一类界面元建模与分析方法及其在装备设计中的应用研究
|
摘要
界面元是指两种连续结构或连续结构与离散介质在接触界面一定范围内的有限单元集或有限单元/粒子单元集。界面元方法是研究界面元区域内单元之间的力作用和结点属性等效传递的一种数字化模拟方法。本文提出界面元方法来模拟和分析装备工作过程中连续结构与离散介质、连续结构与连续结构在相互作用界面的作用力计算、单元结点属性的等效传递问题,研究工作主要体现在以下五个方面：
1针对界面元方法预处理阶段需要快速生成离散颗粒集问题,提出一种几何和物理相结合的颗粒集生成算法,充分利用离散介质颗粒单元的几何特性和颗粒下落时的物理特性,构建了几何与物理特性相结合的颗粒堆积移动模型,快速生成二维域圆形颗粒集和三维域球形颗粒集,生成颗粒集的时间与颗粒数量成线性关系,且颗粒集密度高,生成时间短。
2为了模拟和计算连续结构与离散介质之间的相互作用力,提出基于单元/粒子接触的界面元方法,根据有限单元与粒子单元之间的几何接触情形,采用线弹性模型直接计算单个离散颗粒与有限元面片间的作用力,再将计算得到的作用力等效至有限元节点,进一步计算有限元节点的受力和位移,可视化显示了离散介质的受力、变化状况和连续结构的受力、应变状况。
3针对大规模粒子集在机械结构作用下的应力、应变分析问题,提出基于单元／粒子交迭的界面元模型,将直接受结构作用的区域及其近邻区域用离散元表示,较远区域则用六面体有限单元表示,两种单元区域在它们的相互作用界面有一定程度的交迭。在交迭区,将有限单元内离散粒子的质量、受力等效传递至有限元节点,得有限元节点加速度,将有限元节点的速度、加速度等参插值至离散单元,得离散粒子所在位置的应变和应力,同时以交迭区有限单元的受力作为边界条件求解整个区域的受力和变形状况。
4为了解决多个有限元网格在接触界面的节点不匹配而导致节点属性不能光滑传递的问题,提出异构网格界面元方法,构建了二维异构的四边形单元节点及其错位节点形函数,实现异构四边形单元网格在接触界面属性的光滑传递,将该方法进一步延伸至四边形网格与三角形网格之间的界面元分析；同时研究了三维异构的六面体单元网格之间结点属性的光滑传递方法。通过一个异构网格接触实例验证了方法的正确性,并将方法应用于齿轮的接触分析。
5提出了主/辅网格节点属性等效集成方法，以解决异构有限元网格多场信息难以集成显示的问题。将多个有限元网格模型中的一个作为主网格,其它作为辅网格,将辅网格单元节点信息向主网格节点等效转移,最终在主网格单元节点中实现多场信息的集成显示。研究结果分析了盾构刀盘掘进过程中刀具和刀盘受到的应力场和温度场综合作用分布和多场作用的最强区域,为刀具和刀盘设计提供了依据。
The interface element(IE) is the finite elements within a certain range of the contact interface between two kinds of continuous structures, or finite/discrete elements between continuous structure and discrete media. The interface element method(IEM) is a numerical simulation method of researching the interaction and the equivalent transition of node property between elements within IE region. This paper puts forward the IEM to simulate and analyze the interaction and the equivalent transition of node property on the interactive interface between continuous mechanical structures and between continuous mechanical structure and discrete media in the working process of mechanical equipment. This research work can be reflected in the following five aspects:
First, for a discrete particle assembly should being generated quickly in the preprocessing stage of IEM, an algorithm by considering geometric and physical factors is put forward, this algorithm constructs the moving model of particle packing by making best use of the geometrical and physical properties of discrete element. It can quickly generate circular particle assembly in2D region and sphere particle assembly in3D region. The time to create the granular particles set is linear with the particle number and this process is completed in a comparatively short time with high-density particles set.
Second, a IE model on the direct contact interface of the finite/discrete element is proposed for simulating and computing the interaction between continuous structure and discrete media. According to the geometrical touch type between finite and discrete element, the interaction force between discrete element and finite element patch is calculated with linear elastic model. Then the contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the force and the change of displacement of discrete media can be visualized ideally, and it is the same case with the force and the strain of continuous structure.
Third, aiming at the analysis of stress and strain of discrete media composed of a great number of particles acted by mechanical structure, a IE model is proposed in the overlap region presented by finite and discrete element in one kind of media, The region acted by mechanical structure directly and its near region is presented by discrete element, the far region by finite element with hexahedron, and the regions of these two kind of elements have an overlapping level on their interface. In the overlapping region, first, with the particle-in-cell method, the mass of the discrete particle which lies in the finite element and the force acting on the particle are equivalent to the nodes of the finite elements. Then the velocity and acceleration of the node of the finite element is obtained. Last, the velocity and acceleration are isoparametric interpolated to the discrete element, so the strain and stress on the position of discrete particle can also be obtained. At the same time, the force and strain of the whole region can be solved with the boundary condition of the force of the finite element in the overlapping region.
Fourth, in order to solve the problem that the node property can't transit smoothly on the interface of two or many contact heterogeneous meshes with non-matching nodes, the model and the analysis method of interface element between heterogeneous finite element meshes is put forward, the shape functions of the nodes and the non-matching nodes of2-D heterogeneous quadrilateral element are constructed, the smooth connection of the attributes at the contact face for heterogeneous quadrilateral element is realized, and the method is extended to the analysis of the interface element between the quadrilateral mesh and the triangular mesh. In the meanwhile, the method for the smooth connection of the nodal attributes of the heterogeneous hexahedron elements in3D is studied. For the proposed method, its correctness is verified by one example of heterogeneous interface mesh, and it is applied to the contact analysis of the gears.
Fifth, a primary-secondary-mesh method is put forward which focuses on how to integrate the properties of the multiple physical fields on heterogeneous finite element meshes. That is, one of the heterogeneous meshes is taken as primary mesh and the other the secondary one. The properties of the secondary mesh are equivalent to that of the primary mesh by the inverse isoparametric mapping method, thus, all the different fields on different meshes are integrated and visualized on the primary mesh. This method has already been used to integrate and visualize the stress field and the temperature field on the cutters and cutter head of the shield machine, the strongest effect aera of multi-physical fields is got, and some advice on the structural design of the cutters and the cutter head is given by the finite element analysis.
1针对界面元方法预处理阶段需要快速生成离散颗粒集问题,提出一种几何和物理相结合的颗粒集生成算法,充分利用离散介质颗粒单元的几何特性和颗粒下落时的物理特性,构建了几何与物理特性相结合的颗粒堆积移动模型,快速生成二维域圆形颗粒集和三维域球形颗粒集,生成颗粒集的时间与颗粒数量成线性关系,且颗粒集密度高,生成时间短。
2为了模拟和计算连续结构与离散介质之间的相互作用力,提出基于单元/粒子接触的界面元方法,根据有限单元与粒子单元之间的几何接触情形,采用线弹性模型直接计算单个离散颗粒与有限元面片间的作用力,再将计算得到的作用力等效至有限元节点,进一步计算有限元节点的受力和位移,可视化显示了离散介质的受力、变化状况和连续结构的受力、应变状况。
3针对大规模粒子集在机械结构作用下的应力、应变分析问题,提出基于单元／粒子交迭的界面元模型,将直接受结构作用的区域及其近邻区域用离散元表示,较远区域则用六面体有限单元表示,两种单元区域在它们的相互作用界面有一定程度的交迭。在交迭区,将有限单元内离散粒子的质量、受力等效传递至有限元节点,得有限元节点加速度,将有限元节点的速度、加速度等参插值至离散单元,得离散粒子所在位置的应变和应力,同时以交迭区有限单元的受力作为边界条件求解整个区域的受力和变形状况。
4为了解决多个有限元网格在接触界面的节点不匹配而导致节点属性不能光滑传递的问题,提出异构网格界面元方法,构建了二维异构的四边形单元节点及其错位节点形函数,实现异构四边形单元网格在接触界面属性的光滑传递,将该方法进一步延伸至四边形网格与三角形网格之间的界面元分析；同时研究了三维异构的六面体单元网格之间结点属性的光滑传递方法。通过一个异构网格接触实例验证了方法的正确性,并将方法应用于齿轮的接触分析。
5提出了主/辅网格节点属性等效集成方法，以解决异构有限元网格多场信息难以集成显示的问题。将多个有限元网格模型中的一个作为主网格,其它作为辅网格,将辅网格单元节点信息向主网格节点等效转移,最终在主网格单元节点中实现多场信息的集成显示。研究结果分析了盾构刀盘掘进过程中刀具和刀盘受到的应力场和温度场综合作用分布和多场作用的最强区域,为刀具和刀盘设计提供了依据。
The interface element(IE) is the finite elements within a certain range of the contact interface between two kinds of continuous structures, or finite/discrete elements between continuous structure and discrete media. The interface element method(IEM) is a numerical simulation method of researching the interaction and the equivalent transition of node property between elements within IE region. This paper puts forward the IEM to simulate and analyze the interaction and the equivalent transition of node property on the interactive interface between continuous mechanical structures and between continuous mechanical structure and discrete media in the working process of mechanical equipment. This research work can be reflected in the following five aspects:
First, for a discrete particle assembly should being generated quickly in the preprocessing stage of IEM, an algorithm by considering geometric and physical factors is put forward, this algorithm constructs the moving model of particle packing by making best use of the geometrical and physical properties of discrete element. It can quickly generate circular particle assembly in2D region and sphere particle assembly in3D region. The time to create the granular particles set is linear with the particle number and this process is completed in a comparatively short time with high-density particles set.
