EI、Scopus 收录
Hu Dean, Han Xu, Xiao Yihua, Yang Gang. RESEARCH DEVELOPMENTS OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD AND ITS COUPLING WITH FINITE ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 639-652. doi: 10.6052/0459-1879-13-092
Citation: Hu Dean, Han Xu, Xiao Yihua, Yang Gang. RESEARCH DEVELOPMENTS OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD AND ITS COUPLING WITH FINITE ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 639-652. doi: 10.6052/0459-1879-13-092


doi: 10.6052/0459-1879-13-092
Funds:  The project was supported by the National Natural Science Foundation of China (11272118, 10902038).
  • Received Date: 2013-06-03
  • Publish Date: 2013-09-18
  • The merits and shortcomings are existed simultaneously in finite element method (FEM) and smoothed particle hydrodynamics (SPH) method, in which these methods are established based on Lagrange system. In order to makes use of high computational efficiency of FEM and advantages of SPH method, such as naturally simulation of large deformation of material, the coupling algorithm of FEM with SPH method is presented to calculate region of small deformation by FEM and simulate region of large deformation by SPH method. In this paper, the research and application of FEM, SPH and FEM-SPH coupling algorithm are reviewed. And the problems existing in these methods are also discussed. Finally, the computational accuracy and efficiency of FEM, SPH and FEM-SPH coupling algorithm are investigated by a numerical example, which is a reference for research fellows.


  • loading
  • 张雄, 刘岩. 无网格法. 北京: 清华大学出版社, 2004 (Zhang Xiong, Liu Yan.Meshless Method. Beijing: Tsinghua University Press, 2004 (in Chinese))
    刘更, 刘天祥, 谢琴. 无网格法及其应用. 西安: 西北工业大学出版社, 2005 (LiuGeng, Liu Tianxiang, Xie Qin. Meshless Method and its Application. Xi'an:Northwestern Polytechnical University Press, 2005 (in Chinese))
    Courant R. Variational methods for the solution of problems of equilibriumand vibrations. Bulletin of the American Mathematical Sociaty, 1943, 49(1):1- 23  
    Clough RW. The finite element method in plane stress analysis. In: Proceedings of American Society ofCivil Engineers, 2nd Conference on Electronic Computations, Pittsburg, 1960. 345-378
    李晋先. 活动边界问题的时-空有限元配位法. 数值计算与计算机应用, 1987, 8: 136-144 (Li Jinxian. A space-time finite element collocation method formoving boundary problems. Journal of Numerical Method and ComputerApplications, 1987, 8: 136-144 (in Chinese))
    Yang FL, Chen CH, Young DL. A novel mesh regeneration algorithm for 2DFEM simulations of flows with moving boundary. Journal of ComputationalPhysics, 2011, 230(9): 3276-3301  
    Lucy LB. A numerical approach to the testing of the fission hypothesis.Astronomical Journal, 1977, 82(12): 1013-1024
    Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: Theory and application to non-sphericalstars. Monthly Notices of the Royal Astronomical Society, 1977, 181(2): 375-389
    Gingold RA, Monaghan JJ. Binary fission in damped rotating polytropes.Monthly Notices of the Royal Astronomical Society, 1978, 184(2): 481-499
    Gingold RA, Monaghan JJ. A numerical study of the Roche and Darwinproblems for polytropic stars. Monthly Notices of the Royal AstronomicalSociety, 1979, 188: 45-58
    Gingold RA, Monaghan JJ. The Roche problem for polytropes in centralorbits. Monthly Notices of the Royal Astronomical Society, 1980, 191:897-924
    Gingold RA, Monaghan JJ. Kernel estimates as a basis for general particle methods in hydrodynamics.Journal of Computational Physics, 1982, 46(3): 429- 453  
    Monaghan JJ, Gingold RA. Shock simulation by the particle method SPH. Journal of ComputationalPhysics, 1983, 52(2): 374-89  
    Monaghan JJ. Extrapolating B splines for interpolation. Journal of Computational Physics, 1985,60(2): 253-62  
    Monaghan JJ. Particle methods for hydrodynamics. Computer Physics Reports, 1985, 3(2): 71-124  
    Monaghan JJ. On the problem of penetration in particle methods. Journal of ComputationalPhysics, 1989, 82(1): 1-15  
    Bate MA, Bonnell IA, Bromm V. The formation mechanism of brown dwarfs. Monthly Notice of theRoyal Astronomical Society, 2002, 332(3): 65-68  
    Berczik P. Modeling the star formation in galaxies using the chemo-dynamical SPH code. Astronomyand Astrophysics, 2000, 271(2): 103-126
    Benz W. Applications of smooth particle hydrodynamics (SPH) to astrophysical problems. ComputerPhysics Communication, 1988, 48(1): 97-105
    Rasio FA, Lombardi JC. Smoothed particle hydrodynamics calculations ofstellar interactions. Journal of Computational and Applied Mathematics,1999, 109(1-2): 213-230.  
