,孙秦.稀疏矩阵存储技术.长春理工大学学报.2006,29(3):38-47.
[180]彼得·艾伯哈特,胡斌.现代接触动力学.南京:东南大学出版社,2003.
[181]陆群花.大型稀疏线代数方程组的几种数值算法研究:(硕士学位论文).兰州:兰州大学,2007.
[182]王勖成.有限单元法.北京:清华大学出版社,2003.
[183]傅闻远,卓家寿.无网格的崛起与发展—一种新兴的数值方法评述.河海大学学报.1999,27:51-58.
[184]张雄,刘岩.无网格法.北京:清华大学出版社,2004.
[185]Liu G R,Gu Y T著,王建明等译.无网格法理论及程序设计.济南:山东大学出版社,2007.
[186]张义同.热粘弹性理论.天津:天津大学出版社,2002.
[187]Durbin F.Numerical inversion of Laplace transforms:An efficient improvement to Dubner and Abate's method.The Computer Journal.1973,17(4):371-376.
[188]曹建新.重交通下级配碎石基层材料组成结构与动力特性的研究:哈尔滨:哈尔滨工业大学,2001.
[189]沙庆林.高速公路沥青路面早期破坏与对策.长沙理工大学学报:自然科学版.2006,3(3):1-6.
[190]孙立军,张宏超,刘黎萍.沥青路面初期损坏特点和机理分析.同济大学学报.2002,30(4):416-421.
[191]Hoven J M.Measurement and analysis of pore water pressure in thawing pavement structures subjected to dynamic loading:(Ph.D disseration),the Univ.of Minnesota,USA,1997.
[192]彭永恒,任瑞波,宋凤立.轴对称条件下层状弹性体超孔隙水压力的求解.工程力学.2004,21(4):204-208.
[193]Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid.The Journal of the Acoustical Society of America.1956,28(2):166-191.
[2]邓学钧,黄卫,黄晓明.路面结构计算和设计电算方法.南京:东南大学出版社,1997.
[3]Cundall P A.A computer model for simulating progressive large scale movements in blocky system.Proceedings of the symposium of the International Society of Rock Mechanics,Nancy,France,1971:8-12.
[4]胡霞光.沥青混合料微观力学分析综述.长安大学学报:自然科学版.2005,25(2):6-10.
[5]田莉,刘玉,王秉纲.沥青混合料三维离散元模型及其重构技术.长安大学学报:自然科学版.2007,27(4):23-27.
[6]肖昭然,胡霞光,刘玉.沥青混合料细观结构离散元分析.公路.2007,(4):145-148.
[7]田莉,刘玉,胡霞光等.模拟沥青混合料集料的多面体颗粒随机生成算法及程序.中国公路学报.2007,20(3):5-10.
[8]盛晓军,鲁华征,陈星光.沥青结合料离散元模型.交通标准化.2006,(2):57-60.
[9]黄晚清.SMA粗集料骨架结构的细观力学模型研究:(博士学位论文).成都:西南交通大学,2007.
[10]Chang K G.Micromechanical simulation of hot mix asphalt:(Ph.D dissertation).Newark:New Jersey Institute of Technology,1995.
[11]Chang K G,Meegoda J N.Micromechanical simulation of hot mix asphalt.Journal of Engineering Mechanics.1997,123(5):495-503.
[12]You Z.Development of a Micromechanical Modeling Approach to Predict Asphalt Mixture Stiffness Using Discrete Element Method:(Ph.D dissertation).University of Illinois at Urbana-Champaign,2003.
[13]You Z,Buttlar W G.Discrete Element Modeling to Predict the Modulus of Asphalt Concrete Mixtures.Journal of Materials in CiviI Engineering(ASCE).2004,16(2):140-146.
[14]You Z,Buttlar W G.Application of Discrete Element Modeling Techniques to Predict the Complex Modulus of Asphalt-Aggregate Hollow Cylinders Subjected to Internal Pressure.Journal of the Transportation Research Board National Research Council.2005,1929:218-226.