Second, a IE model on the direct contact interface of the finite/discrete element is proposed for simulating and computing the interaction between continuous structure and discrete media. According to the geometrical touch type between finite and discrete element, the interaction force between discrete element and finite element patch is calculated with linear elastic model. Then the contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the force and the change of displacement of discrete media can be visualized ideally, and it is the same case with the force and the strain of continuous structure.
Third, aiming at the analysis of stress and strain of discrete media composed of a great number of particles acted by mechanical structure, a IE model is proposed in the overlap region presented by finite and discrete element in one kind of media, The region acted by mechanical structure directly and its near region is presented by discrete element, the far region by finite element with hexahedron, and the regions of these two kind of elements have an overlapping level on their interface. In the overlapping region, first, with the particle-in-cell method, the mass of the discrete particle which lies in the finite element and the force acting on the particle are equivalent to the nodes of the finite elements. Then the velocity and acceleration of the node of the finite element is obtained. Last, the velocity and acceleration are isoparametric interpolated to the discrete element, so the strain and stress on the position of discrete particle can also be obtained. At the same time, the force and strain of the whole region can be solved with the boundary condition of the force of the finite element in the overlapping region.
Fourth, in order to solve the problem that the node property can't transit smoothly on the interface of two or many contact heterogeneous meshes with non-matching nodes, the model and the analysis method of interface element between heterogeneous finite element meshes is put forward, the shape functions of the nodes and the non-matching nodes of2-D heterogeneous quadrilateral element are constructed, the smooth connection of the attributes at the contact face for heterogeneous quadrilateral element is realized, and the method is extended to the analysis of the interface element between the quadrilateral mesh and the triangular mesh. In the meanwhile, the method for the smooth connection of the nodal attributes of the heterogeneous hexahedron elements in3D is studied. For the proposed method, its correctness is verified by one example of heterogeneous interface mesh, and it is applied to the contact analysis of the gears.
Fifth, a primary-secondary-mesh method is put forward which focuses on how to integrate the properties of the multiple physical fields on heterogeneous finite element meshes. That is, one of the heterogeneous meshes is taken as primary mesh and the other the secondary one. The properties of the secondary mesh are equivalent to that of the primary mesh by the inverse isoparametric mapping method, thus, all the different fields on different meshes are integrated and visualized on the primary mesh. This method has already been used to integrate and visualize the stress field and the temperature field on the cutters and cutter head of the shield machine, the strongest effect aera of multi-physical fields is got, and some advice on the structural design of the cutters and the cutter head is given by the finite element analysis.
引文
[1]. Florian, F., G. Timo, and E. Peter, Applications of the discrete element method in mechanical engineering[J]. Multibody System Dynamics,2007.18(1):p.81-94.
[2]. Rojek, J. and E. Onate, Multiscale analysis using a coupled discrete/finite element model[J]. Interaction and Multiscale Mechanics,2007.1(1):p.1-31.
[3]. Ivo, B., The finite element method with Lagrangian multipliers[J]. Numeric Mathmatics,1972.20(3):p.179-192.
[4]. Cichosz, T. and M. Bischoff, Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers[J]. Computer Methods in Applied Mechanics and Engineering,2011.200 (9-12):p.1317-1332.
[5]. Babuska, I. and GN. Gatica, On the mixed finite element method with Lagrange multipliers[J]. Numerical Methods for Partial Differential Equations,2003. 19(2):p.192-210.
[6]. McDevitt, T.W. and T.A. Laursen, A mortar-finite element formulation for frictional contact problems[J]. International Journal for Numerical Methods in Engineering,2000.48(10):p.1525-1547.
[7]. Yang, B., T.A. Laursen, and X. Meng, Two dimensional mortar contact methods for large deformation frictional sliding [J]. International Journal for Numerical Methods in Engineering,2005.62(9):p.1183-1225.
[8]. Moaveni, S., Finite Element Analysis:Theory and Application with Ansys[M], 3rd edition.北京：电子工业出版社,2008：p.245-260.
[9]. Abo-Elnor, M., R. Hamilton, and J.T. Boyle, Simulation of soil-blade interaction for sandy soil using advanced 3D finite element analysis[J]. Soil & Tillage Research 2004.75(1):p.61-73.
[10]. Han, K., et al., A combined finite/discrete element simulation of shot peening processes Part I:studies on 2D interaction laws[J]. Engineering Computations, 2000.17(5):p.593-619.
[11]. Walton, O.R., Numerical simulation of inelastic, frictional particle-particle interactions in Roco[M]. Particulate Two-Phase Flow Butterworths, Boston, MA, 1992:p.884-911.
[12]. Timoshenko, S.P. and J.N. Goodier, Theory of Elasticity [J]. International Journal of Bulk Solids Storage in Silos,1970.1(4):p.140-142.
[13]. Oden, J.T. and J.A.C. Martins, Models and computational methods for dynamic friction phenomena[J]. Computer Methods in Applied Mechanics and Engineering,1985.52(1-3):p.527-634.
[14]. Nardin, A., G. Zavarise, and B.A. Schrefler, Modelling of cutting tool-soil interaction-part I:contact behaviour[J]. Computational Mechanics,2003. 31(3-4):p.327-339.
[15]. Nardin, A. and B.A. Schrefler, Modelling of cutting tool-soil interaction-part II:macromechanical model and upscaling[J]. Computational Mechanics,2005. 36(5):p.343-359.
[16]. Lilliu, G. and J.G.M. van Mier,3D lattice type fracture model for concrete[J]. Engineering Fracture Mechanics,2003.70(7-8):p.927-941.
[17]. Han, K., et al., A combined finite/discrete element simulation of shot peening processes Part Ⅱ:3D interaction laws[J]. Engineering Computations (Swansea, Wales),2000.17(Compendex):p.680-702.
[18]. Han, K., D.R.J. Owen, and D. Peric, Combined finite/discrete element and explicit/implicit simulations of peen forming process[J]. Engineering Computations,2002.19(1):p.92-118.
[19]. Dowding, C., T. Belystschko, and H. Yen, A coupled finite element-rigid block method for transient analysis of rock caverns[J]. International Journal for Numerical and Analytical Methods in Geomechanics 1983.7(1):p.117-127.
[20]. Carrillo, A.R., et al., Design of a Large Scale Discrete Element Soil Model for High Performance Computing Systems[C]. Proceedings of the ICM/IEEE Super Computer Conference. Pittsburg, PA, ACM, New York.,1996:p.17-22.
[21]. Tanaka, H., et al., Simulation of loosening at subsurface tillage using a vibrating type subsoiler by means of the distinct element method[J]. Proceedings of the 8th European ISTVS Conference, Umea,2000:p.32-37.
[22]. Horner, D.A., J.F. Peters, and A. Carrillo, Large scale discrete element modeling of vehicle-soil interaction[J]. Journal of Engineering Mechanics,2001.127(10): p.1027-1032.
[23]. Hello, B.L., et al., Coupling finite elements and discrete elements methods, application to reinforced embankment by piles and geosynthetics[C]. Proceedings of the 6th European Conference on Numerical Methods in Geotechnical Engineering-Numerical Methods in Geotechnical Engineering, 2006:p.843-848.
[24]. Villard, P., et al., Coupling between finite and discrete element methods for the modelling of earth structures reinforced by geosynthetic[J]. Computers and Geotechnics,2009.36(5):p.709-717.
[25]. Mohammad, H., D. Denis, and S. Karam, Static and dynamic studies for coupling discrete and continuum media:Application to a simple railway track model[J]. International Journal of Solids and Structures,2010.47(2):p. 276-290.
[26]. Lim, J.H., S. Im, and Y.-S. Cho, MLS (moving least square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering,2007. 196(17-20):p.2216-2228.
[27]. Fakhimi, A., A hybrid discrete-finite element model for numerical simulation of geomaterials[J]. Computers and Geotechnics,2009.36(3):p.386-395.
[28]. Caia, M., et al., FLAC/PFC coupled numerical simulation of AE in large-scale underground excavations[J]. International Journal of Rock Mechanics & Mining Sciences,2007.44(4):p.550-564.
[29]. 周健等,基于颗粒单元接触的二维离散-连续耦合分析方法[J].岩土工程学报,2010.32(10)：p.1479-1484.
[30]. Hazzard, J.F. and R. Young, P, Moment tensors and micromechanical models[J]. Tectonophysics,2002.356(1-3):p.181-97.
[31]. Wang, Z.L., H. Konietzky, and R.F. Shen, Coupled finite element and discrete element method for underground blast in faulted rock masses[J]. Soil Dynamics and Earthquake Engineering,2009.29(6):p.939-945.
[32]. Feng, Y.T., K. Han, and D.R.J. Owen, Filling domains with disks:an advancing front approach[J]. International Journal for Numerical Methods in Engineering, 2003.56(5):p.699-713.
[33]. Bagi, K., An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies[J]. Granular Matter,2005.7(1):p. 31-43.
[34]. Munjiza, A. and K.R.F. Andrews, NBS contact detection algorithm for bodies of similar size[J]. International Journal for Numerical Methods in Engineering, 1998.43(1):p.131-149.
[35]. Benabbou, A., et al., Sphere Packing and Applications to Granular Structure Modeling[C]. Proceedings of the 17th International Meshing Roundtable, Part 1, 2008:p.1-18.
[36]. Gensane, T. and P. Ryckelynck, Producing dense packings of cubes[J]. Discrete Mathematics,2008.308(22):p.5230-5245.
[37]. Munjiza, A., J.P. Latham, and K.R.F. Andrews, Challenges of a coupled combined finite-discrete element approach to explosive induced rock fragmentation[J]. International Journal for Blasting and Fragmentation,1999. 3(3):p.237-250.
[38]. Han, K., Y.T. Feng, and D.R.J. Owen, Sphere packing with a geometric based compression algorithm[J]. Powder Technology,2005.155(1):p.33-41.