    Lattanzio JC, Schwarz MP, Monaghan JJ. Interstellar cloud collisions. Monthly Notices of theRoyal Astronomical Society, 1985, 215(1): 125-148
    Lee WH.Newtonian hydrodynamics of the coalescence of black holes with neutron stars II: Tidallylocked binaries with a soft equation of state.Monthly Notices of the Royal Astronomical Society, 1998,308: 780-794
    Monaghan JJ. Simulating free surface flows with SPH. Journal of Computer Physics, 1994, 110(2):399-406  
    Ferrari A, Dumbser M, Toro EF, et al. A new 3D parallel SPH scheme forfree surface flows. Computers & Fluids, 2009, 38(6): 1203-1217  
    Zhu Y, Fox P J, Morris JP. A pore-scale numerical model for flow throughporous media. International Journal for Numerical and Analytical Methods inGeomechanics, 1999, 23(9): 881-904  3.0.CO;2-K" target="_blank">
    Morris JP, Zhu Y, Fox PJ. Parallel simulations of pore-scale flow throughporous media. Couputers and Geotechnics, 1999, 25(4): 227-246  
    Jiang FM, Mó nica SA Oliveira, Antonio CM Sousa. Mesoscale SPHmodeling of fluid flow in isotropic porous media. Computer PhysicsCommunications, 2007, 176(7): 471-480
    Shao SD. Incompressible SPH flow model for wave interactions with porous media. CoastalEngineering, 2010, 57(3): 304-316
    Pereira GG, Prakash M, Cleary PW. SPH modelling of fluid at the grainlevel in a porous medium. Applied Mathematical Modelling, 2011, 35(4):1666- 1675  
    Monaghan JJ, Kocharyan A. SPH simulation of multi-phase flow. ComputerPhysics Communications, 1995, 87(1-2): 225-235
    Valizadeh A, Shafieefar M, Monaghan JJ, et al. Modeling two-phase flowsusing SPH method. Journal of Applied Sciences, 2008, 8(21): 3817-3826  
    Monaghan JJ. SPH compressible turbulence. Monthly Notice of the RoyalAstronomical Society, 2002, 335(3): 843-852  
    Liu MB, Liu GR, Zong Z, et al. Computer simualation of high explosiveexplosion using smoothed particle hydrodynamics methodology. Computers &Fluids, 2003, 32(3): 305-322  
    强洪夫, 王坤鹏, 高巍然.基于完全变光滑长度SPH方法的高能炸药爆轰过程数值试验. 含能材 料, 2009, 17(1):27-31 (Qiang Hongfu, Wang Kunpeng, Gao Weiran. Numerical simulation of highexplosive detonation process using SPH method with fully variable smoothinglengths. Chinese Journal of Energetic Materials, 2009, 17(1): 27-31 (inChinese))
    Swegle JW, Attaway SW. On the feasibility of using smoothed particlehydrodynamics for underwater explosion. Computational Mechanics, 1995,17(3): 151- 168  
    Liu MB, Liu GR, Zong Z, et al. Smoothed particle hydrodynamics fornumerical simulation of underwater explosions. Computational Mechanics,2003, 30(2): 106 -118  
    Yang G, Han X, Hu DA. Computer simulation of two-dimensionallinear-shaped charge jet using smoothed particle hydrodynamics. EngineeringComputations, 2011, 28 (1): 58-75
    Tanaka K. Numerical studies of explosive welding by SPH. MaterialsScience Forum, 2007, 566: 61-64  
    Wang X, Zheng YY, Liu HX, et al. Numerical study of the mechanism ofexplosive/impact welding using smoothed particle hydrodynamics method.Materials & Design, 2012, 35: 210-219  
    Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentationusing SPH/MLSPH. International Journal for Numerical Methods in Engineering,2003, 56(10): 1421-1444  
    Hayhurst C, Clegg RA. Cylindrically symmetric SPH simulations ofhypervelocity impacts on thin plates. International Journal of ImpactEngineering, 1997, 20 (1-5): 337-348