[15]You Z,Buttlar W G.Micromechanical Modeling Approach to Predict Compressive Complex Moduli of Asphalt Mixture Using Distinct Element Method.Journal of the Transportation Research Board National Research Council,Washington DC.2006,1970:73-83.
[16]You Zhanping,Buttlar W G,Dai Qingli.Aggregate Effect on Asphalt Mixture Properties by Modeling Particle-to-Particle Interaction.Proceedings of Sessions of the 15th U.S.National Congress of Theoretical and Applied Mechanics,Boulder,Colorado,USA, 2006:14-21.
[17]Christoffersion J.,Mehrabadi M.M.,Nemat—nasser S.A micro-mechanical description of granular material behavior.J.Appl.Mech.1981,48:339-344.
[18]Rothenberg L.,Selvadurai A.P.S.Micro-mechanical definition of the cauchy stress tensor of particulate media.Mechanics of Structured Media,Amserdam,1981:469-486.
[19]Chang S.C.Moduli of granular materials with viscoelastic binders.Proceeding of ASME Mechanics and Materials Conference,Baltimore,MD,1996.
[20]Shi Gen-hua.Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block system:(ph.D Thesis).University of California,Berkeley,1988.
[21]周少怀,杨家岭.DDA数值方法及工程应用研究.岩土力学.2000,21(2):123-125.
[22]黄可明,郑鸣芳.块体系统不连续变形分析(DDA)方法评述.水利科技.2004,(1):44-46.
[23]刘军,李仲奎.非连续变形分析(DDA)方法研究现状及发展趋势.岩石力学与工程学报.2004,23(5):839-845.
[24]江巍,郑宏,王彦海.非连续变形分析(DDA)方法理论研究发展现状.黑龙江水专学报.2005,32(4):83-85.
[25]石根华著,裴觉民译.数值流形方法与非连续变形分析.北京:清华大学出版社,1997.
[26]Cundall P A,Strack O D L.A discrete numerical model for granular assembles.Geotechnique.1979,29(1):47-65.
[27]Drescher A,De Jissein De Jong.Photo elastic veification of a granular material.Journal of the Mechanics and Physics of Solids.1972,20:337-351.
[28]李红艳.离散元干-湿颗粒模型研究及应用:(博士学位论文).北京:中国农业大学,2004.
[29]Cundall P A.Computer simulations of dense sphere assemblies.Micromechanics of Granular Materials,Amsterdam,1988:113-123.
[30]Cundall P A.Formulation of a three-dimensional distinct element model-Part Ⅰ:A scheme to detect and represent contacts in a system composed of many polyhedral blocks.International Journal Of Rock Mechanics in Mining Sciences & Geo-mechanics Abstract.1988,25(3):107-116.
[31]Hart R,Cundall P A,Lemos J.Formulation of a three-dimensional distinct element model-Part Ⅱ:Mechanics calculations for motion and interaction of a system composed of many polyhedral blocks.International Journal Of Rock Mechanics in Mining Sciences & Geo-mechanics Abstract.1988,25(3):117-125.
[32]Rothenburg L,Bathurst R J.Micromechanical features of granular assemblies with planar elliptical particles.Geotechnique.1992,42(1):79-95.
[33]Ng T T.Numerical simulation of granular soil using elliptical particles.Computer and Geotechnics.1994,16:153-169.
[34]Ting J M,Khwaja M,Meachum L,et al.An ellipse based discrete element model for granular materials.International Journal for Numerical and Analytical Methods in Geomechanics.1993,17:603-623.
[35]Ng T T.Fabric study of granular materials after compaction.Journal of Engineering Mechanics.1999,125(12):1390-1394.
[36]Lin X,Ng T T.A three-dimensional discrete element model using arrays of ellipsoids.Geotechnique.1997,47(2):319-329.
[37]Williams J R1,O'conner R.A linear complexity intersection algorithm for DEM simulations of arbitrary geometries.Engineering Computations.1995,12:185-201.
[38]Hogue,C.Shape representation and contact detection for discrete elements simulations of arbitrary geometries.Engineering Computations.1998,15(3):374-390.
[39]Favier J F,Kremmer M,Raji A O.Shape representation of axi-symmetrical,non-spherical particles in discrete element simulation using multi-element model particles.Engineering Computations.1999,16(4):467-480.
[40]Thorton C,Barnes D J.Computer simulated deformation of compact granular assemblies.Acta Mechanic.1986,64(1-2):45-61.
[41]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用.沈阳:东北工学院出版社,1991.
[42]麻凤海,范学理,王泳嘉.岩层移动动态过程的离散单元法分析.煤炭学报.1996,21(4):388-392.
[43]焦玉勇,葛修润.三维离散单元法及其在滑坡分析中的应用.岩土工程学报.2000,22(1):101-104.
[44]焦玉勇,张秀丽,刘泉声等.用非连续变形分析方法模拟岩石裂纹扩展.岩石力学与工程学报.2007,26(4):682-691.
[45]焦玉勇,葛修润.三维离散元法地下水及锚杆的模拟.岩石力学与工程学报.1999,18(1):6-11.
[46]张锐,李建桥等.离散单元法在土壤机械特性动态仿真中的应用进展.农业工程学报.2003,19(1):16-19.
[47]徐泳,李艳洁,李红艳.离散元法在农业机械化中应用评述.农机化研究.2004,(5):26-30.
[48]董劲男.基于面向对象技术的离散元法分析设计软件开发研究:(硕士学位论文).长春:吉林大学,2005.
[49]Yu A,Bridgwater J,Burbidge A.On the modeling of the packing of fine particles.Powder Technology.1997,92:185-194.
[50]Xu B,Yu A.Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics.Chemical Engineering Science.1997,52:2786-2809.
[51]Xu B,Yu A,Chew S J.Simulation of the gas-solid flow in a bed with lateral gas blasting.Powder Technology.2000,109:13-26.
[52]刘安源,刘石,姜凡.鼓泡流化床流动特性的欧拉—离散单元方法模拟.燃烧科学与技术. 2003,9(2):148-152.
[53]黎明,谢灼利等.应用离散单元法对二维流化床内流态进行数值模拟研究.北京化工大学学报:自然科学版.2002,29(2):6-10.
[54]俞良群,杨建斌.筒仓内部压力及流场的数值模拟与实验验证.烟台大学学报:自然科学与工程版.1999,12(4):255-262.
[55]徐泳,Kafui K.D.用颗粒离散元法模拟料仓卸料过程.农业工程学报.1999,15(3):65-69.
[56]周德义,马成林.散粒农业物料孔口出流成拱的离散单元仿真.农业工程学报.1996,12(2):186-189.
[57]武锦涛,陈纪忠,阳永荣.模拟颗粒流动的离散元方法及其应用.现代化工.2003,23(4):56-58.
[58]Walton O R.Numerical simulation of inclined chute flows of monodisperse inelastic,frictional spheres.Mechanics of Materials.1993,16:239-247.
[59]Hanes D M,Walton O R.Simulations and physical measurements of glass spheres flowing down a bumpy incline.Powder Technology.2000,109((1-3)):133-144.
[60]Karion A,Hunt M L.Wall stresses in granular Couette flows of mono-sized particles and binary mixtures.Powder Technology.2000,109(1-3):145-163.
[61]Mustoe G G W,Miyata M.Material flow analysis of noncircular-shaped granular media using discrete element methods.Journal of Engineering Mechanics.2001,127(10):1017-1026.
[62]Cleary P W.DEM simulation of industrial particle flows:case studies of dragline excavators,mixing in tumblers and centrifugal mills.Powder Technology.2000,26(2):89-111.
[63]Lorig L J,Brady B H G,Cundall P A.Hybrid discrete element-boundary element analysis of jointed rock.International Journal Rock Mechanics in Mining Science & Geomechanics Abstract.1986,23(4):303-312.
[64]金峰,贾伟伟等.离散元—边界元动力耦合模型.水利学报.2001,(1):23-27.
[65]金峰,王光纶.离散元—边界元动力耦合模型在地下结构动力分析中的应用.水利学报.2001,(2):24-28.
[66]Horner D A,Carrillo A R,Peters J F.High resolution soil vehicle interaction modeling.Mechanics Of Structures And Machines.1998,26(3):305-318.
[67]Homer O A,Peters J F,Carrillo A R.Large scale discrete element modeling of vehicle-soil interaction.Journal of Engineering Mechanics.2001,127(10):1027-1032.
[68]Han K,Peric D,Owen D R J.A combined finite/discrete element simulation of shot peening processes.Part Ⅰ:studies on 20 interaction laws.Engineering Computations.2000,17(5):593-619.
[69]Han K,Peric D,Owen D R J.A combined finite/discrete element simulation of shot peening processes. Part II: 3D interaction laws. Engineering Computations. 2000, 17(65): 680-702.
[70] Owen D R J, Feng Y T. Parallelised finite / discrete element simulation of multi-fracturing solids and discrete systems. Engineering Computations. 2001, 18(3): 557-576.
[71] Buttar W G, You Z P. Discrete element modeling of asphalt concrete: Transportation Research Record. 2001.
[72] 王端宜,张肖宁等. 用虚拟试验方法评价沥青混合料的级配类型. 华南理工大学学报:自然科学版. 2003, 31(2): 48-51.
[73] Johnson K. L. Contact Mechanics. Cambridge: Cambridge University Press, 1989.
[74] Gladwell G. M. L. Contact Probelems in the Classical Theory of Elasticity. Alphen and den Rijn, Sijthoff and Noordhoff, 1980.
[75] Zhu H., Chang C. S., Rish Iii J. M. Normal and tangential compliance for conforming binder contact. I: Elastic binder. Int. J. Solids Stuct. 1996, 33: 4337-4349.
[76] Zhu H., Chang C. S., Rish Iii J. M. Normal and tangential compliance for conforming binder contact. II: visco-elastic binder. Int. J. Solids Stuct. 1996, 33: 4351-4363.
[77] Zhu H., Chang C. S., Rish Iii J. M. Rolling compliance for elastic and viscoelastic conforming binder contact. Int. J. Solids Struct. 1997, 34: 4073-4086.
[78] Zhu Han. A contact mechanism based theory of Maxwell matrix composites. Int. J. Solids Struct. 2001, 38: 4477-4488.
[79] Itasca. PFC2D 2. 00 Particle Flow Code in Two Dimensions. Minneapolis Minnesota., 1998.
[80] Chern J C, Koo C Y, Chen S. Development of Second Order Displacement Function for DDA and Manifold Method. Working Forum on the Manifold Method of Material Analysis, Vicksburg, 1990:183-202.
[81] Koo C Y, Chern J C. The development of DDA with third order displacement function. Proceedings of the First International Forum Discontinuous Deformation Analysis (DDA) and Simulations Discontinuous media, Berkeley, U. S. A, 1996:342-350.
[82] Ma Max Y, Zaman Musharraf, Zhou J H. Discontinuous deformation Analysis using the third order displacement function. Proceedings of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous media, Berkeley, U. S. A, 1996:383-394.
[83] Shi G H. Block System Modeling By Discontinuous Deformation Analysis. Southampton, UK and Boston, USA: Computational Mechanics Publications, 1993.
[84] Bernard Amadei, Chihsen Lin, Jerry Dwyer. Recent Extensions to the DDA Method. proc. 1st Int. Forum on DDA, Berkeley, U.S.A. 1996:1-30.
[85] Hilbert L B Jr, Yi W, Cook N G W. A new discontinuous finite element method for interaction of many deformable bodies ingeomechanics. Pro 8'h Int. Conf. meth adv, Geomech.,1994.
[86]Cai Yongen,Liang Cuo-pin,Shi Geng-hua,et al.Studing impact problem by LDDA method:Discontinuous Deformation analysis(DDA) and Simulations of discontinuous media.TSI Press,1996.
[87]Liang Guo-pin,Wang Cheng-guo.LDDA on the high speed catenary-pantograph system dynamics:Discontinuous Deformation analysis(DDA) and simulations of discontinuous media.TSI press,1996.
[88]Wang Chung-yue,Chuang Ching-chiang,Sheng Jopan.Time Integration Theories for the DDA Method with Finite Element Meshes.proc.1st Int.Forum on DDA,Berkeley,U.S.A,1996:263-287.
[89]Dong Xuecheng,Wu Aiqing,Ren Fang.A Preliminary Application of Discontinuous Deformation Analysis(DDA) to the Three Gorges Project on Yangtze River,China.proc.1st Int.Forum on DDA,Berkeley,U.S.A.,1996:310-317.
[90]Ke Te-chih.Application of DDA to Stability Analysis of Rock Masses.proc.1st Int.Forum on DDA,Berkeley,U.S.A,1996:334-341.
[91]裴觉民,石根华.岩石滑坡体的块体动态稳定和非连续变形分析.水利学报.1993,(3):28-34.
[92]吴洪词.用改进的DDA法模拟岩体的破裂.岩石力学与工程学报.1997,15(增):556-558.
[93]Chris Pearce,Nenad Bicanic,Appapillai Thavalingham,Zhi Hong Liao.On the DDA Framework for Modelling Concrete Fracture.3rd.Int.Conf.on DDA,Colorado,USA,1999.
[94]Yuzo Ohnishi,Shigeru Miki.Development of Circular and Elliptic Disc Elements for DDA.proc.1st Int.Forum on DDA,Berkeley,USA,1996:44-51.
[95]Patricia A Thomas,Jonathan D Bray,Fe-chih Ke.Discontinuous Reformation Analysis for soil mechanics,proc.1st Int.Forum on DDA,Berkeley,USA,1996:454-462.
[96]Guangqi Chen,Shigeru Miki,Yuzo Ohnishi.Development of the interactive visualization system for DDA.Proceedings of The 9th Int.Conf,on computer Methods and Advances in Geomechanics,Wuhan,China,1997:495-500.
[97]Zhang Yonghui,Cheng Yungming.The extension and application of DDA method.岩土工程学报.1998,20(2):109-111.
[98]吴益民.节理岩体三维不连续变形分析方法研究及应用:(博士学位论文).武汉:武汉大学,2003.
[99]Shi Gen-hua.Applications of Discontinuous Deformation Analysis and Manifold Method.3rd Int.Conf.on DDA,Colorado,USA,1999:3-15.
[100]王如路,陈乃明,刘宝深.三维块体不连续变形分析理论简析.岩石力学与工程学报.1996,15(3):219-224.
[101]姜清辉.三维非连续变形分析方法的研究:(博士学位论文).武汉:中国科学院武汉岩土力 学研究所,2000.
[102]Lin Jeen-shang.Continuous and Discontinuous Analysis using the Manifold Method.Proceedings of the First International Conference on Analysis of Discontinuous deformation,Taipei,1995.
[103]Hideomi Ohtsubo,et al.Utilization of Finite Covers in the Manifold Method for Accuracy Control.Proceedings of the 2rd international Conference on Analysis of Discontinuous Deformation,Kyoto,1997.
[104]蔡永吕,张湘伟.流形方法的矩形覆盖系统及其全自动生成算法.重庆大学学报:自然科学版.2001,24(1):42-46.
[105]蔡永吕,朱合华,夏才初.流形方法覆盖系统自动生成算法.同济大学学报:自然科学版.2004,32(5):585-590.
[106]骆少明,姜冬茹等.金属成形过程的数值流形模拟方法研究.机械工程学报.2002,38(8):105-109.
[107]骆少明,蔡永吕等.数值流形方法中的网格重分技术及其应用.重庆大学学报:自然科学版.2001,24(4):34-37.
[108]王水林,葛修润.四个物理覆盖构成一个单元的流形方法及应用.岩石力学与工程学报.1999,18(3):312-316.
[109]田荣,Ugai K.高阶流形方法及其应用.工程力学.2001,18(2):21-26.
[110]Lu Ming.High-Order Manifold Methed With Simplex Integration.Proceedings of ICADD-5,2002.
[111]张国新,彭静.二阶流形元法与结构变形分析.力学学报.2002,34(2):261-269.
[112]Zhang Guoxin,Zhu Bofang,Lu Zhengchao.Cracking Simulation of the Wuqiangxi Ship Lock by Manifold Method.The 6th International conference on analysis of discontinuous deformation,Trondheim,Norway.,2003.
[113]Zhang G X,Sugiura Y,Hasegawa H.Crack propagation and thermal fracture analysis by manifold method.Proceedings of the second international conference on analysis of discontinuous deformation,Kyoto Japan,1997:282-297.
[114]章光,王水林.数值流形方法及其应用介绍.岩土工程界.2000,3(12):44-46.
[115]Sasaki T,Morikawa S,Ishii D,et al.Elastic-plastic analysis of jointed rock models by manifold method.In:Proc.of the 2nd International Conference on Analysis of Discontinuous Deformation,Kyoto,Japan,1997:309-316.
[116]王书法,朱维中等.岩体弹塑性分析的数值流形方法.岩石力学与工程学报.2002,21(6):900-904.
[117]曹文贵,速宝王.岩体锚固支护的数值流形方法模拟及其应用.岩土工程学报.2001,23(5):581-583.
[118]王书法,朱维中等.加锚岩体变形分析的数值流形方法.岩石力学与工程学报.2002,21(8):1120-1123.
[119]王芝银,李云鹏.数值流形方法中的几点改进.岩土工程学报.1998,20(6):33-36.
[120]王芝银,李刚.岩体力学中的增量数值流形方法及其应用.西安矿业学院学报.1998,18(A09):23-27.
[121]朱以文,曾又林.岩石大变形分析的增量流形方法.岩石力学与工程学报.1999,18(1):1-5.
[122]Ke Te-chih,Tang Jyh-haw.Modeling of solid-fluid interaction using the manifold method.In:Proceedings of 2nd North American Rock Mechanics Symposium,Montreal,Quebec,Canada,1996:1815-1822.
[123]王水林.数值流形方法介绍及其应用.岩土工程界.2000,3(12):44-46.
[124]Yuzo Ohnishi,Makoto Tanaka,Tomofumi Koyama.Manifold method in saturated-unsaturated groundwater flow analysis.In:3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice,Vail,Colorado,USA,1999:1213-1228.
[125]林绍忠.单纯形积分的递推公式.长江科学院院报.2005,22(3):32-34.
[126]Lin Dezhang,Mo Haihong.Manifold method of material analysis.In:Working Forum on the Manifold of Material Analysis,Jenner,California,USA,1995:147-164.
[127]周维垣,杨若琼.流形元法及其在工程中的应用.岩石力学与工程学报.1996,15(3):211-218.
[128]周维垣,黄岩松,林鹏.三维无单元伽辽金法及其在拱坝分析中的应用.水利学报.2005,36(6):644-649.
[129]胡云进,周维垣,寇晓东.三维无单元法及其应用.岩石力学与工程学报.2004,23(7):1136-1140.
[130]田荣.连续与非连续变形分析的有限覆盖无单元方法及其应用研究:(博士学位论文).大连:大连理工大学,2000.
[131]张国新,王光纶等.基于流形的结构体破坏分析.岩石力学与工程学报.2001,20(3):281-287.
[132]祁勇峰.数值流形法在三维弹性连续体静力分析中的应用研究:(硕士学位论文).武汉:长江科学院,2005.
[133]梁国平,何江衡.广义有限元方法——一类新的逼近空间.力学进展.1995,25(4):562-565.
[134]王玉杰,张大克.广义有限元法的两个超收敛定理.工科数学.2000,16(2):27-29.
[135]彭自强,李小凯,葛修润.广义有限元法对动态裂纹扩展的数值模拟.岩石力学与工程学报.2004,23(18):3132-3137.
[136]栾茂田,田荣.广义节点有限元法.计算力学学报.2000,17(2):192-200.
[137]曹国金,姜弘道.无单元法研究和应用现状及动态.力学进展.2002,32(4):526-534.
[138]Genki Yagawa,Tomonari Furukawa.Recent Developments of Free Mesh Method.Int.J.Numer.Mech.Engng.2000,47:1419-1443.
[139] Belytschko T, Krongauz Y, Organ D. Meshless methods: an overview and recent developments. Computer Methods In Applied Mechanics And Engineering. 1996, 139:3-47.
[140] 张雄,宋康祖,陆明万. 无网格法研究进展及其应用. 计算力学学报. 2003, 20(6):730-742.
[141] Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astron Journal. 1977, 8: 1013-1024.
[142] Monaghan J J. An introduction to SPH. Comp Phys Comm. 1988, 48: 89-96.
[143] Liu W K, Jun S L, Shaofau A, et al. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering. 1995, 38: 1655-1679.
[144] Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse Approximation and diffuse elements. Computational Mechanics. 1992, 10: 307-318.
[145] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin Methods. International Journal for Numerical Methods in Engineering. 1994, 37: 229-256.
[146] Arluri S N, Zhu T. A New Meshless Local Pretrov-Galerkin Approach in Computational Mechanics. Computational Mechanics. 1998, 22(2): 117-127.
[147] Zhu T, Zhang J, Arluri S N. A Meshless Local Boundary Integral Equation Method for Solving Nonlinear Problems. Computational Mechanics. 1998, 22(3): 174-186.
[148] Melen J M, Babuska I. The Partition of Unity Finite Element Method: Basic Theory and Application. Comp. Methods in Appl. Mech. and Engng. 1996, 139: 289-314.
[149] Sukumar N, Moran B Belytschko T. The Natural Element Method in Solid Mechanics. Int. J. Numer. Methods Engng. 1998, 43: 839-887.
[150] Natarajan Sukumar. The Natural Element Method in Solid Mechanics: (ph. D Dissertation). Northwestern University, 1998.
[151] Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Comput Mech. 1999, 23: 219-230.
[152] Belytschko T, Krongauz Y, Organ D Et Al. Smoothing and acclerated computations in the element free Galerkin method. J. Comput. Appl. Math. 1996, 74: 111-126.
[153] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. Int J Numer Methods Engrg. 1998, 41: 1215-1233.
[154] Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. Int J Numer Methods Engrg. 1996, 29: 923-938.
[155] Belytschko T, Lu Y Y, Gu L. Crack propagation by element-free Galerkin methods. Engrg Frac Mech. 1995, 51: 295-315.
[156] Liu G R, Gu Y T. Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Comput Mech. 2000, 26: 166-173.
[157] Belytschko T, Organ D, Krongauz Y. A coupled finite element-element free Galerkin method.Comput Mech.1995,17:186-195.
[158]Zhang X,Liu X H,Song K Z Et Al.Least-square collocation meshless method.Int J Numer Methods Engrg.2001,51(9):1089-1100.
[159]张雄,胡炜,潘小飞等.加权最小二乘无网格法.中国计算力学大会2001论文集,广州,2001:333-338.
[160]石金龙.计算机辅助设计与工程分析中的数值流形方法:(硕士学位论文).长沙:国防科学技术大学,2004.
[161]Jia Lu,Liu Chengxue.Introduction of Element-Free Gaierkin Method(EFGM) and Its Preliminary Application in Asphalt Pavement Mechanical Analysis.Transportation Research Board(TRB) 87th Annual Meeting,Washington DC,2008.
[162]Bathurst R J,Rothenburg L.Micromechanical aspects of isotropic granular assemblies with linear contact interactions..J.Appl.Mech.Am.Soc.Mech.Engrs.1988,55:17-23.
[163]Lin X,Ng T T.Contact detection algorithms for three-dimensional ellipsoids in discrete element modeling.International Journal for Numerical and Analytical Methods in Geomechanics.1995,(19):653-659.
[164]Thomas P.Discontinuous deformation analysis of particulate media:(Ph.D disseration).Univ.of California,Berkeley,1977.