[39]. Thomas, P., Discontinuous deformation analysis of particulate media[D]. Berkeley, University of California,1997:p.30-35.
[40]. Bagi, K., A quasi-static numerical model for micro-level analysis of granular assemblies[J]. Mechanics of Materials,1993.16(1-2):p.101-110.
[41]. Lin, X. and T.T. Ng, A three-dimensional discrete element model using arrays of ellipsoids[J]. Geotechnique,1997.47(2):p.319-329.
[42]. Sakaguchi, h. and a. Murakami, Initial packing in discrete element modeling[J]. Discrete Element Methods,3rd International Conference,ASCE,New Mexico, 2002(23-25):p.104-106.
[43]. Sullivan, c. The application of discrete element modelling to finite deformation problems in geomechanics[D]. Berkeley, University of California,2002:p. 35-48.
[44]. Benabbou, A., et al., Numerical modeling of nanostructured materials[J]. Finite Elements in Analysis and Design,2010.46(1-2):p.165-180.
[45]. Haggstrom, O. and R. Meester, Nearest neighbour and hard sphere models in continuum percolation[J]. Random Structures and Algorithms,1996.9(3):p. 295-315.
[46]. Stoyan, D., Models of random systems of non-intersecting spheres[J].,1998. Stochastics'98, JCMF, in:Prague:p.543-547.
[47]. Cui, L. and C. O'Sullivan, Analysis of a triangulation based approach for specimen generation for discrete element simulations[J]. Granular Matter 2003. 5(3):p.135-145.
[48]. E1-Hamalawi, A., A 2D combined advancing front-Delaunay mesh generation scheme[J]. Finite Elements in Analysis and Design,2004.40(9-10):p.967-989.
[49]. Lo, S.H. and W.X. Wang, Generation of finite element mesh with variable size over an unbounded 2D domain[J]. Computer methods in appllied mechanics and engineering,2005.194(45-47):p.4668-4684.
[50]. Wang, W.X., C.Y. Ming, and S.H. Lo, Generation of triangular mesh with specified size by circle packing[J]. Advances in Engineering Software,2007. 38(2):p.133-142.
[51]. Benabbou, A., H. Borouchaki, and P. Laug, Geometrical modeling of granular structures in two and three dimensions[J]. International Journal for Numerical Methods in Engineering,2009.80(4):p.425-454.
[52]. Ferrez, J.-a., Dynamic triangulations for efficient 3D simulation of granular materials[D]. Lausanne,EPFL,2001:p.18-26.
[53]. Munjiza, A., E. Rougier, and N.W.M. John, MR linear contact detection algorithm[J]. International Journal for Numerical Methods in Engineering,2006. 66(1):p.46-71.
[54]. Perkins, E. and J.R. Williams, A fast contact detection algorithm insensitive to object sizes[J]. Engineering Computations,2001.18(1-2):p.48-61.
[55]. Williams, J.R., E. Perkins, and B. Cook, A contact algorithm for partitioning arbitrary sized objects [J]. Engineering Computations:Int J for Computer-Aided Engineering,2004.21(2-3):p.235-248.
[56].王燕民,李竟先,E. Forssberg,颗粒堆积现象的计算机模拟[J].硅酸盐学报,2003.31(2)：p.169-178.
[57]. 刘浩斌,颗粒尺寸分布与堆积理论[J].硅酸盐学报,1991.19(2)：p.164-172
[58]. 李艳洁,徐泳,用离散元模拟颗粒堆积问题[J].农机化研究,2005.27(2)：p.57-59.
[59]. 刘军,刘汉龙,用Monte Carlo方法模拟砂土的自然堆积过程[J].岩土力学,2005.26(增刊1)：p.113-116.
[60]. 刘凯欣,高凌天,离散元法研究的评述[J].力学进展,2003.33(4)：p.483-490.
[61]. Cundall, P.A., A computer model for simulating progressive, large-scale movements in blocky rock systems[J]. In Rock fracture, proc. int. symp. on rock fracture, Nancy,1971. p.2-8.
[62]. Maini, T. and P.A. Cundall, Computer modeling of jointed rock mases[J]. Technical report N-78-4, U.S. Army Engineer Waterways Experiment station, Vicksburg, Mississippi,1978.
[63]. Cundall, P.A. and O.D.L. Strack, The development of constitutive laws for soil using the distinct element method[J]. Proc.3rd Numerical Methods In Geomechanics. Aachen,1979:p.289-298.
[64]. Thornton, C. and D.J. Barnes, Computer simulated deformmion of compact granular assemblies[J]. Acta Mechanica,1986.64(1):p.45-61.
[65]. Thornton, C., On the relationship between the modulus of particulate media and the surface energy ofthe constituent particles[J]. Journal of Physics D:Applied Physics,1993.26(10):p.1587-1591.
[66]. Liu, K., L.T. Gao, and S. Tanimura, Application of discrete element method in impact problems[J]. JSME International Journal,2004.47(2):p.138-145.
[67]. Liu, K. and L.T. Gao, The application of discrete element method in solving three dimension impact dynamics problems[J]. Acta Mechniaca Solid,2003. 16(3):p.256-261.
[68]. 川井忠彦,都井裕,平面歪问题の离散化解析に[J].生产研究,1977.29(4)：p.204-207.
[69]. Sawamoto, Y., H. Tsubota, and Y. Kasai, Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method[J]. Nuclear Engineering and Design,1998.179(2):p.157-177.
[70]. Potyondy, D.O. and P.A. Cundall, Abonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004.41(8):p. 1329-1364.
[71]. Shmulevich, I., Z. Asaf, and D. Rubinstein, Interaction between soil and a wide cutting blade using the discrete element method[J]. Soil&Tillage Research,2007. 97(1):p.37-50.
[72]. Ali, A.Y. and S.M. Bradshaw, Bonded-particle modelling of microwave-induced damage in ore particles[J]. Minerals Engineering,2010.23(10):p.780-790.
[73]. Franco, Y, D. Rubinstein, and I. Shmulevich, Determination of discrete element model parameters for soil-bulldozer blade interaction[J]. Proceedings of the 15th International Conference of the ISTVS Hayama, Japan, September,2005:p. 25-29.
[74]. Asaf, Z., D. Rubinstein, and I. Shmulevich, Determination of discrete element model parameters required for soil tillage[J]. Soil & Tillage Research 2007. 92(1-2):p.227-242.
[75]. Campbell, C.S. and C.E. Brennen, Computer simulation of chute flows of granular materials[J]. IUTAM Conference on Deformation and Failure of Granular Materials of Granular Materials, Delft,,1982. Netherlands,31 August-3 September 1982:p.515-521.
[76]. Langston, P.A., U. Tuzun, and D.M. Heyes, Discrete element simulation of granular flow in 2d and 3d hoppers:dependence of discharge rate and wall stress on particle interactions[J]. Chemical Engineering Science,1995.50(6):p. 967-987.
[77]. Walton, O.R., Numerical simulation of inclined chute flows of monodisperse,inelastic, frictional spheres [J]. Mechanics of Materials 1993. 16(1-2):p.239-247.
[78]. Hirshfeld, D., Y. Radzyner, and D.C. Rapaport, Molecular dynamics studies of granular flow through an aperture[J]. PHYSICAL REVIEW E 1997.56(4):p. 4404-4415.
[79]. Cleary, P.W. and M.L. Sawley, DEM modelling of industrial granular flows:3D case studies and the effect of particle shape on hopper discharge[J]. Applied Mathematical Modelling,2002.26(2):p.89-111.
[80]. Goda, T.J. and F. Ebert, Three-dimensional discrete element simulations in hoppers and silos[J]. Powder Technology,2005.158(1-3):p.58-68.
[81]. Shimizu, Y. and P.A. Cundall, Three-dimensional DEM simulations of bulk handling by screw conveyors[J]. Journal of Engineering Mechanics,2001. 127(9):p.864-872.
[82]. Owen, P.J. and P.W. Cleary, Prediction of screw conveyor performance using the Discrete Element Method (DEM)[J]. Powder Technology,2009.193(3):p. 274-288.
[83]. Moysey, P.A. and M.R. Thompson, Modelling the solids inflow and solids conveying of single-screw extruders using the discrete element method[J]. Powder Technology,2005.153(2):p.95-107.
[84]. Cleary, P.W., The filling of dragling buckets[J]. Mathematical Engineering in Industry,1998.7(1):p.1-24.
[85]. Mishra, B.K., Study of media mechanics in tumbling mills by thediscrete element method(D). The University of Utah,1991:p.43-48.
[86]. Mishra, B.K. and R.K. Rajamani, The discrete element method for simulation of ball mills[J]. Applied Mathematical Modelling,1992.16(11):p.598-604.
[87]. Mishra, B.K. and R.K. Rajamani, Simulation of charge motion in ball mills:Part 1. Experimental verifications[J]. International Journal of Mineral Processing, 1994.40(3-4):p.171-186.
[88]. Djordjevic, N., Discrete element modelling of the influence of lifters on power draw of tumbling mills[J]. Minerals Engineering,2003.16(4):p.331-336.
[89]. Djordjevic, N., F.N. Shi, and R.D. Morrison, Applying discrete element modelling to vertical and horizontal shaft impact crushers [J]. Minerals Engineering,2003.16(10):p.983-991.
[90]. 王泳嘉,离散单元法-一种适用于节理岩石力学分析的数值方法[C].第一届全国岩石力学数值计算及模型试验讨论会论文集,中国,江西,吉安,1986：p.215-230.
[91].鞠剑,基于超圆颗粒模型的离散元软件开发研究[D].中国,大连,大连理工大学,2006：p.45-60.
[92]. 王泳嘉,宋文洲,赵艳娟,离散单元法软件系统2D-block的现代化特点[J].岩石力学与工程学报,2000.6((增刊))：p.1057-1060.