    Hiermaier S, K\"{onke D, Stilp A J, et al. Computational simulation ofthe hypervelocity impact of Al-spheres on thin plates of differentmaterials. International Journal of Impact Engineering, 1997, 20(1-5):363- 374  
    Faraud M, Destefanis R, Palmieri D, et al. SPH simulations of debris impacts using two differentcomputer codes. International Journal of Impact Engineering, 1999, 23(1): 249-260  
    贾光辉, 黄海 ,胡震东. 超高速撞击数值仿真结果分析. 爆炸与冲击, 2005,25(1): 47-53 (Jia Guanghui, Huang Hai, Hu Zhendong. Simulation analyse ofhypervelocity impact perforation. Explosion and Shock Waves, 2005, 25(1):47-5 3(in Chinese))
    贾光辉, 黄海. 超高速撞击航天器二次碎片云能量特性分析.北京航空航天大学学报, 2007, 33(3): 257-260 (Jia Guanghui, Huang Hai.Characters on kinetics energy of debris cloud in spacecraft. Journal ofBeijing University of Aeronautics and Astronautics, 2007, 33(3): 257-260 (inChinese))
    管公顺, 张伟, 庞宝君, 等. 铝球弹丸高速正撞击薄铝板穿孔研究.高压物理学报,2005, 19 (2): 132-138 (Guan Gongshun, Zhang Wei, Pang Baojun,et al. A studyof penetration hole diameter in thin al-plate by hypervelocity impact ofal-spheres. Chinese Journal of High Pressure Physics, 2005, 19(2): 132-138(in Chinese))
    贾斌, 马志涛, 庞宝君. 含泡沫铝防护结构的超高速撞击数值模拟研究. 高压物理学报, 2009, 23(6): 453-459(Jia Bin, Ma Zhitao, Pang Baojun. Numerical simulation investigation in hypervelocity impact on shieldstructure containing aluminum foam. Chinese Journal of High Pressure Physics, 2009, 23(6): 453-459 (inChinese))
    徐金中, 汤文辉, 徐志宏. 超高速碰撞碎片云特征的SPH方法数值分析. 高压物理学报, 2008, 22(4): 377-383 (XuJinzhong, Tang Wenhui, Xu Zhihong. Numerical analysis of the characteristics of debris clouds produced byhypervelocity impacts using SPH method. Chinese Journal of High Pressure Physics, 2008, 22(4): 377-383(in Chinese))
    Seo S, Min O, Lee J. Application of an improved contact algorithm forpenetration analysis in SPH. International Journal of Impact Engineering,2008, 35(6): 578 -588  
    Lee M, Yoo YH. Analysis of ceramic/metal armour systems. InternationalJournal of Impact Engineering, 2001, 25(9): 819-829  
    张伟, 胡德安, 韩旭. 弹体侵彻运动陶瓷/金属复合装甲SPH模拟. 固体力学学报, 2010, 31 (S1): 70-75 (ZhangWei, Hu Dean, Han Xu. Simulation on projectile penetrating into moving ceramic/metal composite armor usingSPH method. Acta Mechanica Solida Sinica, 2010, 31(S1): 70-75 (in Chinese))
    Benz W, Asphaug E. Simulations of brittle solids using smooth particlehydrodynamics. Computer Physics Communications, 1995, 87(1-2): 253- 265  
    Bonet J, Kulasegaram S. Correction and stabilization of smooth particlehydrodynamics methods with applications in metal forming simulations.International Journal for Numerical Method in Engineering, 2000, 47(6):1189-1214  3.0.CO;2-I" target="_blank">
    Cleary PW, Prakash M, Ha J. Novel applications of smoothed particlehydrodynamics (SPH) in metal forming. Journal of Materials ProcessingTechnology, 2006, 177 (1-3): 41-48  
    Heinstein M, Segalman D. Simulation of orthogonal cutting with smoothed particle hydrodynamics.Report no. SAND97-1961, Sandia National Laboratoties, 1997
    Limido J, Espinosa C, Salaun M, et al. A new approach of high speedcutting modelling: SPH method. Journal of Physiscs IV, 2006, 134(1):1195-1200
    姜涛, 张宪, 乔欣, 等. 基于SPH法的土壤切削刀具三维数值模拟及优化. 机电工程, 2009, 26(6): 44-46 (JiangTao, Zhang Xian, Qiao Xin, et al. 3-D numerical simulation and optimization of solid cutting tool based onSPH. Journal of Mechanical and Electrical Engineering, 2009, 26(6): 44-46 (in Chinese))
    Oger G, Doring M, Alessandrini B, et al. Two-dimensional SPH simulationsof wedge water entries. Journal of Computational Physics, 2006, 213(2):803- 822  