[165]Feng Y T,Han K,Owen D R J.Filling domains with disks:An advancing front approach.Inter.J.Numer.Methods in Engineering.2003,56(5):699-731.
[166]O'sullivan C,Bray J D,Riemer M F.Influence of particle shape and surface friction variability on response of rod-shaped particulate media.ASCE J.Engineering Mechanics.2002,128(11):1182-1192.
[167]Ferrez J A.Dynamic triangulations for efficient 3-D simulation of granular materials:(Ph.D disseration),Lausanne,:Ecole Polytechnique Federal de Lausanne,2001.
[168]Bagi K.From order to chaos:The mechanical behavior of regular and irregular assemblies.Proceedings QuaDPM'03 Workshop,BUTE Budapest,2003:33-42.
[169]Cui L,O'sullivan C.Analysis of a triangulation based approach for specimen generation for discrete element simulations.Granular Matter.2003,5:135-145.
[170]张登良.沥青与沥青混合料.北京:人民交通出版社,1993.
[171]沈金安.沥青及沥青混合料路用性能·.北京:人民交通出版社,2001.
[172]Vemuri B C,Chen L,Vu-quou L,et al.Efficient and accurate collision detection for granular flow simulation.Graphical Models and Image Processing.1998,60:403-422.
[173]Asmar B N,Langston P A.Validation tests on a distinct element model of vibrating cohesive particle systems.Computers and Chemical Engineering.2002,26:785-802.
[174]Vu-quoc L,Zhang X,Walton O R.A 3-D discrete-element method for dry granular flows of ellipsoidal particles.Comput.Methods Appl.Mech.Engrg.2000,187:483-528.
[175]姜清辉,杨文柱,吴益民等.三维非连续变形分析方法中摩擦接触问题的研究.岩石力学与工程学报.2002,21(增2):2418-2421.
[176]郑榕明,张勇慧.基于六面体覆盖的三维数值流形方法的理论探讨与应用.岩石力学与工程学报.2004,23(10):1745-1754.
[177]姜清辉,张煜.三维离散块体边-边接触模拟.岩土力学.2006,27(8):1369-1373.
[178]郑金华.稀疏矩阵的存储结构和乘法运算.湘潭大学自然科学学报.1994,16(2):133-136.
[179]张永杰,孙秦.稀疏矩阵存储技术.长春理工大学学报.2006,29(3):38-47.
[180]彼得·艾伯哈特,胡斌.现代接触动力学.南京:东南大学出版社,2003.
[181]陆群花.大型稀疏线代数方程组的几种数值算法研究:(硕士学位论文).兰州:兰州大学,2007.
[182]王勖成.有限单元法.北京:清华大学出版社,2003.
[183]傅闻远,卓家寿.无网格的崛起与发展—一种新兴的数值方法评述.河海大学学报.1999,27:51-58.
[184]张雄,刘岩.无网格法.北京:清华大学出版社,2004.
[185]Liu G R,Gu Y T著,王建明等译.无网格法理论及程序设计.济南:山东大学出版社,2007.
[186]张义同.热粘弹性理论.天津:天津大学出版社,2002.
[187]Durbin F.Numerical inversion of Laplace transforms:An efficient improvement to Dubner and Abate's method.The Computer Journal.1973,17(4):371-376.
[188]曹建新.重交通下级配碎石基层材料组成结构与动力特性的研究:哈尔滨:哈尔滨工业大学,2001.
[189]沙庆林.高速公路沥青路面早期破坏与对策.长沙理工大学学报:自然科学版.2006,3(3):1-6.
[190]孙立军,张宏超,刘黎萍.沥青路面初期损坏特点和机理分析.同济大学学报.2002,30(4):416-421.
[191]Hoven J M.Measurement and analysis of pore water pressure in thawing pavement structures subjected to dynamic loading:(Ph.D disseration),the Univ.of Minnesota,USA,1997.
[192]彭永恒,任瑞波,宋凤立.轴对称条件下层状弹性体超孔隙水压力的求解.工程力学.2004,21(4):204-208.
[193]Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid.The Journal of the Acoustical Society of America.1956,28(2):166-191.