[93]. 王泳嘉,刘连峰,三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996.15(3)：p.200-210.
[94]. 郑文刚,刘凯欣,离散元法工程计算软件的前后处理系统[J].计算机工程与科学,2000.22(6)：p.14-17.
[95]. 刘凯欣,郑文刚,高凌天,脆性材料动态破坏过程的数值模拟[J].计算力学学报,2003.20(2)：p.127-132.
[96]. Laurent, B. and S. Taoufik, Mixed finite element formulation in large deformation frictional contact problem[J]. Revue Europeenne des Elements 2005.14(2-3):p.1-19.
[97]. Park, K.C. and C.A. Felippa, Variational principle for the formulation of partitioned structural systems[J]. International Journal for Numerical Methods in Engineering,2000.47(1):p.395-418.
[98]. Lamichhane, B.P. and B.I. Wohlmuth, Mortar finite elements for interface problems[J]. Computing,2004.72(3-4):p.333-348.
[99]. Andrade Filho, M. and P. Ricardo Ganime Alves, Mortar method using lagrange multiplier applied to the analysis of horseshoe-shaped waveguide[J]. Journal of Infrared, Millimeter, and Terahertz Waves,2010.31(4):p.422-429.
[100]. Flemisch, B., J.M. Melenk, and B.I. Wohlmuth. Mortar methods with curved interfaces [C]. in Selected papers from the 16th Chemnitz Finite Element Symposium 2003, September 22,2003-September 24,2005:Elsevier.
[101]. Seshaiyer, P. and M. Suri, Hp submeshing via non-conforming finite element methods[J]. Computer Methods in Applied Mechanics and Engineering,2000. 189(3):p.1011-1030.
[102]. Dohrmann, C.R., S.W. Key, and M.W. Heinstein, Methods for connecting dissimilar three-dimensional finite element meshes[J]. International Journal for Numerical Methods in Engineering,2000.47(5):p.1057-1080.
[103]. Cho, Y.-S. and S. Im, MLS-based variable-node elements compatible with quadratic interpolation. Part I:Formulation and application for non-matching meshes[J]. International Journal for Numerical Methods in Engineering,2006. 65(4):p.494-516.
[104]. Cho, Y.-S. and S. Im, MLS-based variable-node elements compatible with quadratic interpolation. Part II:Formulation and application for non-matching meshes[J]. International Journal for Numerical Methods in Engineering,2006. 65(4):p.517-547.
[105]. Long, L. and B. Brady, A hybrid computational scheme for excavation and support design in jointed rock media[C]. In:Brown ET, Hudson JA, editors. Proceedings of the international symposium on design and performance of underground excavations. British Geotechnical Society.1984:p.105-112.
[106]. Munjiza, A. and N.W.M. John, Mesh size sensitivity of the combined FEM/DEM Fracture and Fragmentation Algorithms[J]. Engineering Fracture Mechanics,2002.69(2):p.281-295.
[107]. Onate, E. and J. Rojek, Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems [J]. Computer Methods in Applied Mechanics and Engineering,2004.193(27-29):p.3087-3128.
[108]. Azevedo, N.M. and J.V. Lemos, Hybrid discrete element/finite element method for fracture analysis [J]. Computer Methods in Applied Mechanics and Engineering,2006.195(33-36):p.4579-4593.
[109]. Hofstetter, K., Analytic method to predict the dynamic interaction of dozer blade with earthen material [C]. Proceedings of the 14th International Conference of the ISTVS, Vicksburg, MS, USA,2002:p.65-87.
[110]. Asaf, Z., D. Rubinstein, and I. Shmulevich, Evaluation of link-track performances using DEM[J]. Journal of Terramechanics,2006.43(2):p. 141-161.
[111]. Karami, A. and D. Stead, Asperity Degradation and Damage in the Direct Shear Test:A Hybrid FEM/DEM Approach[J]. Rock Mechanics and Rock Engineering,2008.41(2):p.229-266.
[112]. Rousseau, J., et al., Multidomain finite and discrete elements method for impact analysis of a concrete structure[J]. Engineering Structures,2009.31(11):p. 2735-2743.
[113]. Bhuvaraghan, B., et al., Shot peening simulation using discrete and finite element methods[J]. Advances in Engineering Software,2010.41(12):p. 1266-1276.
[114]. Bazant, Z., et al., Random particle model for the fracture of aggregate or fiber composites[J]. J. Engrg. Mech., ASCE,1990.116(8):p.1686-1705.
[115]. Rattanadit, K., Coupled dem-fem for dynamic analysis of granular systems in bending[D]. University of Nebraska-Lincoln,2010:p.102-133.
[116].张忠,固体炸药冲击起爆的物质点法研究(D).中国,哈尔滨,哈尔滨工程大学,2010：p.35-45.
[117].黄鹏,金属及岩土冲击动力学问题的物质点法研究(D).中国,北京,清华大学,2010：p.38-45.
[118]. Coetzee, C.J., The Modelling of Granular Flow Using the Particle-in-Cell Method[D]. South Africa, University of Stellenbosch,2004:p.55-62.
[119]. Li, S., Meshfree and particle methods and their applications[J]. Applied Mechanics Reviews,2002.55(1):p.1-34.
[120]. Shen, J. and R.L. Kushwaha, Investigation of an algorithm for non-linear and dynamic problems in soil-machine systems[J]. Computers and Electronics in Agriculture,1995.13(1):p.51-66.
[121]. Singh, S. and H. Cannon, Modeling and Identification of Soil-tool Interaction in Automated Excavation[C]. Proceedings of the 1998 IEEURSJ Intl. Conference on Intelligent Robots and Systems Victoria, B.C., Canada,1998.
[122]. Fielke, J.M., Finite Element Modelling of the Interaction of the Cutting Edge of Tillage Implements with Soil[J]. Journal of Agricultural Engineering Research, 1999.74(1):p.91-101.
[123]. Shmulevich, I., State of the art modeling of soil-tillage interaction using discrete element method[J]. Soil & Tillage Research,2010.111(1):p.41-53.
[124]. Chen, J.K., J.E. Beraun, and C.J. Jih, An improvement for tensile instability in smoothed particle hydrodynamics [J]. Computational Mechanics,1999.23(4):p. 279-287.
[125].王吉,光滑粒子法与有限元的耦合算法及其在冲击动力学中的应用[D].中国,合肥,中国科学技术大学,2006：p.40-48.
[126]. Idelsohn, S.R. and D.P.F. Onate E, The particle finite element method:a powerful tool to solve incompressible flows with free-surfaces and breaking waves[J]. International Journal for Numerical Methods in Engineering,2004. 61(7):p.964-989.
[127].马上,冲击爆炸问题的物质点无网格法研究[D].中国,北京,清华大学,2006：p.32-50.
[128].鲍德松,张训生,颗粒物质与颗粒流.浙江大学学报(理学版),2003.30(5)：p.514-517.
[129]. Ferrez, j.-a., Dynamic triangulations for efficient 3D simulation of granular materials[J]. Lausanne, EPFL,2001.
[130]. Iwashita, K. and M. Oda, Micro-deformation mechanism of shear banding process based on modified distinct element method[J]. Powder Technology, 2000.109(1-3):p.192-205.
[131]. Tanaka, H., Simulation of soil deformation and resistance at bar penetration by the distinct element method[J]. Journal of Terramechanics,2000.37(1):p. 41-56.
[132].徐中华,有限元法分析土壤切削问题的研究进展[J].农业机械学报,2005.36(1)：p.134-137.
[133]. Hong, T., J.Y. Ooi, and B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses[J]. Engineering Failure Analysis,2008.15(8):p.1097-1110.
[134]. Majzoobi, G.H., R. Azizi, and A. A. Nia, A three-dimensional simulation of shot peening process using multiple shot impacts[J]. Journal of Materials Processing Technology,2005.164-165:p.1226-1234.
[135]. Frija, M., et al., Finite element modelling of shot peening process:Prediction of the compressive residual stresses, the plastic deformations and the surface integrity[J]. Materials Science and Engineering A,2006.426(1-2):p.173-180.
[136]. Bhuvaraghan, B., et al., Shot peening simulation using discrete and finite element methods Advances in Engineering Software[J]. Advances in Engineering Software,2010.41(12):p.1266-1276.
[137].洪滔,王志伟,袁巨龙,喷丸强化过程的有限元和离散元模拟[J].中国机械工程,2008.19(11)：p.1321-1325.
[138].傅华等,冲击动力学中离散元与有限元相结合的计算方法研究[J].高压物理学报,2006.20(4)：p.379-385.
[139]. Bagherzadeh Kh, A., A.A. Mirghasemi, and S. Mohammadi, Numerical simulation of particle breakage of angular particles using combined DEM and FEM[J]. Powder Technology,2011.205(1-3):p.15-29.
[140]. Karmakar, S. and R.L. Kushwaha, Dynamic modeling of soil-tool interaction:An overview from a fluid flow perspective[J]. Journal of Terra mechanics,2006. 43(4):p.411-425.
[141]. Xiao, S.P. and T. Belytschko, A bridging domain method for coupling continua with molecular dynamics[J]. Computer Methods in Applied Mechanics and Engineering,2004.193 (17-20):p.1645-1669.
[142]. Cleary, P.W., Large scale industrial DEM modeling[J]. Engineering Computations,2004.21(2-4):p.169-204.
[143]. Group, I.C., Pfc3d manuals[M],2nd Edition Minneapolis, Minnesota, USA, 2003.
[144]. Komodromos, P.I. and J.R. Williams, Dynamic simulation of multiple deformation bodies using combined discrete and finite element methods[J]. Engineering Computations,2004.21(2-4):p.431-448.
[145]. Zhu, H.P. and A.B. Yu, Averaging method of granular materials[J]. Physical Review E,2002.66(2):p.1-10.