    Gong K. Water entry with of a wedge based on SPH model with an improvedboundary treatment. Journal of Hydrodynmics, 2009, 21(6): 750-757  
    Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid-structureinteraction by SPH. Computers & Structures, 2007, 85(11-14): 879-890
    Rafiee A, Thiagarajan KP. An SPH projection method for simulatingfluid-hypoelastic structure interaction. Computer Methods in AppliedMechanics and Engineering, 2009, 198(33-36): 2785-2795
    Müller M, Schirm S, Teschner M. Interactive blood simulation forvirtual surgery based on smoothed particle hydrodynamics. Technology andHealth Care, 2004, 12(1): 25-31
    Sinnott M, Cleary PW, Prakash M. An investigation of pulsatile blood flow in a bifurcation arteryusing a grid-free method. In: Fifth International Conference on CFD in the Process Industries. Melbourne,2006. 13-15
    Jin Q,-Pang WM,-Nguyen BP, et al. Particle-based simulation of blood flow and vessel wallinteractions in virtual surgery. In: 2010 Symposium on Information and Communication Technology. Hanoi,-2010.128-133
    Tanaka N, Takano T, Masuzawa T. 3-dimensional micro-simulation of blood flow with SPH method. Nihon Kikai Gakkai Ryutai Kogaku Bumon Koenkai Koen Ronbunshu (CD-ROM), 2004, 82: 7-12
    Tanaka N, Takano T. Microscopic-scale simulation of blood flow uing SPHmethod. International Journal of Computational Methods, 2005, 2(4): 555- 568  
    Tsubota K, Wada S, Kamada H, et al. A particle method for blood flowsimulation, application to flowing red blood cells and platelets. Journal ofthe Earth Simulator, 2006, 5: 2-7
    Bonet J, Lok T -S L. Variational and momentum preservation aspects ofsmooth particle hydrodynamic formulations. Computer Methods in AppliedMechanics and Engineering, 1999, 180(1-2): 97-115  
    Bonet J, Kulasegaram S, Rodriguez-Paz MX, et al. Variational formulationfor the smooth particle hydrodynamics (SPH) simulation of fluid and solidproblems. Computer Methods in Applied Mechanics and Engineering, 2004,193(12-14): 1245-1256
    Swegle JW, Hicks DL, Attaway SW. Smoothed particle hydrodynamicsstability analysis. Journal of Computational Physics, 1995, 116(1): 123- 134  
    Dyka CT, Ingel RP. An approach for tension instability in smoothedparticle hydrodynamics. Computers & Structures, 1995, 57(4): 573-580  
    Dyka CT, Randles PW, Ingel RP. Stress points for tension instability inSPH. International Journal for Numerical Methods in Engineering, 1997,40(13): 2325 -2341  3.0.CO;2-8" target="_blank">
    Randles PW, Libersky LD. Normalized SPH with stress pointss.International Journal for Numerical Method in Engineering, 2000, 48(10):1445-1462  3.0.CO;2-9" target="_blank">
    Hicks DL, Swegle JW, Attaway SW. Conservative smoothing stabilizesdiscrete- numerical instabilities in SPH material dynamics computations.Applied Mathematics and Computation, 1997, 85(2-3): 209-226
    Monaghan JJ. SPH without a tensile instability. Journal of ComputationalPhysics, 2000, 159(2): 290-311  
    Gray JP, Monaghan JJ, Swift R P. SPH elastic dynamics. Computer Methods in Applied Mechanics andEngineering, 2001, 190(49-50): 6641-6662
    Sigalotti LDG, Ló pez H. Adaptive kernel estimation and SPH tensileinstability. Computers & Mathematics with Applications, 2008, 55 (2):23-50
    傅学金, 强洪夫, 杨月诚. 固体介质中方法的拉伸不稳定性问题研究进展. 力学进展, 2007, 37(3): 375-388.(FuXuejin,Qiang Hongfu,Yang Yuecheng.Advances in the tensile instability of smoothed particle hydrodynamicsapplied to solid dynamics. Advances in Mechanics, 2007, 37(3): 375-388 (in Chinese))
    Campbell PM. Some new algorithms for boundary value problems in smoothed particle hydrodynamics.Report no. DNA-TR-88-286, Mission Research Corporation, 1989
    Libersky LD, Petschek AG, Carney TC, et al. High strain Lagrangianhydrodynamics: A three-dimensional SPH code for dynamic material response.Journal of Computational Physics, 1993, 109(1): 67-75  
    Randles PW, Libersky LD. Smoothed particle hydrodynamics: some recentimprovements and applications. Computer Methods in Applied Mechanics andEngineering, 1996, 139(1-4): 375-408  
    Randles PW, Libersky LD. Boundary conditions for a dual particle method.Computers & Structures, 2005, 83(17-18): 1476-1486
    Monaghan JJ, Kajtar JB. SPH particle boundary forces for arbitraryboundaries. Computer Physics Communications, 2009, 180(10): 1811-1820  
    Campbell J, Vignjevic R, Libersky LD. A contact algorithm for smoothedparticle hydrodynamics. Computer Methods in Applied Mechanics andEngineering, 2000, 184(1): 49-65  
    Seo S, Min O. Axisymmetric SPH simulation of elasto-plastic contact inthe low velocity impact. Computer Physics Communications, 2006, 175(9):583- 603  
    Xiao YH, Hu DA, Han X, et al. Simulation of normal perforation of aluminum plates using axisymmetricsmoothed particle hydrodynamics with contact algorithm. Computational Methods, 2013, 10(3): 1-21
    周星, 许厚谦. 计算含动边界非定常流动的无网格算法. 力学与实践, 2010,32(3): 16-22 (Zhou Xing, Xu Houqian. The meshless method for unsteady flowwith moving boundary. Mechanics in Engineering, 2010, 32(3): 16-22(inChinese))
    Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods.International Journal for Numerical Methods in Engineering, 1995, 20(8-9):1081-1106
    Johnson GR, Beissel SR. Normalized smoothing functions for SPH impactcomputations. International Journal for Numerical Methods in Engineering,1996, 39(16): 2725 -2741  3.0.CO;2-9" target="_blank">
    Chen JK, Beraun JE, Carney TC. A corrective smoothed particle method forboundary value problems in heat conduction. International Journal forNumerical Methods in Engineering, 1999, 46(2): 231-252  3.0.CO;2-K" target="_blank">
    Zhang GM, Batra RC. Modified smoothed particle hydrodynamics method andits application to transient problems. Computational Mechanics, 2004, 34(2):137- 146
    Batra RC, Zhang GM. SSPH basis functions for meshless methods, andcomparison of solutions with strong and weak formulations. ComputationalMechanics, 2008, 41 (4): 527-545
    Liu MB, Xie WP, Liu GR. Modeling incompressible flows using a finite particle method. AppliedMathematical Modelling, 2005, 29(12): 1252-1270
    Liu MB, Liu GR. Restoring particle consistency in smoothed particle hydrodynamics. AppliedNumerical Mathematics, 2006, 56(1): 19-36
    Shintate K, Sekine H. Numerical simulation of hypervelocity impacts of aprojectile on laminated composite plate targets by means of improved SPHmethod. Composites: Part A, 2004, 35(6): 683-692  
    卞梁, 王肖钧, 章杰. 高速碰撞数值计算中的SPH自适应粒子分布法. 爆炸与冲击, 2009, 29 (6): 607-612 (Bian Liang, Wang Xiaojun, Zhang Jie. A new adaptiveSPH method for hypervelocity impact simulation. Explosion and Shock Waves,2009, 29(6): 607- 612 (in Chinese))
    Xu F, Chen JS, Huang QQ. The study of numerical stability in the SPH method. Advanced MaterialsResearch, 2008, 33-37(1-4): 839-844