[146]. Cundall, P.A. and O.D.L. Strack, A discrete numerical model for granular assemblies [J]. Geotechnique,1979.29(1):p.47-65
[147]. Zhu, H.P, Y.H. Wu, and A.B. Yu, Discrete and continuum modelling of granular flow[J]. China Particuology,2005.3(6):p.354-363.
[148]. Zhu, H.P. and A.B. Yu, Steady-state granular flow in a 3D cylindrical hopper with flat bottom:macroscopic analysis[J]. Granular Matter 2005.7(2-3):p. 97-107.
[149]. Latzel, M., S. Luding, and H. Herrmann, From discontinuous models towards a continuum description, Continuous and Discontinuous Modelling of Cohesive-Frictional Materials[M], P. Vermeer, et al., Editors.2001, Springer Berlin/Heidelberg, p.215-230.
[150]. Luding, S., et al., From discrete element simulations to a continuum model[J]. Computer Methods in Applied Mechanics and Engineering,2001.191(1-2):p. 21-28.
[151]. Luding, S., M. Latzel, and H.J. Herrmann, From discrete element simulations towards a continuum description of particulate solids[M], in Handbook of Powder Technology, A. Levy and H. Kalman, Editors.2001, Elsevier Science B.V. p.39-44.
[152]. Latzel, M., From microscopic simulations towards a macroscopic description of granular media[D]. University of Stuttgart,2003. p.40-48.
[153]. Ehlers, W., et al., From particle ensembles to Cosserat continua:homogenization of contact forces towards stresses and couple stresses[J]. International Journal of Solids and Structures,2003.40(24):p.6681-6702.
[154]. Schalangen, E., Experimental and numerical analysis of fracture process in concrete[D]. Delft university of Tech., the Netherlands,1993. p.77-83.
[155].蒋玉川,李章政,弹性力学与有限元简明教程[M].中国,北京,化学工业出版社,2010：p.118-126.
[156]. Demkowicz, L., P. Devloo, and J. Oden, On an h-type mesh-refinement strategy based on minimization of interpolation errors[J]. Computer Methods in Applied Mechanics and Engineering,1985.53(1):p.67-89.
[157]. Strouboulis, T. and K. Haque, Recent experiences with error estimation and adaptivity. Part Ⅱ:error estimation for h-adaptive approximations on grid of triangle and quadrilaterals[J]. Computer Methods in Applied Mechanics and Engineering 1992.100(3):p.359-430.
[158]. Farhat, C. and F. Roux, A method of finite-element tearing and interconnecting and its parallel solution algorithm[J]. International Journal for Numerical Methods in Engineering,1991.32(6):p.1205-1227.
[159]. Quiroz, L. and P. Beckers, Non-conforming mesh gluing in the finite element method[J]. International Journal for Numerical Methods in Engineering,1995. 38(13):p.2165-2184.
[160]. Belgacem, F., The mortar finite element method with Lagrange multipliers[J]. Numer. Math.,1999.84(2):p.173-197.
[161]. Bernardi, C, Y Maday, and A. Patera, A new nonconforming approach to domain decomposition; the mortar element method[C], in:H. Brezis, J.L. Lions (Eds.), Nonlinear Partial Differential Equations and Their Applications, Pitman, New York.1994.
[162]. Braess, D., M. Dryja, and W. Hackbusch, A multigrid method for nonconforming FE-discretisations with application to non-matching grids[J]. Computing (Vienna/New York),1999.63(1):p.1-25.
[163]. Seshaiyer, P. and M. Suri, hp submeshing via non-conforming finite element methods[J]. Comput. Meth. Appl. Mech. Engrg,2000.189(3):p.1011-1030.
[164]. McDevitt, T.W. and T.A. Laursen, A mortar-finite element formulation for frictional contact problems[J]. Int. J. Numer. Meth. Engrg.,2000.48(10):p. 1525-1547.
[165]. Kim, H., Interface Element Method (IEM) for a partitioned system with non-matching interfaces[J]. Computer Methods in Applied Mechanics and Engineering,2002.191(29-30):p.3165-3194.
[166]. Kim, H., Interface element method:treatment of non-matching nodes at the ends of interfaces between partitioned domains[J]. Computer Methods in Applied Mechanics and Engineering,2003.192(15):p.1841-1858.
[167]. Kim, H., Arbitrary placement of local meshes in a global mesh by the Interface-Element Method (IEM)[J]. International Journal for Numerical Methods in Engineering,2003.56(15):p.2279-2312.
[168]. Cho, Y, et al., An improved interface element with variable nodes for non-matching finite element meshes[J]. Computer Methods in Applied Mechanics and Engineering,2005.194(27-29):p.3022-3046.
[169].李春光等,六面体单元等参逆变换的一种迭代解法[J].岩土力学,2004.25(7)：p.1050-1052.
[170].郝东升,齿轮啮合数值分析建模方法及其应用研究[D].中国,大连,大连理工大学,2012：p.110-123.
[171].王东方等,柴油机气缸盖多场耦合三维有限元分析[J].力学季刊,2005.26(3)：p.511-516.
[172].蒋志强,基于ANSYS的发电设各热及热—结构藕合分析[D].中国,杭州, 浙江大学,2006：p.34-45.
[173]. Zhao, C.B., et al., A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements[J]. International Journal for Numerical Methods in Engineering,1999. 45(10):p.1509-1526.
[174].刘振宇,傅云,谭建荣,基于异构网格耦合的产品多物理场有限元数据集成与可视化仿真[J].机械工程学报,2010.46(7)：p.114-121.
[175].傅云,复杂产品数字样机多性能祸合分析与仿真的若干关键技术研究及其应用[D].中国,杭州,浙江大学,2008：p.56-72.
[176].孙家广,杨长贵,计算机图形学[M].中国,北京,清华大学出版社,1994：p.112-120.
[177]. Lane, J., An efficient point in polyhrdron algorithm[J]. Computer vision, graphics, and image processing,1984.26(1):p.118-125.
[178].徐燕萍等,等参元逆变换插值法的研究及其应用[J].岩土力学,2001.22(2)：p.226-232.
[179].钱向东,任青文,赵引,一种高效的等参有限元逆变换算法[J].计算力学学报,1998.15(4)：p.437-441.
[2]. Rojek, J. and E. Onate, Multiscale analysis using a coupled discrete/finite element model[J]. Interaction and Multiscale Mechanics,2007.1(1):p.1-31.
[3]. Ivo, B., The finite element method with Lagrangian multipliers[J]. Numeric Mathmatics,1972.20(3):p.179-192.
[4]. Cichosz, T. and M. Bischoff, Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers[J]. Computer Methods in Applied Mechanics and Engineering,2011.200 (9-12):p.1317-1332.
[5]. Babuska, I. and GN. Gatica, On the mixed finite element method with Lagrange multipliers[J]. Numerical Methods for Partial Differential Equations,2003. 19(2):p.192-210.
[6]. McDevitt, T.W. and T.A. Laursen, A mortar-finite element formulation for frictional contact problems[J]. International Journal for Numerical Methods in Engineering,2000.48(10):p.1525-1547.
[7]. Yang, B., T.A. Laursen, and X. Meng, Two dimensional mortar contact methods for large deformation frictional sliding [J]. International Journal for Numerical Methods in Engineering,2005.62(9):p.1183-1225.
[8]. Moaveni, S., Finite Element Analysis:Theory and Application with Ansys[M], 3rd edition.北京：电子工业出版社,2008：p.245-260.
[9]. Abo-Elnor, M., R. Hamilton, and J.T. Boyle, Simulation of soil-blade interaction for sandy soil using advanced 3D finite element analysis[J]. Soil & Tillage Research 2004.75(1):p.61-73.
[10]. Han, K., et al., A combined finite/discrete element simulation of shot peening processes Part I:studies on 2D interaction laws[J]. Engineering Computations, 2000.17(5):p.593-619.
[11]. Walton, O.R., Numerical simulation of inelastic, frictional particle-particle interactions in Roco[M]. Particulate Two-Phase Flow Butterworths, Boston, MA, 1992:p.884-911.
[12]. Timoshenko, S.P. and J.N. Goodier, Theory of Elasticity [J]. International Journal of Bulk Solids Storage in Silos,1970.1(4):p.140-142.
[13]. Oden, J.T. and J.A.C. Martins, Models and computational methods for dynamic friction phenomena[J]. Computer Methods in Applied Mechanics and Engineering,1985.52(1-3):p.527-634.
[14]. Nardin, A., G. Zavarise, and B.A. Schrefler, Modelling of cutting tool-soil interaction-part I:contact behaviour[J]. Computational Mechanics,2003. 31(3-4):p.327-339.
[15]. Nardin, A. and B.A. Schrefler, Modelling of cutting tool-soil interaction-part II:macromechanical model and upscaling[J]. Computational Mechanics,2005. 36(5):p.343-359.
[16]. Lilliu, G. and J.G.M. van Mier,3D lattice type fracture model for concrete[J]. Engineering Fracture Mechanics,2003.70(7-8):p.927-941.
[17]. Han, K., et al., A combined finite/discrete element simulation of shot peening processes Part Ⅱ:3D interaction laws[J]. Engineering Computations (Swansea, Wales),2000.17(Compendex):p.680-702.
[18]. Han, K., D.R.J. Owen, and D. Peric, Combined finite/discrete element and explicit/implicit simulations of peen forming process[J]. Engineering Computations,2002.19(1):p.92-118.
[19]. Dowding, C., T. Belystschko, and H. Yen, A coupled finite element-rigid block method for transient analysis of rock caverns[J]. International Journal for Numerical and Analytical Methods in Geomechanics 1983.7(1):p.117-127.
[20]. Carrillo, A.R., et al., Design of a Large Scale Discrete Element Soil Model for High Performance Computing Systems[C]. Proceedings of the ICM/IEEE Super Computer Conference. Pittsburg, PA, ACM, New York.,1996:p.17-22.