    赵燕, 徐绯, 李玉龙, 陈刘定. 一种改进的可阻止SPH数值断裂的方法.爆炸与冲击, 2009, 29(5): 503-508 (Zhao Yan, Xu Fei, Li Yulong, et al. Animproved SPH method for preventing numerical fractures. Explosion and ShockWaves, 2009, 29(5): 503-508 (in Chinese))
    Zhao Y, Xu F, Li YL, et al. A simple method in preventing numericalfractures of SPH computations. Advanced Materials Research, 2008,33-37(1-4): 845-850
    赵燕, 徐绯, 李玉龙. 一种适用于颗粒非规则分布的阻止SPH 数值断裂的方法.航空学报, 2009, 30(11): 2100-2105 (Zhao Yan, Xu Fei, Li Yulong. A method ofpreventing SPH numerical fracture for irregular particle models. ActaAeronautica Astronautica Sinica, 2009, 30(11): 2100-2105 (in Chinese))
    陈刘定, 姚磊江, 李自山, 等. 光滑质点流体动力学方法中数值断裂的防止. 机械强度, 2010, 32(1): 148-152(Chen Liuding, Yao Leijiang, Li Zishan, et al. Prevention of numerical fracture in smoothed particlehydrodynamics method. Journal of Mechanical Strength, 2010, 32(1): 148-152(in Chinese))
    Hernquis L. Some cautionary remarks about smoothed particlehydrodynamics. The Astrophysical Journal, 1993, 404(2): 717-722
    Nelson RP, Papalozizou JCB. Variable smoothing lengths and energy conservation in smoothed particlehydrodynamics. Monthly Notices of the Royal Astronomical Society, 1994, 270(1): 1-20
    Springel V, Hernquist L. Cosmological smoothed particle hydrodynamics simulations: the entropyequation. Astronomy & Astrophysics, 2002, 333(3): 649-664
    强洪夫, 高巍然. 修正变光滑长度SPH方法及其应用. 解放军理工大学, 2007, 8(5): 419- 424 (Qiang Hongfu,Gao Weiran. Modified SPH method considering full variable smoothing lengths effects and its applications.Journal of PLA University of Science and Technology, 2007, 8(5): 419-424 (in Chinese))
    Johnson GR, Beissel SR. SPH for high velocity impact computations.Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4):347-373  
    Johnson GR. Linking of Lagrangian particle methods to standard finiteelement methods for high velocity impact simulations. Nuclear Engineeringand Design, 1994, 150(2-3): 265-274
    Attaway SW, Heinstein MW, Swegle JW. Coupling of smooth particle hydrodynamic with finite elementmethod. Nuclear Engineering and Design, 1994, 150(2-3): 199-205
    De Vuyst T, Vignjevic R, Campbell JC. Coupling between meshless and finite element methods. International Journal of Impact Engineering, 2005, 31(8): 1054- 1064  
    Sauer M. Adaptive Kopplung des Netzfreien SPH-Verfahrens mit Finiten Elementen zur Berechnung vonImpaktvorgängen: [PhD Thesis]. Munich: Universität der Bundeswehr München, 2000  
    Fernández-Méndez S, Bonet J, Huerta A. Continuousblending of SPH with finite elements. Computers and Structures, 2005,83(17-18): 1448-1458
    Rabczuk T, Xiao SP, Sauer M. Coupling of mesh-free method with finiteelements: basic concepts and test results. Communications for NumericalMethods in Engineering, 2006, 22(10): 1031-1065
    Johnson GR, Stryk RA, Stephen R, et al. An algorithm to automaticallyconvert distorted finite elements into meshless particles during dynamicdeformation. International Journal of Impact Engineering, 2002, 27(10):997- 1013  
    Johnson GR, Stryk RA. Conversion of 3D distorted elements into meshlessparticles during dynamic deformation. International Journal of ImpactEngineering, 2003, 28(9): 947-966
    Xiao YH, Han X, Hu DA. A coupling algorithm of finite element method andsmoothed particle hydrodynamics for impact computations. Computers,Materials & Continua, 2011, 23(1): 9-34
    王吉, 王肖钧, 卞梁.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. 爆炸与冲 击, 2007,27(6): 522-528 (Wang Ji, Wang Xiaojun, Bian Liang. Linking of smoothedparticle hydrodynamics method to standard finite element method and itsapplication in impact dynamics. Explosion and Shock Waves, 2007, 27(6):522-528 (in Chinese))
    张志春, 强洪夫, 高巍然.一种光滑粒子流体动力学-有限元法转换算法及其在冲击动力学中 的应用. 西安交通大学学报, 2011, 45(1): 105-110 (Zhang Zhichun, Qiang Hongfu, Gao Weiran. Conversion of3D distorted finite elements into SPH particles during impact dynamicdeformation. Journal of Xi'an Jiaotong University, 2011, 45(1): 105-110 (inChinese))
    Beissel SR, Gerlach CA, Johnson GR. Hypervelocity impact computationswith finite elements and meshfree particles. International Journal of ImpactEngineering, 2006, 33(1-12): 80-90
    Johnson GR. Numerical algorithms and material models for high-velocityimpact computations. International Journal of Impact Engineering, 2011,38(6): 456- 472  
    Johnson GR, Petersen EH, Stryk RA. Incorporation of an SPH option intothe EPIC code for a wide range of high velocity impact computations.International Journal of Impact Engineering, 1993, 14(1-4): 385-394  
    Sauer M. Simulation of high velocity impact in fluid-filled containersusing finite elements with adaptive coupling to smoothed particlehydrodynamics. International Journal of Impact Engineering, 2011, 38(6):511-520  
    Caleyron F, Chuzel-Marmot Y, Combescure A. Modeling of reinforcedconcrete through SPH-FE coupling and its application to the simulation of aprojectile's impact onto a slab. International Journal for Numerical Methodsin Biomedical Engineering, 2009, 27(6): 882-898
    Lu Y, Wang ZQ, Chong K. A comparative study of buried structure in soilsubjected to blast load using 2D and 3D numerical simulations. Soil Dynamicsand Earthquake Engineering, 2005, 25(4): 275-288  
    蔡清裕, 崔伟峰, 向东, 等. 模拟刚性动能弹丸侵彻混凝土的FE-SPH方法. 国防科学技术大 学学报, 2003, 25(6):87-90 (Cai Qingyu, Cui Weifeng, Xiang Dong, et al.Simulation of concrete penetrated by rigid projectile withcoupled FE-SPH methods. Journal of National University of Defence Technology, 2003, 25(6): 87-90 (inChinese))
    纪冲, 龙源, 方向.基于FEM-SPH耦合法的弹丸侵彻钢纤维混凝土数值模拟.振动与冲击, 2010, 29(7):69-74 (Ji Chong, Long Yuan, Fang Xiang. Numerical simulation for projectilepenetrating steel fiber reinforced concrete with FEM -SPH couplingalgorithm. Journal of Vibration and Shock, 2010, 29(7): 69-74 (in Chinese))
    嵇晓宇. 弹丸撞击问题的FE-SPH耦合模拟. [硕士论文]. 合肥:中国科学技术大学, 2007 (Ji Xiaoyu. Numerical simulation for projectileimpact problems with FE-SPH coupling algorithm: [Master Thesis]. Hefei:University of Science and Technology of China, 2007 (in Chinese))
    宋顺成, 才鸿年. 模拟战斗部对混凝土侵彻与爆炸耦合作用的计算.弹道学, 2004,16(4): 23-28 (Song Shuncheng, Cai Hongnian. Computations for coupled actionsof simulated projectile penetrating and detonating to concrete. Journal ofBallistics, 2004, 16(4): 23-28 (in Chinese))
    Xu JX, Liu XL. Analysis of structural response under blast loads usingthe coupled SPH-FEM approach. Journal of Zhejiang University Science A,2008, 9(9): 1184- 1192  
    张忠, 陈卫东, 陈浩. FEM/SPH耦合算法的射弹冲击起爆仿真. 系统仿真学报,2009, 21(22): 7080-7083 (Zhang Zhong, Chen Weidong, Chen Hao. Numericalsimulation of column projectile impact shielded explosive using FE/SPHcoupling method. Journal of System Simulation, 2009, 21(22): 7080-7083(inChinese))
    武玉玉, 何远航, 李金柱. 耦合方法在超高速碰撞数值模拟中的应用.高压物理学报, 2005, 19(4): 385-389 (Wu Yuyu, He Yuanhang, Li Jinzhu.Application of the coupling method in simulating hypervelocity impact.Chinese Journal of High Pressure Physics, 2005, 19(4): 385-389 (in Chinese))