[21]. Tanaka, H., et al., Simulation of loosening at subsurface tillage using a vibrating type subsoiler by means of the distinct element method[J]. Proceedings of the 8th European ISTVS Conference, Umea,2000:p.32-37.
[22]. Horner, D.A., J.F. Peters, and A. Carrillo, Large scale discrete element modeling of vehicle-soil interaction[J]. Journal of Engineering Mechanics,2001.127(10): p.1027-1032.
[23]. Hello, B.L., et al., Coupling finite elements and discrete elements methods, application to reinforced embankment by piles and geosynthetics[C]. Proceedings of the 6th European Conference on Numerical Methods in Geotechnical Engineering-Numerical Methods in Geotechnical Engineering, 2006:p.843-848.
[24]. Villard, P., et al., Coupling between finite and discrete element methods for the modelling of earth structures reinforced by geosynthetic[J]. Computers and Geotechnics,2009.36(5):p.709-717.
[25]. Mohammad, H., D. Denis, and S. Karam, Static and dynamic studies for coupling discrete and continuum media:Application to a simple railway track model[J]. International Journal of Solids and Structures,2010.47(2):p. 276-290.
[26]. Lim, J.H., S. Im, and Y.-S. Cho, MLS (moving least square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering,2007. 196(17-20):p.2216-2228.
[27]. Fakhimi, A., A hybrid discrete-finite element model for numerical simulation of geomaterials[J]. Computers and Geotechnics,2009.36(3):p.386-395.
[28]. Caia, M., et al., FLAC/PFC coupled numerical simulation of AE in large-scale underground excavations[J]. International Journal of Rock Mechanics & Mining Sciences,2007.44(4):p.550-564.
[29]. 周健等,基于颗粒单元接触的二维离散-连续耦合分析方法[J].岩土工程学报,2010.32(10)：p.1479-1484.
[30]. Hazzard, J.F. and R. Young, P, Moment tensors and micromechanical models[J]. Tectonophysics,2002.356(1-3):p.181-97.
[31]. Wang, Z.L., H. Konietzky, and R.F. Shen, Coupled finite element and discrete element method for underground blast in faulted rock masses[J]. Soil Dynamics and Earthquake Engineering,2009.29(6):p.939-945.
[32]. Feng, Y.T., K. Han, and D.R.J. Owen, Filling domains with disks:an advancing front approach[J]. International Journal for Numerical Methods in Engineering, 2003.56(5):p.699-713.
[33]. Bagi, K., An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies[J]. Granular Matter,2005.7(1):p. 31-43.
[34]. Munjiza, A. and K.R.F. Andrews, NBS contact detection algorithm for bodies of similar size[J]. International Journal for Numerical Methods in Engineering, 1998.43(1):p.131-149.
[35]. Benabbou, A., et al., Sphere Packing and Applications to Granular Structure Modeling[C]. Proceedings of the 17th International Meshing Roundtable, Part 1, 2008:p.1-18.
[36]. Gensane, T. and P. Ryckelynck, Producing dense packings of cubes[J]. Discrete Mathematics,2008.308(22):p.5230-5245.
[37]. Munjiza, A., J.P. Latham, and K.R.F. Andrews, Challenges of a coupled combined finite-discrete element approach to explosive induced rock fragmentation[J]. International Journal for Blasting and Fragmentation,1999. 3(3):p.237-250.
[38]. Han, K., Y.T. Feng, and D.R.J. Owen, Sphere packing with a geometric based compression algorithm[J]. Powder Technology,2005.155(1):p.33-41.
[39]. Thomas, P., Discontinuous deformation analysis of particulate media[D]. Berkeley, University of California,1997:p.30-35.
[40]. Bagi, K., A quasi-static numerical model for micro-level analysis of granular assemblies[J]. Mechanics of Materials,1993.16(1-2):p.101-110.
[41]. Lin, X. and T.T. Ng, A three-dimensional discrete element model using arrays of ellipsoids[J]. Geotechnique,1997.47(2):p.319-329.
[42]. Sakaguchi, h. and a. Murakami, Initial packing in discrete element modeling[J]. Discrete Element Methods,3rd International Conference,ASCE,New Mexico, 2002(23-25):p.104-106.
[43]. Sullivan, c. The application of discrete element modelling to finite deformation problems in geomechanics[D]. Berkeley, University of California,2002:p. 35-48.
[44]. Benabbou, A., et al., Numerical modeling of nanostructured materials[J]. Finite Elements in Analysis and Design,2010.46(1-2):p.165-180.
[45]. Haggstrom, O. and R. Meester, Nearest neighbour and hard sphere models in continuum percolation[J]. Random Structures and Algorithms,1996.9(3):p. 295-315.
[46]. Stoyan, D., Models of random systems of non-intersecting spheres[J].,1998. Stochastics'98, JCMF, in:Prague:p.543-547.
[47]. Cui, L. and C. O'Sullivan, Analysis of a triangulation based approach for specimen generation for discrete element simulations[J]. Granular Matter 2003. 5(3):p.135-145.
[48]. E1-Hamalawi, A., A 2D combined advancing front-Delaunay mesh generation scheme[J]. Finite Elements in Analysis and Design,2004.40(9-10):p.967-989.
[49]. Lo, S.H. and W.X. Wang, Generation of finite element mesh with variable size over an unbounded 2D domain[J]. Computer methods in appllied mechanics and engineering,2005.194(45-47):p.4668-4684.
[50]. Wang, W.X., C.Y. Ming, and S.H. Lo, Generation of triangular mesh with specified size by circle packing[J]. Advances in Engineering Software,2007. 38(2):p.133-142.
[51]. Benabbou, A., H. Borouchaki, and P. Laug, Geometrical modeling of granular structures in two and three dimensions[J]. International Journal for Numerical Methods in Engineering,2009.80(4):p.425-454.
[52]. Ferrez, J.-a., Dynamic triangulations for efficient 3D simulation of granular materials[D]. Lausanne,EPFL,2001:p.18-26.
[53]. Munjiza, A., E. Rougier, and N.W.M. John, MR linear contact detection algorithm[J]. International Journal for Numerical Methods in Engineering,2006. 66(1):p.46-71.
[54]. Perkins, E. and J.R. Williams, A fast contact detection algorithm insensitive to object sizes[J]. Engineering Computations,2001.18(1-2):p.48-61.
[55]. Williams, J.R., E. Perkins, and B. Cook, A contact algorithm for partitioning arbitrary sized objects [J]. Engineering Computations:Int J for Computer-Aided Engineering,2004.21(2-3):p.235-248.
[56].王燕民,李竟先,E. Forssberg,颗粒堆积现象的计算机模拟[J].硅酸盐学报,2003.31(2)：p.169-178.
[57]. 刘浩斌,颗粒尺寸分布与堆积理论[J].硅酸盐学报,1991.19(2)：p.164-172
[58]. 李艳洁,徐泳,用离散元模拟颗粒堆积问题[J].农机化研究,2005.27(2)：p.57-59.
[59]. 刘军,刘汉龙,用Monte Carlo方法模拟砂土的自然堆积过程[J].岩土力学,2005.26(增刊1)：p.113-116.
[60]. 刘凯欣,高凌天,离散元法研究的评述[J].力学进展,2003.33(4)：p.483-490.
[61]. Cundall, P.A., A computer model for simulating progressive, large-scale movements in blocky rock systems[J]. In Rock fracture, proc. int. symp. on rock fracture, Nancy,1971. p.2-8.
[62]. Maini, T. and P.A. Cundall, Computer modeling of jointed rock mases[J]. Technical report N-78-4, U.S. Army Engineer Waterways Experiment station, Vicksburg, Mississippi,1978.
[63]. Cundall, P.A. and O.D.L. Strack, The development of constitutive laws for soil using the distinct element method[J]. Proc.3rd Numerical Methods In Geomechanics. Aachen,1979:p.289-298.
[64]. Thornton, C. and D.J. Barnes, Computer simulated deformmion of compact granular assemblies[J]. Acta Mechanica,1986.64(1):p.45-61.
[65]. Thornton, C., On the relationship between the modulus of particulate media and the surface energy ofthe constituent particles[J]. Journal of Physics D:Applied Physics,1993.26(10):p.1587-1591.
[66]. Liu, K., L.T. Gao, and S. Tanimura, Application of discrete element method in impact problems[J]. JSME International Journal,2004.47(2):p.138-145.
[67]. Liu, K. and L.T. Gao, The application of discrete element method in solving three dimension impact dynamics problems[J]. Acta Mechniaca Solid,2003. 16(3):p.256-261.
[68]. 川井忠彦,都井裕,平面歪问题の离散化解析に[J].生产研究,1977.29(4)：p.204-207.
[69]. Sawamoto, Y., H. Tsubota, and Y. Kasai, Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method[J]. Nuclear Engineering and Design,1998.179(2):p.157-177.
[70]. Potyondy, D.O. and P.A. Cundall, Abonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004.41(8):p. 1329-1364.
[71]. Shmulevich, I., Z. Asaf, and D. Rubinstein, Interaction between soil and a wide cutting blade using the discrete element method[J]. Soil&Tillage Research,2007. 97(1):p.37-50.
[72]. Ali, A.Y. and S.M. Bradshaw, Bonded-particle modelling of microwave-induced damage in ore particles[J]. Minerals Engineering,2010.23(10):p.780-790.
[73]. Franco, Y, D. Rubinstein, and I. Shmulevich, Determination of discrete element model parameters for soil-bulldozer blade interaction[J]. Proceedings of the 15th International Conference of the ISTVS Hayama, Japan, September,2005:p. 25-29.
[74]. Asaf, Z., D. Rubinstein, and I. Shmulevich, Determination of discrete element model parameters required for soil tillage[J]. Soil & Tillage Research 2007. 92(1-2):p.227-242.
[75]. Campbell, C.S. and C.E. Brennen, Computer simulation of chute flows of granular materials[J]. IUTAM Conference on Deformation and Failure of Granular Materials of Granular Materials, Delft,,1982. Netherlands,31 August-3 September 1982:p.515-521.
[76]. Langston, P.A., U. Tuzun, and D.M. Heyes, Discrete element simulation of granular flow in 2d and 3d hoppers:dependence of discharge rate and wall stress on particle interactions[J]. Chemical Engineering Science,1995.50(6):p. 967-987.
[77]. Walton, O.R., Numerical simulation of inclined chute flows of monodisperse,inelastic, frictional spheres [J]. Mechanics of Materials 1993. 16(1-2):p.239-247.
[78]. Hirshfeld, D., Y. Radzyner, and D.C. Rapaport, Molecular dynamics studies of granular flow through an aperture[J]. PHYSICAL REVIEW E 1997.56(4):p. 4404-4415.
[79]. Cleary, P.W. and M.L. Sawley, DEM modelling of industrial granular flows:3D case studies and the effect of particle shape on hopper discharge[J]. Applied Mathematical Modelling,2002.26(2):p.89-111.
[80]. Goda, T.J. and F. Ebert, Three-dimensional discrete element simulations in hoppers and silos[J]. Powder Technology,2005.158(1-3):p.58-68.
[81]. Shimizu, Y. and P.A. Cundall, Three-dimensional DEM simulations of bulk handling by screw conveyors[J]. Journal of Engineering Mechanics,2001. 127(9):p.864-872.
[82]. Owen, P.J. and P.W. Cleary, Prediction of screw conveyor performance using the Discrete Element Method (DEM)[J]. Powder Technology,2009.193(3):p. 274-288.
[83]. Moysey, P.A. and M.R. Thompson, Modelling the solids inflow and solids conveying of single-screw extruders using the discrete element method[J]. Powder Technology,2005.153(2):p.95-107.
[84]. Cleary, P.W., The filling of dragling buckets[J]. Mathematical Engineering in Industry,1998.7(1):p.1-24.
[85]. Mishra, B.K., Study of media mechanics in tumbling mills by thediscrete element method(D). The University of Utah,1991:p.43-48.
[86]. Mishra, B.K. and R.K. Rajamani, The discrete element method for simulation of ball mills[J]. Applied Mathematical Modelling,1992.16(11):p.598-604.
[87]. Mishra, B.K. and R.K. Rajamani, Simulation of charge motion in ball mills:Part 1. Experimental verifications[J]. International Journal of Mineral Processing, 1994.40(3-4):p.171-186.
[88]. Djordjevic, N., Discrete element modelling of the influence of lifters on power draw of tumbling mills[J]. Minerals Engineering,2003.16(4):p.331-336.
[89]. Djordjevic, N., F.N. Shi, and R.D. Morrison, Applying discrete element modelling to vertical and horizontal shaft impact crushers [J]. Minerals Engineering,2003.16(10):p.983-991.
[90]. 王泳嘉,离散单元法-一种适用于节理岩石力学分析的数值方法[C].第一届全国岩石力学数值计算及模型试验讨论会论文集,中国,江西,吉安,1986：p.215-230.
[91].鞠剑,基于超圆颗粒模型的离散元软件开发研究[D].中国,大连,大连理工大学,2006：p.45-60.
[92]. 王泳嘉,宋文洲,赵艳娟,离散单元法软件系统2D-block的现代化特点[J].岩石力学与工程学报,2000.6((增刊))：p.1057-1060.
[93]. 王泳嘉,刘连峰,三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996.15(3)：p.200-210.
[94]. 郑文刚,刘凯欣,离散元法工程计算软件的前后处理系统[J].计算机工程与科学,2000.22(6)：p.14-17.
[95]. 刘凯欣,郑文刚,高凌天,脆性材料动态破坏过程的数值模拟[J].计算力学学报,2003.20(2)：p.127-132.
[96]. Laurent, B. and S. Taoufik, Mixed finite element formulation in large deformation frictional contact problem[J]. Revue Europeenne des Elements 2005.14(2-3):p.1-19.
[97]. Park, K.C. and C.A. Felippa, Variational principle for the formulation of partitioned structural systems[J]. International Journal for Numerical Methods in Engineering,2000.47(1):p.395-418.
[98]. Lamichhane, B.P. and B.I. Wohlmuth, Mortar finite elements for interface problems[J]. Computing,2004.72(3-4):p.333-348.
[99]. Andrade Filho, M. and P. Ricardo Ganime Alves, Mortar method using lagrange multiplier applied to the analysis of horseshoe-shaped waveguide[J]. Journal of Infrared, Millimeter, and Terahertz Waves,2010.31(4):p.422-429.
[100]. Flemisch, B., J.M. Melenk, and B.I. Wohlmuth. Mortar methods with curved interfaces [C]. in Selected papers from the 16th Chemnitz Finite Element Symposium 2003, September 22,2003-September 24,2005:Elsevier.
[101]. Seshaiyer, P. and M. Suri, Hp submeshing via non-conforming finite element methods[J]. Computer Methods in Applied Mechanics and Engineering,2000. 189(3):p.1011-1030.
[102]. Dohrmann, C.R., S.W. Key, and M.W. Heinstein, Methods for connecting dissimilar three-dimensional finite element meshes[J]. International Journal for Numerical Methods in Engineering,2000.47(5):p.1057-1080.
[103]. Cho, Y.-S. and S. Im, MLS-based variable-node elements compatible with quadratic interpolation. Part I:Formulation and application for non-matching meshes[J]. International Journal for Numerical Methods in Engineering,2006. 65(4):p.494-516.
[104]. Cho, Y.-S. and S. Im, MLS-based variable-node elements compatible with quadratic interpolation. Part II:Formulation and application for non-matching meshes[J]. International Journal for Numerical Methods in Engineering,2006. 65(4):p.517-547.
[105]. Long, L. and B. Brady, A hybrid computational scheme for excavation and support design in jointed rock media[C]. In:Brown ET, Hudson JA, editors. Proceedings of the international symposium on design and performance of underground excavations. British Geotechnical Society.1984:p.105-112.
[106]. Munjiza, A. and N.W.M. John, Mesh size sensitivity of the combined FEM/DEM Fracture and Fragmentation Algorithms[J]. Engineering Fracture Mechanics,2002.69(2):p.281-295.
[107]. Onate, E. and J. Rojek, Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems [J]. Computer Methods in Applied Mechanics and Engineering,2004.193(27-29):p.3087-3128.
[108]. Azevedo, N.M. and J.V. Lemos, Hybrid discrete element/finite element method for fracture analysis [J]. Computer Methods in Applied Mechanics and Engineering,2006.195(33-36):p.4579-4593.
[109]. Hofstetter, K., Analytic method to predict the dynamic interaction of dozer blade with earthen material [C]. Proceedings of the 14th International Conference of the ISTVS, Vicksburg, MS, USA,2002:p.65-87.
[110]. Asaf, Z., D. Rubinstein, and I. Shmulevich, Evaluation of link-track performances using DEM[J]. Journal of Terramechanics,2006.43(2):p. 141-161.
[111]. Karami, A. and D. Stead, Asperity Degradation and Damage in the Direct Shear Test:A Hybrid FEM/DEM Approach[J]. Rock Mechanics and Rock Engineering,2008.41(2):p.229-266.
[112]. Rousseau, J., et al., Multidomain finite and discrete elements method for impact analysis of a concrete structure[J]. Engineering Structures,2009.31(11):p. 2735-2743.
[113]. Bhuvaraghan, B., et al., Shot peening simulation using discrete and finite element methods[J]. Advances in Engineering Software,2010.41(12):p. 1266-1276.
[114]. Bazant, Z., et al., Random particle model for the fracture of aggregate or fiber composites[J]. J. Engrg. Mech., ASCE,1990.116(8):p.1686-1705.
[115]. Rattanadit, K., Coupled dem-fem for dynamic analysis of granular systems in bending[D]. University of Nebraska-Lincoln,2010:p.102-133.
[116].张忠,固体炸药冲击起爆的物质点法研究(D).中国,哈尔滨,哈尔滨工程大学,2010：p.35-45.
[117].黄鹏,金属及岩土冲击动力学问题的物质点法研究(D).中国,北京,清华大学,2010：p.38-45.
[118]. Coetzee, C.J., The Modelling of Granular Flow Using the Particle-in-Cell Method[D]. South Africa, University of Stellenbosch,2004:p.55-62.
[119]. Li, S., Meshfree and particle methods and their applications[J]. Applied Mechanics Reviews,2002.55(1):p.1-34.
[120]. Shen, J. and R.L. Kushwaha, Investigation of an algorithm for non-linear and dynamic problems in soil-machine systems[J]. Computers and Electronics in Agriculture,1995.13(1):p.51-66.
[121]. Singh, S. and H. Cannon, Modeling and Identification of Soil-tool Interaction in Automated Excavation[C]. Proceedings of the 1998 IEEURSJ Intl. Conference on Intelligent Robots and Systems Victoria, B.C., Canada,1998.
[122]. Fielke, J.M., Finite Element Modelling of the Interaction of the Cutting Edge of Tillage Implements with Soil[J]. Journal of Agricultural Engineering Research, 1999.74(1):p.91-101.
[123]. Shmulevich, I., State of the art modeling of soil-tillage interaction using discrete element method[J]. Soil & Tillage Research,2010.111(1):p.41-53.
[124]. Chen, J.K., J.E. Beraun, and C.J. Jih, An improvement for tensile instability in smoothed particle hydrodynamics [J]. Computational Mechanics,1999.23(4):p. 279-287.
[125].王吉,光滑粒子法与有限元的耦合算法及其在冲击动力学中的应用[D].中国,合肥,中国科学技术大学,2006：p.40-48.
[126]. Idelsohn, S.R. and D.P.F. Onate E, The particle finite element method:a powerful tool to solve incompressible flows with free-surfaces and breaking waves[J]. International Journal for Numerical Methods in Engineering,2004. 61(7):p.964-989.
[127].马上,冲击爆炸问题的物质点无网格法研究[D].中国,北京,清华大学,2006：p.32-50.
[128].鲍德松,张训生,颗粒物质与颗粒流.浙江大学学报(理学版),2003.30(5)：p.514-517.
[129]. Ferrez, j.-a., Dynamic triangulations for efficient 3D simulation of granular materials[J]. Lausanne, EPFL,2001.
[130]. Iwashita, K. and M. Oda, Micro-deformation mechanism of shear banding process based on modified distinct element method[J]. Powder Technology, 2000.109(1-3):p.192-205.
[131]. Tanaka, H., Simulation of soil deformation and resistance at bar penetration by the distinct element method[J]. Journal of Terramechanics,2000.37(1):p. 41-56.
[132].徐中华,有限元法分析土壤切削问题的研究进展[J].农业机械学报,2005.36(1)：p.134-137.
[133]. Hong, T., J.Y. Ooi, and B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses[J]. Engineering Failure Analysis,2008.15(8):p.1097-1110.
[134]. Majzoobi, G.H., R. Azizi, and A. A. Nia, A three-dimensional simulation of shot peening process using multiple shot impacts[J]. Journal of Materials Processing Technology,2005.164-165:p.1226-1234.
[135]. Frija, M., et al., Finite element modelling of shot peening process:Prediction of the compressive residual stresses, the plastic deformations and the surface integrity[J]. Materials Science and Engineering A,2006.426(1-2):p.173-180.
[136]. Bhuvaraghan, B., et al., Shot peening simulation using discrete and finite element methods Advances in Engineering Software[J]. Advances in Engineering Software,2010.41(12):p.1266-1276.
[137].洪滔,王志伟,袁巨龙,喷丸强化过程的有限元和离散元模拟[J].中国机械工程,2008.19(11)：p.1321-1325.
[138].傅华等,冲击动力学中离散元与有限元相结合的计算方法研究[J].高压物理学报,2006.20(4)：p.379-385.
[139]. Bagherzadeh Kh, A., A.A. Mirghasemi, and S. Mohammadi, Numerical simulation of particle breakage of angular particles using combined DEM and FEM[J]. Powder Technology,2011.205(1-3):p.15-29.
[140]. Karmakar, S. and R.L. Kushwaha, Dynamic modeling of soil-tool interaction:An overview from a fluid flow perspective[J]. Journal of Terra mechanics,2006. 43(4):p.411-425.
[141]. Xiao, S.P. and T. Belytschko, A bridging domain method for coupling continua with molecular dynamics[J]. Computer Methods in Applied Mechanics and Engineering,2004.193 (17-20):p.1645-1669.
[142]. Cleary, P.W., Large scale industrial DEM modeling[J]. Engineering Computations,2004.21(2-4):p.169-204.
[143]. Group, I.C., Pfc3d manuals[M],2nd Edition Minneapolis, Minnesota, USA, 2003.
[144]. Komodromos, P.I. and J.R. Williams, Dynamic simulation of multiple deformation bodies using combined discrete and finite element methods[J]. Engineering Computations,2004.21(2-4):p.431-448.
[145]. Zhu, H.P. and A.B. Yu, Averaging method of granular materials[J]. Physical Review E,2002.66(2):p.1-10.
[146]. Cundall, P.A. and O.D.L. Strack, A discrete numerical model for granular assemblies [J]. Geotechnique,1979.29(1):p.47-65
[147]. Zhu, H.P, Y.H. Wu, and A.B. Yu, Discrete and continuum modelling of granular flow[J]. China Particuology,2005.3(6):p.354-363.
[148]. Zhu, H.P. and A.B. Yu, Steady-state granular flow in a 3D cylindrical hopper with flat bottom:macroscopic analysis[J]. Granular Matter 2005.7(2-3):p. 97-107.
[149]. Latzel, M., S. Luding, and H. Herrmann, From discontinuous models towards a continuum description, Continuous and Discontinuous Modelling of Cohesive-Frictional Materials[M], P. Vermeer, et al., Editors.2001, Springer Berlin/Heidelberg, p.215-230.
[150]. Luding, S., et al., From discrete element simulations to a continuum model[J]. Computer Methods in Applied Mechanics and Engineering,2001.191(1-2):p. 21-28.
[151]. Luding, S., M. Latzel, and H.J. Herrmann, From discrete element simulations towards a continuum description of particulate solids[M], in Handbook of Powder Technology, A. Levy and H. Kalman, Editors.2001, Elsevier Science B.V. p.39-44.
[152]. Latzel, M., From microscopic simulations towards a macroscopic description of granular media[D]. University of Stuttgart,2003. p.40-48.
[153]. Ehlers, W., et al., From particle ensembles to Cosserat continua:homogenization of contact forces towards stresses and couple stresses[J]. International Journal of Solids and Structures,2003.40(24):p.6681-6702.
[154]. Schalangen, E., Experimental and numerical analysis of fracture process in concrete[D]. Delft university of Tech., the Netherlands,1993. p.77-83.
[155].蒋玉川,李章政,弹性力学与有限元简明教程[M].中国,北京,化学工业出版社,2010：p.118-126.
[156]. Demkowicz, L., P. Devloo, and J. Oden, On an h-type mesh-refinement strategy based on minimization of interpolation errors[J]. Computer Methods in Applied Mechanics and Engineering,1985.53(1):p.67-89.
[157]. Strouboulis, T. and K. Haque, Recent experiences with error estimation and adaptivity. Part Ⅱ:error estimation for h-adaptive approximations on grid of triangle and quadrilaterals[J]. Computer Methods in Applied Mechanics and Engineering 1992.100(3):p.359-430.
[158]. Farhat, C. and F. Roux, A method of finite-element tearing and interconnecting and its parallel solution algorithm[J]. International Journal for Numerical Methods in Engineering,1991.32(6):p.1205-1227.
[159]. Quiroz, L. and P. Beckers, Non-conforming mesh gluing in the finite element method[J]. International Journal for Numerical Methods in Engineering,1995. 38(13):p.2165-2184.
[160]. Belgacem, F., The mortar finite element method with Lagrange multipliers[J]. Numer. Math.,1999.84(2):p.173-197.
[161]. Bernardi, C, Y Maday, and A. Patera, A new nonconforming approach to domain decomposition; the mortar element method[C], in:H. Brezis, J.L. Lions (Eds.), Nonlinear Partial Differential Equations and Their Applications, Pitman, New York.1994.
[162]. Braess, D., M. Dryja, and W. Hackbusch, A multigrid method for nonconforming FE-discretisations with application to non-matching grids[J]. Computing (Vienna/New York),1999.63(1):p.1-25.
[163]. Seshaiyer, P. and M. Suri, hp submeshing via non-conforming finite element methods[J]. Comput. Meth. Appl. Mech. Engrg,2000.189(3):p.1011-1030.
[164]. McDevitt, T.W. and T.A. Laursen, A mortar-finite element formulation for frictional contact problems[J]. Int. J. Numer. Meth. Engrg.,2000.48(10):p. 1525-1547.
[165]. Kim, H., Interface Element Method (IEM) for a partitioned system with non-matching interfaces[J]. Computer Methods in Applied Mechanics and Engineering,2002.191(29-30):p.3165-3194.
[166]. Kim, H., Interface element method:treatment of non-matching nodes at the ends of interfaces between partitioned domains[J]. Computer Methods in Applied Mechanics and Engineering,2003.192(15):p.1841-1858.
[167]. Kim, H., Arbitrary placement of local meshes in a global mesh by the Interface-Element Method (IEM)[J]. International Journal for Numerical Methods in Engineering,2003.56(15):p.2279-2312.
[168]. Cho, Y, et al., An improved interface element with variable nodes for non-matching finite element meshes[J]. Computer Methods in Applied Mechanics and Engineering,2005.194(27-29):p.3022-3046.
[169].李春光等,六面体单元等参逆变换的一种迭代解法[J].岩土力学,2004.25(7)：p.1050-1052.
[170].郝东升,齿轮啮合数值分析建模方法及其应用研究[D].中国,大连,大连理工大学,2012：p.110-123.
[171].王东方等,柴油机气缸盖多场耦合三维有限元分析[J].力学季刊,2005.26(3)：p.511-516.
[172].蒋志强,基于ANSYS的发电设各热及热—结构藕合分析[D].中国,杭州, 浙江大学,2006：p.34-45.
[173]. Zhao, C.B., et al., A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements[J]. International Journal for Numerical Methods in Engineering,1999. 45(10):p.1509-1526.
[174].刘振宇,傅云,谭建荣,基于异构网格耦合的产品多物理场有限元数据集成与可视化仿真[J].机械工程学报,2010.46(7)：p.114-121.
[175].傅云,复杂产品数字样机多性能祸合分析与仿真的若干关键技术研究及其应用[D].中国,杭州,浙江大学,2008：p.56-72.
[176].孙家广,杨长贵,计算机图形学[M].中国,北京,清华大学出版社,1994：p.112-120.
[177]. Lane, J., An efficient point in polyhrdron algorithm[J]. Computer vision, graphics, and image processing,1984.26(1):p.118-125.
[178].徐燕萍等,等参元逆变换插值法的研究及其应用[J].岩土力学,2001.22(2)：p.226-232.
[179].钱向东,任青文,赵引,一种高效的等参有限元逆变换算法[J].计算力学学报,1998.15(4)：p.437-441.
© 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 |