    冷冰林, 许金余, 邵宁, 等. 刚性弹丸侵彻金属靶体的FEM-SPH耦合计算.弹箭与制导学报, 2008, 28(5): 105-108 (Leng Binglin, Xu Jinyu, Shao Ning, etal. Computation of steel penetrated by rigid projectile with coupled FEM-SPHmethods. Journal of Projectiles, Rockets, Missiles and Guidance, 2008,28(5): 105-108 (in Chinese))
    卞梁, 王肖钧, 章杰.SPH/FEM耦合算法在陶瓷复合靶抗侵彻数值模拟中的应用.高压物理学报 , 2010, 24(3):161-167 (Bian Liang, Wang Xiaojun, Zhang Jie. Numerical simulations of anti-penetration of confined ceramic targets by SPH/ FEM coupling method. ChineseJournal of High Pressure Physics, 2010, 24(3): 161-167 (in Chinese))
    张洪涛, 赵美英, 任磊, 等. SPH和FEM耦合方法分析机翼前缘鸟撞的响应问题.科学技术工程 , 2009, 9(7): 1802-1806 (Zhang Hongtao, Zhao Meiying, Ren Lei,et al. Bird impact on aircraft leading edge simulation with SPH and FEMcoupling method. Science Technology an Engineering, 2009, 9(7): 1802-1806(in Chinese))
    宿崇, 唐亮, 侯俊铭, 等. 基于FEM与SPH耦合算法的金属切削仿真研究.系统仿真学报, 2009, 21(16): 5002-5005 (Su Chong, Tang Liang, Hou Junming, etal. Simulation research of metal cutting based on FEM and SPH. Journal ofSystem Simulation, 2009, 21 (16): 5002-5005 (in Chinese))
    刘飞宏, 王建明, 余丰, 等. 基于SPH耦合有限元法的喷丸残余应力场数值模拟.山东大学学 报, 2010, 40(6): 67-71 (Liu Feihong, Wang Jianming, Yu Feng, etal. Numerical simulation for compressive residual stress of shot peeningbased on SPH coupled FEM. Journal of Shandong University, 2010, 40(6): 67-71(in Chinese))
    王建明, 余丰, 刘飞宏, 等. SPH和FEM耦合法模拟磨料水射流中单磨粒加速过程.山东大学学 报, 2011, 41(5): 114-119 (Wang Jianming, Yu Feng, Liu Feihong, etal. Numerical simulation of single particle acceleration process by SPHcoupled FEM for abrasive water-jet cutting. Journal of Shandong University,2011, 41(5): 114-119 (in Chinese))
    马利, 陶伟明, 郭乙木, 等. SPH耦合有限元方法的水射流弹塑性碰撞模拟. 浙江大学学报, 2008, 42(2):259-263 (Ma Li, Tao Weiming, Guo Yimu, et al. Elastic/plastic impact simulation of water jet using smoothedparticle hydrodynamics and finite element method. Journal of Zhejiang University, 2008, 42(2): 259-263(in Chinese))
    Fourey G, Oger G, Le Touzé D, et al. Violent fluid-structure interaction simulations using acoupled SPH/FEM method. IOP Conference Series: Materials Science and Engineering, 2010, 10(1): 012041
    Groenenboom PHL, Cartwright BK. Hydrodynamics and fluid-structureinteraction by coupled SPH-FE method. Journal of Hydraulic Research, 2010,48(S1): 61- 73  
    许庆新, 沈荣瀛. 充液容器跌落过程的SPH模拟方法. 振动与冲击, 2007, 27(6):13-16 (Xu Qingxin, Shen Rongying. Dropping emulation analysis offluid-filled tank using SPH method. Noise and Vibration Control, 2007,27(6): 13-16 (in Chinese))
    Johnson GR, Stryk SR, Beissel SR. Interface effects for SPH impactcomputations. Structures under shock and impact IV, 1996: 285-294
    Hanchak SJ, Forrestal MJ, Young ER, et al. Perforation of concrete slabs with 48MPa (7ksi) and140MPa (20ksi) compressive strengths. International Journal of Impact Engineering, 1992, 12: 1-7  
    Johnson GR, Cook WH. A constitutive model and data for metals subjectedto large strains, high strain rates and high temperatures. Proceedings ofthe Seventh International Symposium on Ballistics, The Hague, theNetherlands, 1983
    Holmquist TJ, Johnson GR, Cook WH. A computational constitutive model for concrete subjected tolarge strains, high strain rates, and high pressures. In: Proc of the 14th International Symposium onBallistics, Qucbec, 1993. 591-600
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2082) PDF downloads(3295) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint