FEM与DEM耦合方法研究及在汽车玻璃冲击破坏问题中的应用
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摘要
汽车玻璃是汽车不可或缺的一个重要组成部分,汽车自生产之日起,就离不开车用玻璃。大量交通事故表明,汽车玻璃破坏机理的研究对行人保护、汽车被动安全和事故再现等方面有着十分重要的理论和实际意义。汽车玻璃冲击破坏过程本质上是材料由连续体向非连续体转化的一个复杂的力学过程,实验以及单纯使用有限元法或离散元法在研究这一问题中存在着一些困难和不足。本文系统地研究了适用于汽车玻璃冲击破坏分析的有限元与离散元耦合方法。
首先,提出了一种颗粒离散元和有限元分区域耦合算法。该算法将待求区域划分为独立的离散元域和有限元域进行求解,使用罚函数法计算各求解区域耦合界面处的相互作用,实现了汽车夹层玻璃等层状复合材料的分区域耦合计算。通过与纯有限元法计算结果的比较,验证了该方法在弹性范围内的计算精度。在此基础上,对汽车夹层玻璃板冲击破坏过程进行了仿真分析。结果表明,耦合算法有望对冲击力等宏观量进行预测。
然后,扩展了Single/Smeared破坏模型并将其应用于三维FEM/DEM方法。Single/Smeared破坏模型是基于试验应力-应变曲线的一种数值模型。该模型假设裂纹发生的位置与有限单元边界一致,针对材料不同阶段的力学行为,分别使用不同方法计算:应变硬化阶段使用标准的本构关系计算,应变软化阶段使用单一裂纹模型计算。Single/Smeared破坏模型最初只适用于二维I型破坏问题,扩展后可用于分析三维I型和II型破坏问题。在算例验证了该模型正确性的基础上,应用三维FEM/DEM方法模拟了汽车夹层玻璃冲击破坏过程,结合试验结果初步验证了该方法的有效性。
最后,针对汽车玻璃结构,系统地提出了一种适合于板壳结构冲击破坏问题的FEM/DEM方法。基于板壳结构的受力特点,构造了一种简单高效的“solid-shell”板壳单元;基于势函数的罚函数法,发展了相应的接触算法用于处理板壳单元间接触力的计算;基于Single/Smeared模型,发展了相应的破坏模型用于破坏力学分析。通过对若干典型算例的计算,验证了该方法在大位移小应变条件下的板壳结构问题的求解精度。在此基础上,模拟了普通玻璃板的冲击破坏过程,通过与相关文献所介绍的试验研究的比较,初步验证了该方法的有效性。
以上方法均通过软件实现。其中,基于颗粒离散元和有限元分区域耦合算法,使用Fortran 95语言和面向对象程序编制思想,开发了通用的三维求解系统CDFP。关于FEM/DEM方法的工作均应用于通用的求解程序Y。
The laminated glass is an indispensable part to automobile. A great number of traffic acci-dents have shown that the study on impact fracture mechanism of automobile laminated glass isof theoretical and practical importance in the field of pedestrian protection, passive safety andtraffic accident reconstruction. Due to the fact that the dynamic damage and failure processes ofautomobile glass in essence are the materials transferring from continuum to non-continuum,traditional numerical methods such as finite element method (FEM) and/or discrete elementmethod (DEM), as well as experimental study encountered sticky problems. In this disserta-tion, the combined finite element and discrete element methods in the context of automobilelaminated glass are studied systematically.
Firstly, an algorithm combining three-dimensional (3D) particle-based discrete and finiteelement methods is proposed to analyze the dynamic mechanical behavior of laminated com-posite material like laminated glass. This new approach is conducted by decomposing the cal-culation domain into a finite element (FE) calculation domain and a particle based discreteelement (DE) calculation domain; the interaction between the two sub-domains is processed byusing a penalty function method. Comparing the results calculated by the present method withthat from FEM, the precision of the present method in the elastic range is proved. After that, theimpact fracture behavior of a laminated glass plate is simulated, and the numerical experimentsshow that the combined model could be used to predict some macroscopical physical quantities,such as the impact force of impactor.
Secondly, the Single/Smeared crack model based on accurate approximation of experi-mental stress-strain curves, is extended into three-dimensional in the context of the combinedfinite-discrete element method (FEM/DEM). The crack model, in which the cracks are assumedto coincide with the element edges, is conducted by calculating the mechanics behaviors of ma-terial at different stages by using different methods, say, the finite element method in a standardway through the constitutive law is implemented at the strain hardening stage while the single-crack model is used at the strain softening stage. After extension, the Single/Smeared crackmodel, which is aimed at mode I loaded cracks and 2D plane stress problems only in its originalform, could be used to simulate the situations with both mode I and mode II loaded cracks in3D. After proving the validity of the model through several simple numerical examples, the impact fracture process of automobile laminated glass is simulated by 3D FEM/DEM, whichpreliminarily verifies the validation of the present method.
Finally, a combined finite-discrete element method aiming to analyze the impact fractureprocess of shell structure, is projected. The developed method includes there aspects: (1) asimple and efficient solid-shell element, (2) the corresponding algorithm for contact interactionbased on a penalty function method, and (3) the corresponding crack model based on the Sin-gle/Smeared model. The accuracy of the proposed method in the field of larger deformation andsmall strain is verified through a large number of numerical tests. And then, the impact fracturebehavior of a glass plate is simulated, and the validation of the present method is preliminarilyverified through the comparison with experiment reported in references.
All the above-mentioned methods are realized through numerical codes. Based on thealgorithm combining 3D particle-based discrete and finite element methods, a general purpose3D numerical analysis code CDFP is developed by using Fortran95 programming languageand the Object Oriented Analysis (OOA) method. All the relative work on FEM/DEM, i.e. 3DSingle/Smeared model and FEM/DEM method for shell fracture and fragmentation, has beenimplemented into the general purpose Y code.
首先,提出了一种颗粒离散元和有限元分区域耦合算法。该算法将待求区域划分为独立的离散元域和有限元域进行求解,使用罚函数法计算各求解区域耦合界面处的相互作用,实现了汽车夹层玻璃等层状复合材料的分区域耦合计算。通过与纯有限元法计算结果的比较,验证了该方法在弹性范围内的计算精度。在此基础上,对汽车夹层玻璃板冲击破坏过程进行了仿真分析。结果表明,耦合算法有望对冲击力等宏观量进行预测。
然后,扩展了Single/Smeared破坏模型并将其应用于三维FEM/DEM方法。Single/Smeared破坏模型是基于试验应力-应变曲线的一种数值模型。该模型假设裂纹发生的位置与有限单元边界一致,针对材料不同阶段的力学行为,分别使用不同方法计算:应变硬化阶段使用标准的本构关系计算,应变软化阶段使用单一裂纹模型计算。Single/Smeared破坏模型最初只适用于二维I型破坏问题,扩展后可用于分析三维I型和II型破坏问题。在算例验证了该模型正确性的基础上,应用三维FEM/DEM方法模拟了汽车夹层玻璃冲击破坏过程,结合试验结果初步验证了该方法的有效性。
最后,针对汽车玻璃结构,系统地提出了一种适合于板壳结构冲击破坏问题的FEM/DEM方法。基于板壳结构的受力特点,构造了一种简单高效的“solid-shell”板壳单元;基于势函数的罚函数法,发展了相应的接触算法用于处理板壳单元间接触力的计算;基于Single/Smeared模型,发展了相应的破坏模型用于破坏力学分析。通过对若干典型算例的计算,验证了该方法在大位移小应变条件下的板壳结构问题的求解精度。在此基础上,模拟了普通玻璃板的冲击破坏过程,通过与相关文献所介绍的试验研究的比较,初步验证了该方法的有效性。
以上方法均通过软件实现。其中,基于颗粒离散元和有限元分区域耦合算法,使用Fortran 95语言和面向对象程序编制思想,开发了通用的三维求解系统CDFP。关于FEM/DEM方法的工作均应用于通用的求解程序Y。
The laminated glass is an indispensable part to automobile. A great number of traffic acci-dents have shown that the study on impact fracture mechanism of automobile laminated glass isof theoretical and practical importance in the field of pedestrian protection, passive safety andtraffic accident reconstruction. Due to the fact that the dynamic damage and failure processes ofautomobile glass in essence are the materials transferring from continuum to non-continuum,traditional numerical methods such as finite element method (FEM) and/or discrete elementmethod (DEM), as well as experimental study encountered sticky problems. In this disserta-tion, the combined finite element and discrete element methods in the context of automobilelaminated glass are studied systematically.
Firstly, an algorithm combining three-dimensional (3D) particle-based discrete and finiteelement methods is proposed to analyze the dynamic mechanical behavior of laminated com-posite material like laminated glass. This new approach is conducted by decomposing the cal-culation domain into a finite element (FE) calculation domain and a particle based discreteelement (DE) calculation domain; the interaction between the two sub-domains is processed byusing a penalty function method. Comparing the results calculated by the present method withthat from FEM, the precision of the present method in the elastic range is proved. After that, theimpact fracture behavior of a laminated glass plate is simulated, and the numerical experimentsshow that the combined model could be used to predict some macroscopical physical quantities,such as the impact force of impactor.
Secondly, the Single/Smeared crack model based on accurate approximation of experi-mental stress-strain curves, is extended into three-dimensional in the context of the combinedfinite-discrete element method (FEM/DEM). The crack model, in which the cracks are assumedto coincide with the element edges, is conducted by calculating the mechanics behaviors of ma-terial at different stages by using different methods, say, the finite element method in a standardway through the constitutive law is implemented at the strain hardening stage while the single-crack model is used at the strain softening stage. After extension, the Single/Smeared crackmodel, which is aimed at mode I loaded cracks and 2D plane stress problems only in its originalform, could be used to simulate the situations with both mode I and mode II loaded cracks in3D. After proving the validity of the model through several simple numerical examples, the impact fracture process of automobile laminated glass is simulated by 3D FEM/DEM, whichpreliminarily verifies the validation of the present method.
Finally, a combined finite-discrete element method aiming to analyze the impact fractureprocess of shell structure, is projected. The developed method includes there aspects: (1) asimple and efficient solid-shell element, (2) the corresponding algorithm for contact interactionbased on a penalty function method, and (3) the corresponding crack model based on the Sin-gle/Smeared model. The accuracy of the proposed method in the field of larger deformation andsmall strain is verified through a large number of numerical tests. And then, the impact fracturebehavior of a glass plate is simulated, and the validation of the present method is preliminarilyverified through the comparison with experiment reported in references.
All the above-mentioned methods are realized through numerical codes. Based on thealgorithm combining 3D particle-based discrete and finite element methods, a general purpose3D numerical analysis code CDFP is developed by using Fortran95 programming languageand the Object Oriented Analysis (OOA) method. All the relative work on FEM/DEM, i.e. 3DSingle/Smeared model and FEM/DEM method for shell fracture and fragmentation, has beenimplemented into the general purpose Y code.
引文
[1]公安部交通管理局.中华人民共和国道路交通事故统计资料汇编[G].北京:公安部交通管理局. 2001-2009
[2] Xu J, Li YB. Crack analysis in PVB laminated windshield impacted by pedestrian headin traffic accident[J]. International Journal of Crashworthiness. 2009, 14(1):63–71
[3]刘志海.夹层玻璃的发展现状及趋势[J].中国建材. 2003, 9:64–66
[4]许骏,李一兵.人车碰撞事故再现技术综述[J].汽车工程. 2009, 31(11):1029–1033
[5] AL, Browne. 2-Ply windshields: laboratory impactor tests of the polyvinyl bu-tyral/polyester construction[J]. SAE-Paper. 1995, No. 950047
[6] Brendler S, Haufe A, Ummenhofer T. A detailed numerical investigation of insulatedglass subjected to the standard pendulum test[J]. Proceedings of the third LS-DYNAForum, Bamberg, Germany. 2004, F-I-57/64
[7] Du Bois PA, Kolling S, Fassnacht W. Modelling of safety glass for crash simulation[J].Computational Materials Science. 2003, 28(3-4):675–683
[8] Ji FS, Dharani LR, Behr RA. Damage probability in laminated glass subjected to lowvelocity small missile impacts[J]. Journal of Materials Science. 1998, 33(19):4775–4782
[9] Timmel M, Kolling S, et al. A finite element model for impact simulation with laminatedglass[J]. International Journal of Impact Engineering. 2007, 34(8):1465–1478
[10]孙宏图,刘学术,等.汽车碰撞变形计算机模拟研究[J].大连理工大学学报. 42(6)
[11]张晓云,金先龙,等.面向事故分析的车身关键参数数值模拟计算[J].上海交通大学学报. 2006, 40(6):958–967
[12] Dharani LR, Ji FS. Dynamic analysis of normal impact of occupant head on laminatedglass[J]. SAE-paper. 1998, No. 980862
[13] Azari Z Ismail J, Zairi F, Nait-Abdelaziz M. Computational modelling of staticindentation-induced damage in glass[J]. Computational Materials Science. 2008,42(3):407–415
[14] Flocker FW, Dharani LR. Modelling fracture in laminated architectural glass subject tolow velocity impact[J]. Journal of Materials Science. 1997, 32(10):2587–2594
[15] Seshadri M, Bennison SJ, Jagota A et al. Mechanical response of cracked laminatedplates[J]. Acta Materialia. 2002, 50(18):4477–4490
[16] Pyttel T, Liebertz H, Cai J. Failure criterion for laminated glass under impact loadingand its application in finite element simulation[J]. International Journal of Impact Engi-neering. 2011, 38(4):252–263
[17] Tokunaga H, Kaizu K, Ikeda K et al. Impact fracture analysis of thermally tempered glassby the extended distinct element method[J]. Journal of Solid Mechanics and MaterialsEngineering. 2007, 1(8):986–997
[18] Oda J, Zang MY, et al. Simulation of dynamic fracture behavior of laminated glass byDEM[J]. Trans, 8th Calculation Dynamics, Symp, JSME. 1995:429–430
[19] Oda J, Zang MY. Analysis of impact fracture behavior of laminated glass of bi-layer typeusing discrete element method[J]. Key Engineering Materials. 1998, 145-149:349–354
[20] Zang MY, Oda J. Investigation of impact fracture behavior of automobile glass by dis-crete element method[J]. Computational Methods. 2006, PTS 1 and 2:387–392
[21] Zang MY, Lei Z, Wang SF. Investigation of impact fracture behavior of automobilelaminated glass by 3D discrete element method[J]. Computational Mechanics. 2007,41(1):73–83
[22]雷周.三维离散元法的研究及其在汽车玻璃冲击破坏问题中的应用[D].长沙:湖南大学. 2007
[23]徐泳,孙其诚,张凌等.颗粒离散元法研究进展[J].力学进展. 2003, 33(2):251–260
[24]刘凯欣,高凌天.离散元法研究的评述[J].力学进展. 2003, 23(4):483–490
[25] Munjiza A, Owen DRJ, Bicanic N. A combined finite-discrete element method in tran-sient dynamics of fracturing solids[J]. Engineering Computations. 1995, 12(2):145–174
[26] Owen DRJ, Feng YT, Cottrell MG et al. Computational issues in the simulation of blastand impact problems: an industrial perspective[J]. In: Ibrahimbegovic′A, Kozar I (eds)NATO Security through Science Series: extreme man-made and natural hazards in dy-namics of structures. 2007:3–35
[27] Karami A, Stead D. Asperity degradation and damage in the direct shear test: a hybridFEM/DEM approach[J]. Rock Mechanics and Rock Engineering. 2008, 41(2):229–266
[28] Lewis RW, Gethin DT, Yang XS et al. A combined finite-discrete element method for sim-ulating pharmaceutical powder tableting[J]. International Journal for Numerical Methodsin Engineering. 2005, 62(7):853–869
[29] Gethin DT, Yang XS, Lewis RW. A two dimensional combined discrete and finite el-ement scheme for simulating the ?ow and compaction of systems comprising irregu-lar particulates[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43):5552–5565
[30] G Frenning. An efficient finite/discrete element procedure for simulating compression of3D particle assemblies[J]. Computer Methods in Applied Mechanics and Engineering.2008, 197(49-50):4266–4272
[31] Choi JL, Gethin DT. A discrete finite element modelling and measurements for powdercompaction[J]. Modelling and Simulation in Materials Science and Engineering. 2009,17:035005
[32] Komodromos PI, Williams JR. Dynamic simulation of multiple deformable bodies usingcombined discrete and finite element methods[J]. Engineering Computations. 2004,21(2/3/4):431–448
[33] PI, Komodromos. A simplified updated Lagrangian approach for combining discrete andfinite element methods[J]. Computational Mechanics. 2005, 35(4):305–313
[34] Mahabadi OK, Grasselli G, Munjiza A. Y-GUI: A graphical user interface and pre-processor for the combined finite-discrete element code, Y2D, incorporating materialheterogeneity[J]. Computers & Geosciences. 2010, 36(2):241–252
[35] A. Munjiza, KRF Andrews. NBS contact detection algorithm for bodies of similarsize[J]. International Journal for Numerical Methods in Engineering. 1998, 43(1):131–149
[36] Munjiza A, Andrews KRF, White JK. Combined single and smeared crack model incombined finite-discrete element analysis. International Journal for Numerical Methodsin Engineering. 1999, 44(1):41–57
[37] Munjiza A, Latham JP, Andrews KRF. Detonation gas model for combined finite-discreteelement simulation of fracture and fragmentation[J]. International Journal for NumericalMethods in Engineering. 2000, 49(12):1495–1520
[38] Latham JP, Lu Y, Munjiza A. A random method for simulating loose packs of angularparticles using tetrahedra[J]. Geotechnique. 2001, 51(10):871–880
[39] Latham JP, Munjiza A, Lu Y. On the prediction of void porosity and packing of rockparticulates[J]. Powder Technology. 2002, 125(1):10–27
[40] Munjiza A, John NWM. Mesh size sensitivity of the combined FEM/DEM fracture andfragmentation algorithms[J]. Engineering Fracture Mechanics. 2002, 69(2):281–295
[41] Bangash T, Munjiza A. Experimental validation of a computationally efficient beam el-ement for combined finite–discrete element modelling of structures in distress[J]. Com-putational Mechanics. 2003, 30(5):366–373
[42] Munjiza A, Bangash T, John NWM. The combined finite-discrete element method forstructural failure and collapse[J]. Engineering Fracture Mechanics. 2004, 71(4-6):469–483
[43] Munjiza A, Latham JP. Comparison of experimental and FEM/DEM results for gravita-tional deposition of identical cubes[J]. Engineering Computations. 2004, 21(2/3/4):249–264
[44] Rougier E, Munjiza A, John NWM. Numerical comparison of some explicit time in-tegration schemes used in DEM, FEM/DEM and molecular dynamics[J]. InternationalJournal for Numerical Methods in Engineering. 2004, 61(6):856–879
[45] Latham JP, Munjiza A. The modelling of particle systems with real shapes[J]. Philo-sophical Transactions of the Royal Society of London Series A: Mathematical, Physicaland Engineering Sciences. 2004, 362(1822):1953
[46] Munjiza A, Latham JP. Some computational and algorithmic developments in com-putational mechanics of discontinua[J]. Philosophical Transactions of the Royal So-ciety of London Series A: Mathematical, Physical and Engineering Sciences. 2004,362(1822):1817
[47] Munjiza A, Rougier E, John NWM. MR linear contact detection algorithm[J]. Interna-tional Journal for Numerical Methods in Engineering. 2006, 66(1):46–71
[48] A, Munjiza. Contact mechanics for analysis of fracturing and fragmenting solids inthe combined finite-discrete element method[J]. Analysis and Simulation of ContactProblems. 2006, 27/2006:49–61
[49] Latham JP, Munjiza A, Garcia X et al. Three-dimensional particle shape acquisition anduse of shape library for DEM and FEM/DEM simulation[J]. Minerals Engineering. 2008,21(11):797–805
[50] Latham JP, Munjiza A, Mindel J et al. Modelling of massive particulates for breakwaterengineering using coupled FEMDEM and CFD[J]. Particuology. 2008, 6(6):572–583
[51] Xiang JS, Munjiza A, Latham JP et al. On the validation of DEM and FEM/DEM modelsin 2D and 3D[J]. Engineering Computations. 2009, 26(6):673–687
[52] Xiang JS, Munjiza A, Latham JP. Finite strain, finite rotation quadratic tetrahedral ele-ment for the combined finite–discrete element method[J]. International Journal for Nu-merical Methods in Engineering. 2009, 79(8):946–978
[53] Mohammadi S, Owen DRJ, Peric D. A combined finite/discrete element algorithm fordelamination analysis of composites[J]. Finite Elements in Analysis and Design. 1998,28(4):321–336
[54] Owen DRJ, Jr M Vaz. Computational techniques applied to high-speed machining underadiabatic strain localization conditions[J]. Computer Methods in Applied Mechanics andEngineering. 1999, 171(3-4):445–461
[55] Han K, Peric D, Crook AJL et al. A combined finite/discrete element simulation of shotpeening processes–Part I: studies on 2D interaction laws[J]. Engineering Computations.2000, 17(5):593–620
[56] Owen DRJ, Feng YT. Parallelised finite/discrete element simulation of multi-fracturingsolids and discrete systems[J]. Engineering Computations. 2001, 18(3/4):557–576
[57] D. Owen, Y. Feng, J. Yu, D. Peric′. Finite/discrete element analysis of multi-fractureand multi-contact phenomena[J]. Vector and Parallel Processing―VECPAR 2000.2001:483–505
[58] Han K, Peric D, Owen DRJ et al. A combined finite/discrete element simulation ofshot peening process– Part II: 3D interaction laws[J]. Engineering Computations. 2002,17(6-7):683–702
[59] Owen DRJ, Feng YT, Cottrell MG et al. Discrete/Finite Element Modelling of Indus-trial Applications with Multi-fracturing and Particulate Phenomena[C]. 3rd Int Conf onDiscrete Element Methods Santa Fe, New Mexico, USA, September 23-25, 2002
[60] Han K, Owen DRJ, Peric D. Combined finite/discrete element and explicit/implicit sim-ulations of peen forming process[J]. Engineering Computations. 2002, 19(1):92–118
[61] Wang F, Feng YT, Owen DRJ. Interprocessor communication schemes in parallelfinite-discrete element analysis on PC clusters[J]. Engineering Computations. 2003,20(8):1065–1084
[62] Owen DRJ, Feng YT, de Souza Neto EA et al. The modelling of multi-fracturing solidsand particulate media[J]. International Journal for Numerical Methods in Engineering.2004, 60(1):317–339
[63] Wang FJ, Feng YT, Owen DRJ. PARALLELISATION for finite-discrete element anal-ysis in a distributed-memory environment[J]. International Journal of ComputationalEngineering Sciences. 2004, 5(1):1–23
[64] A, Munjiza. The combined finite-discrete element method[M]. England: John Wiley &Sons Ltd. 2004
[65] On?ate E, Rojek J. Combination of discrete element and finite element methods for dy-namic analysis of geomechanics problems[J]. Computer Methods in Applied Mechanicsand Engineering. 2004, 193(27-29):3087–3128
[66] Rojek J, Zarate F, de Saracibar CA et al. Discrete element modelling and simulation ofsand mould manufacture for the lost foam process[J]. International Journal for NumericalMethods in Engineering. 2005, 62(11):1421–1441
[67] Nakashima H, Oida A. Algorithm and implementation of soil-tire contact analysis codebased on dynamic FE-DE method[J]. Journal of Terramechanics. 2004, 41(2-3):127–137
[68] Bierawski LG, Maeno S. DEM-FEM model of highly saturated soil motion due toseepage force[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering. 2006,132(5):401–409
[69]胥建龙,唐志平.离散元与有限元结合的多尺度方法及其应用[J].计算物理. 2003,20(006):477–482
[70]唐志平,胥建龙.离散元与壳体有限元结合的多尺度方法及其应用[J].计算力学学报. 2007, 24(005):591–596
[71]傅华,刘仓理,王文强等.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(004):379–385
[72]王勖成.有限单元法[M].北京:清华大学出版社. 2003
[73]张雄,王天舒.计算动力学[M].北京:清华大学出版社. 2007
[74]张汝清.固体力学变分原理及其应用[M].重庆:重庆大学出版社. 1991
[75] Zienkiewicz OC, Taylor RL. The finite element method: the basis, Volume 1[M]. 5thedition. Oxford: Butterworth-Heinemann, 2000
[76] Liu GR, Quek SS. The finite element method: a practical course[M]. Burlington MA:Elsevier Science Ltd., 2003
[77] Bonet J, Wood RD. Nonlinear continuum mechanics for finite element analysis[M].Cambridge University Press, 1997
[78]赵隆茂,杨桂通.动力响应数值分析中的hourglass现象[J].计算力学学报. 2003,20(1):53–58
[79]程俊霞.有限元程序网格沙漏变形的分析与控制[J].计算物理. 2007, 24(4):402–406
[80] Flanagan DP, Belytschko T. A uniform strain hexahedron and quadrilateral with orthog-onal hourglass control[J]. International Journal for Numerical Methods in Engineering.1981, 17(5):679–706
[81] JO, Hallquist. LS-DYNA theoretical manual[M]. Livermore Software Technology Cor-poration, 1998
[82] PA, Cundall. A computer model for simulating progressive large scale movements inblocky systems[J]. Symposium ISRM, Proc. 1971, 2:129–136
[83]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版杜, 1991
[84] Kawai T, Toi Y. A new element in discrete analysis of plane strain problems[J]. SeisanKenkyu. 1977, 29(4):204–207
[85]森川博司,冈野昌明,小林伸浩.应用离散元法的钢筋混凝土破坏分析[C].日本建筑学会大会学术讲演论文集. 1985
[86]目黑公郎,博野元彦.用粒状体模拟对混凝土结构的破坏分析[R].东京大学地质研究所汇报,第63号,第4册:409–468
[87]上田真念,毛井祟博,川井忠彦.应用离散元法解决钢筋混凝土结构的非线性问题[C].日本混凝土协会文集. 1986, 12:179–186
[88]白井孝治,依藤千浩,大沼博志.飞来物冲击条件下混凝土局部破坏分析中的离散元的适用性[C].构造工学数值专题讨论会论文集. 1991, 1:409–411
[89] Sawamoto Y, Tsubota H, et al. Analytical studies on local damage to reinforced concretestructures under impact loading by discrete element method[J]. Nuclear Engineering andDesign. 1998, 179:157–177
[90] Griffiths DV, Mustoe GGW. Modelling of elastic continua using a grillage of structuralelements based on discrete element concepts[J]. International Journal for NumericalMethods in Engineering. 2001, 50:1759–1775
[91] Liu K, Zheng W, et al. A numerical analysis for stress wave propagation of anisotropicsolids by discrete element method[J]. Hokamoto K eds Chiba A, Tanimura S, (Editor)Proceedings of the 4th International Symposium on Impact Engineering, Kumamoto,Japan: UK: Elsevier Science Ltd, 2001. 589–594
[92] Liu K, Gao L. The application of discrete element method in solving three dimensionalimpact dynamics problems[J]. Acta Mechniaca Solida. 2003, 16(3):256–261
[93] Liu K, Gao L, Tanimura S. Application of discrete element method in impact prob-lems[J]. JSME International Journal Series A. 2004, 47(2):138–145
[94] Liu K, Liu W. Application of discrete element method for continuum dynamic prob-lems[J]. Archive of Applied Mechanics. 2006, 76(3):229–243
[95] Cheng M, Liu W, Liu K. New discrete element models for elastoplastic problems[J].Acta Mechanica Sinica. 2009, 25(5):629–637
[96] Kazerani T, Zhao GF, Zhao J. Dynamic fracturing simulation of brittle material using thedistinct lattice spring method with a full rate-dependent cohesive law[J]. Rock Mechanicsand Rock Engineering. 2010:1–10
[97] Balevi?cius R, D?ziugys A, et al. Discrete element method and its application to the analy-sis of penetration into granular media[J]. Journal of Civil Engineering and Management.2004, 10(1):3–14
[98] Iwai T, Hong C.-W, Greil P. Fast Particle Pair Detection Algorithms for Particle Simula-tions[J]. International Journal of Modern Physics C. 1999, 10(5):823–837
[99] Feng YT, Owen DRJ. An augmented spatial digital tree algorithm for contact detectionin computational mechanics[J]. International Journal for Numerical Methods in Engi-neering. 2002, 55(2):159–176
[100] Williams JR, Perkins E, Cook B. A contact algorithm for partitioning N arbitrary sizedobjects[J]. Engineering Computations. 2004, 21(2-4):235–248
[101] Mio H, Shimosaka A, et al. Optimum cell size for contact detection in the algorithmof the discrete element method[J]. Journal of Chemical Engineering of Japan. 2005,38(12):969–975
[102] Mio H, Shimosaka Y, et al. Optimum cell condition for contact detection having a largeparticle size ratio in the discrete element method[J]. Journal of Chemical Engineering ofJapan. 2006, 39(4):409–416
[103] Li CF, Feng YT, Owen DRJ. SMB: Collision detection based on temporal coherence[J].Computer Methods in Applied Mechanics and Engineering. 2006, 195(19-22):2252–2269
[104] K. Han, YT Feng, DRJ Owen. Performance comparisons of tree-based and cell-basedcontact detection algorithms[J]. Engineering Computations. 2007, 24(2):165–181
[105] Akin, J.E.. Object-oriented programming via Fortran 90/95[M]. Cambridge UniversityPress, 2003
[106] Cary, S.G. Shasharina, J.C. Cummings, J.V.W. Reynders, P.J. Hinker, J.R.. Comparisonof C++ and Fortran 90 for object-oriented scientific programming[J]. Computer PhysicsCommunications. 1997, 105(1):20–36
[107] Lemmon, J.L. Schafer, D.R.. Developing statistical software in Fortran 95[M]. Springer-Verlag New York Inc, 2005
[108]彭国伦. Fortran 95程序设计[M].中国电力出版社, 2002
[109] ZP, Tang. Three-dimensional DEM theory and its application to impact mechanics[J].Science in China (Ser E). 2001, 44(6):561–571
[110] A. Munjiza, KRF Andrews. Penalty function method for combined finite–discrete ele-ment systems comprising large number of separate bodies[J]. International Journal forNumerical Methods in Engineering. 2000, 49(11):1377–1396
[111]臧孟炎,雷周,尾田十八.汽车玻璃的静力学特性和冲击破坏现象[J].机械工程学报. 2009, 45(002):268–272
[112] Xu J, Li Y, Chen X et al. Characteristics of windshield cracking upon low-speed impact:Numerical simulation based on the extended finite element method[J]. ComputationalMaterials Science. 2010, 48(3):582–588
[113] Bennett WW, Hess KM. Criminal investigation[M]. Eighth edition. Thomson Learning,Inc., 2007
[114] Bertino AJ, Bertino PN. Forensic science: fundamentals and investigations[M]. South-Western Pub, 2008
[2] Xu J, Li YB. Crack analysis in PVB laminated windshield impacted by pedestrian headin traffic accident[J]. International Journal of Crashworthiness. 2009, 14(1):63–71
[3]刘志海.夹层玻璃的发展现状及趋势[J].中国建材. 2003, 9:64–66
[4]许骏,李一兵.人车碰撞事故再现技术综述[J].汽车工程. 2009, 31(11):1029–1033
[5] AL, Browne. 2-Ply windshields: laboratory impactor tests of the polyvinyl bu-tyral/polyester construction[J]. SAE-Paper. 1995, No. 950047
[6] Brendler S, Haufe A, Ummenhofer T. A detailed numerical investigation of insulatedglass subjected to the standard pendulum test[J]. Proceedings of the third LS-DYNAForum, Bamberg, Germany. 2004, F-I-57/64
[7] Du Bois PA, Kolling S, Fassnacht W. Modelling of safety glass for crash simulation[J].Computational Materials Science. 2003, 28(3-4):675–683
[8] Ji FS, Dharani LR, Behr RA. Damage probability in laminated glass subjected to lowvelocity small missile impacts[J]. Journal of Materials Science. 1998, 33(19):4775–4782
[9] Timmel M, Kolling S, et al. A finite element model for impact simulation with laminatedglass[J]. International Journal of Impact Engineering. 2007, 34(8):1465–1478
[10]孙宏图,刘学术,等.汽车碰撞变形计算机模拟研究[J].大连理工大学学报. 42(6)
[11]张晓云,金先龙,等.面向事故分析的车身关键参数数值模拟计算[J].上海交通大学学报. 2006, 40(6):958–967
[12] Dharani LR, Ji FS. Dynamic analysis of normal impact of occupant head on laminatedglass[J]. SAE-paper. 1998, No. 980862
[13] Azari Z Ismail J, Zairi F, Nait-Abdelaziz M. Computational modelling of staticindentation-induced damage in glass[J]. Computational Materials Science. 2008,42(3):407–415
[14] Flocker FW, Dharani LR. Modelling fracture in laminated architectural glass subject tolow velocity impact[J]. Journal of Materials Science. 1997, 32(10):2587–2594
[15] Seshadri M, Bennison SJ, Jagota A et al. Mechanical response of cracked laminatedplates[J]. Acta Materialia. 2002, 50(18):4477–4490
[16] Pyttel T, Liebertz H, Cai J. Failure criterion for laminated glass under impact loadingand its application in finite element simulation[J]. International Journal of Impact Engi-neering. 2011, 38(4):252–263
[17] Tokunaga H, Kaizu K, Ikeda K et al. Impact fracture analysis of thermally tempered glassby the extended distinct element method[J]. Journal of Solid Mechanics and MaterialsEngineering. 2007, 1(8):986–997
[18] Oda J, Zang MY, et al. Simulation of dynamic fracture behavior of laminated glass byDEM[J]. Trans, 8th Calculation Dynamics, Symp, JSME. 1995:429–430
[19] Oda J, Zang MY. Analysis of impact fracture behavior of laminated glass of bi-layer typeusing discrete element method[J]. Key Engineering Materials. 1998, 145-149:349–354
[20] Zang MY, Oda J. Investigation of impact fracture behavior of automobile glass by dis-crete element method[J]. Computational Methods. 2006, PTS 1 and 2:387–392
[21] Zang MY, Lei Z, Wang SF. Investigation of impact fracture behavior of automobilelaminated glass by 3D discrete element method[J]. Computational Mechanics. 2007,41(1):73–83
[22]雷周.三维离散元法的研究及其在汽车玻璃冲击破坏问题中的应用[D].长沙:湖南大学. 2007
[23]徐泳,孙其诚,张凌等.颗粒离散元法研究进展[J].力学进展. 2003, 33(2):251–260
[24]刘凯欣,高凌天.离散元法研究的评述[J].力学进展. 2003, 23(4):483–490
[25] Munjiza A, Owen DRJ, Bicanic N. A combined finite-discrete element method in tran-sient dynamics of fracturing solids[J]. Engineering Computations. 1995, 12(2):145–174
[26] Owen DRJ, Feng YT, Cottrell MG et al. Computational issues in the simulation of blastand impact problems: an industrial perspective[J]. In: Ibrahimbegovic′A, Kozar I (eds)NATO Security through Science Series: extreme man-made and natural hazards in dy-namics of structures. 2007:3–35
[27] Karami A, Stead D. Asperity degradation and damage in the direct shear test: a hybridFEM/DEM approach[J]. Rock Mechanics and Rock Engineering. 2008, 41(2):229–266
[28] Lewis RW, Gethin DT, Yang XS et al. A combined finite-discrete element method for sim-ulating pharmaceutical powder tableting[J]. International Journal for Numerical Methodsin Engineering. 2005, 62(7):853–869
[29] Gethin DT, Yang XS, Lewis RW. A two dimensional combined discrete and finite el-ement scheme for simulating the ?ow and compaction of systems comprising irregu-lar particulates[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43):5552–5565
[30] G Frenning. An efficient finite/discrete element procedure for simulating compression of3D particle assemblies[J]. Computer Methods in Applied Mechanics and Engineering.2008, 197(49-50):4266–4272
[31] Choi JL, Gethin DT. A discrete finite element modelling and measurements for powdercompaction[J]. Modelling and Simulation in Materials Science and Engineering. 2009,17:035005
[32] Komodromos PI, Williams JR. Dynamic simulation of multiple deformable bodies usingcombined discrete and finite element methods[J]. Engineering Computations. 2004,21(2/3/4):431–448
[33] PI, Komodromos. A simplified updated Lagrangian approach for combining discrete andfinite element methods[J]. Computational Mechanics. 2005, 35(4):305–313
[34] Mahabadi OK, Grasselli G, Munjiza A. Y-GUI: A graphical user interface and pre-processor for the combined finite-discrete element code, Y2D, incorporating materialheterogeneity[J]. Computers & Geosciences. 2010, 36(2):241–252
[35] A. Munjiza, KRF Andrews. NBS contact detection algorithm for bodies of similarsize[J]. International Journal for Numerical Methods in Engineering. 1998, 43(1):131–149
[36] Munjiza A, Andrews KRF, White JK. Combined single and smeared crack model incombined finite-discrete element analysis. International Journal for Numerical Methodsin Engineering. 1999, 44(1):41–57
[37] Munjiza A, Latham JP, Andrews KRF. Detonation gas model for combined finite-discreteelement simulation of fracture and fragmentation[J]. International Journal for NumericalMethods in Engineering. 2000, 49(12):1495–1520
[38] Latham JP, Lu Y, Munjiza A. A random method for simulating loose packs of angularparticles using tetrahedra[J]. Geotechnique. 2001, 51(10):871–880
[39] Latham JP, Munjiza A, Lu Y. On the prediction of void porosity and packing of rockparticulates[J]. Powder Technology. 2002, 125(1):10–27
[40] Munjiza A, John NWM. Mesh size sensitivity of the combined FEM/DEM fracture andfragmentation algorithms[J]. Engineering Fracture Mechanics. 2002, 69(2):281–295
[41] Bangash T, Munjiza A. Experimental validation of a computationally efficient beam el-ement for combined finite–discrete element modelling of structures in distress[J]. Com-putational Mechanics. 2003, 30(5):366–373
[42] Munjiza A, Bangash T, John NWM. The combined finite-discrete element method forstructural failure and collapse[J]. Engineering Fracture Mechanics. 2004, 71(4-6):469–483
[43] Munjiza A, Latham JP. Comparison of experimental and FEM/DEM results for gravita-tional deposition of identical cubes[J]. Engineering Computations. 2004, 21(2/3/4):249–264
[44] Rougier E, Munjiza A, John NWM. Numerical comparison of some explicit time in-tegration schemes used in DEM, FEM/DEM and molecular dynamics[J]. InternationalJournal for Numerical Methods in Engineering. 2004, 61(6):856–879
[45] Latham JP, Munjiza A. The modelling of particle systems with real shapes[J]. Philo-sophical Transactions of the Royal Society of London Series A: Mathematical, Physicaland Engineering Sciences. 2004, 362(1822):1953
[46] Munjiza A, Latham JP. Some computational and algorithmic developments in com-putational mechanics of discontinua[J]. Philosophical Transactions of the Royal So-ciety of London Series A: Mathematical, Physical and Engineering Sciences. 2004,362(1822):1817
[47] Munjiza A, Rougier E, John NWM. MR linear contact detection algorithm[J]. Interna-tional Journal for Numerical Methods in Engineering. 2006, 66(1):46–71
[48] A, Munjiza. Contact mechanics for analysis of fracturing and fragmenting solids inthe combined finite-discrete element method[J]. Analysis and Simulation of ContactProblems. 2006, 27/2006:49–61
[49] Latham JP, Munjiza A, Garcia X et al. Three-dimensional particle shape acquisition anduse of shape library for DEM and FEM/DEM simulation[J]. Minerals Engineering. 2008,21(11):797–805
[50] Latham JP, Munjiza A, Mindel J et al. Modelling of massive particulates for breakwaterengineering using coupled FEMDEM and CFD[J]. Particuology. 2008, 6(6):572–583
[51] Xiang JS, Munjiza A, Latham JP et al. On the validation of DEM and FEM/DEM modelsin 2D and 3D[J]. Engineering Computations. 2009, 26(6):673–687
[52] Xiang JS, Munjiza A, Latham JP. Finite strain, finite rotation quadratic tetrahedral ele-ment for the combined finite–discrete element method[J]. International Journal for Nu-merical Methods in Engineering. 2009, 79(8):946–978
[53] Mohammadi S, Owen DRJ, Peric D. A combined finite/discrete element algorithm fordelamination analysis of composites[J]. Finite Elements in Analysis and Design. 1998,28(4):321–336
[54] Owen DRJ, Jr M Vaz. Computational techniques applied to high-speed machining underadiabatic strain localization conditions[J]. Computer Methods in Applied Mechanics andEngineering. 1999, 171(3-4):445–461
[55] Han K, Peric D, Crook AJL et al. A combined finite/discrete element simulation of shotpeening processes–Part I: studies on 2D interaction laws[J]. Engineering Computations.2000, 17(5):593–620
[56] Owen DRJ, Feng YT. Parallelised finite/discrete element simulation of multi-fracturingsolids and discrete systems[J]. Engineering Computations. 2001, 18(3/4):557–576
[57] D. Owen, Y. Feng, J. Yu, D. Peric′. Finite/discrete element analysis of multi-fractureand multi-contact phenomena[J]. Vector and Parallel Processing―VECPAR 2000.2001:483–505
[58] Han K, Peric D, Owen DRJ et al. A combined finite/discrete element simulation ofshot peening process– Part II: 3D interaction laws[J]. Engineering Computations. 2002,17(6-7):683–702
[59] Owen DRJ, Feng YT, Cottrell MG et al. Discrete/Finite Element Modelling of Indus-trial Applications with Multi-fracturing and Particulate Phenomena[C]. 3rd Int Conf onDiscrete Element Methods Santa Fe, New Mexico, USA, September 23-25, 2002
[60] Han K, Owen DRJ, Peric D. Combined finite/discrete element and explicit/implicit sim-ulations of peen forming process[J]. Engineering Computations. 2002, 19(1):92–118
[61] Wang F, Feng YT, Owen DRJ. Interprocessor communication schemes in parallelfinite-discrete element analysis on PC clusters[J]. Engineering Computations. 2003,20(8):1065–1084
[62] Owen DRJ, Feng YT, de Souza Neto EA et al. The modelling of multi-fracturing solidsand particulate media[J]. International Journal for Numerical Methods in Engineering.2004, 60(1):317–339
[63] Wang FJ, Feng YT, Owen DRJ. PARALLELISATION for finite-discrete element anal-ysis in a distributed-memory environment[J]. International Journal of ComputationalEngineering Sciences. 2004, 5(1):1–23
[64] A, Munjiza. The combined finite-discrete element method[M]. England: John Wiley &Sons Ltd. 2004
[65] On?ate E, Rojek J. Combination of discrete element and finite element methods for dy-namic analysis of geomechanics problems[J]. Computer Methods in Applied Mechanicsand Engineering. 2004, 193(27-29):3087–3128
[66] Rojek J, Zarate F, de Saracibar CA et al. Discrete element modelling and simulation ofsand mould manufacture for the lost foam process[J]. International Journal for NumericalMethods in Engineering. 2005, 62(11):1421–1441
[67] Nakashima H, Oida A. Algorithm and implementation of soil-tire contact analysis codebased on dynamic FE-DE method[J]. Journal of Terramechanics. 2004, 41(2-3):127–137
[68] Bierawski LG, Maeno S. DEM-FEM model of highly saturated soil motion due toseepage force[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering. 2006,132(5):401–409
[69]胥建龙,唐志平.离散元与有限元结合的多尺度方法及其应用[J].计算物理. 2003,20(006):477–482
[70]唐志平,胥建龙.离散元与壳体有限元结合的多尺度方法及其应用[J].计算力学学报. 2007, 24(005):591–596
[71]傅华,刘仓理,王文强等.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(004):379–385
[72]王勖成.有限单元法[M].北京:清华大学出版社. 2003
[73]张雄,王天舒.计算动力学[M].北京:清华大学出版社. 2007
[74]张汝清.固体力学变分原理及其应用[M].重庆:重庆大学出版社. 1991
[75] Zienkiewicz OC, Taylor RL. The finite element method: the basis, Volume 1[M]. 5thedition. Oxford: Butterworth-Heinemann, 2000
[76] Liu GR, Quek SS. The finite element method: a practical course[M]. Burlington MA:Elsevier Science Ltd., 2003
[77] Bonet J, Wood RD. Nonlinear continuum mechanics for finite element analysis[M].Cambridge University Press, 1997
[78]赵隆茂,杨桂通.动力响应数值分析中的hourglass现象[J].计算力学学报. 2003,20(1):53–58
[79]程俊霞.有限元程序网格沙漏变形的分析与控制[J].计算物理. 2007, 24(4):402–406
[80] Flanagan DP, Belytschko T. A uniform strain hexahedron and quadrilateral with orthog-onal hourglass control[J]. International Journal for Numerical Methods in Engineering.1981, 17(5):679–706
[81] JO, Hallquist. LS-DYNA theoretical manual[M]. Livermore Software Technology Cor-poration, 1998
[82] PA, Cundall. A computer model for simulating progressive large scale movements inblocky systems[J]. Symposium ISRM, Proc. 1971, 2:129–136
[83]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版杜, 1991
[84] Kawai T, Toi Y. A new element in discrete analysis of plane strain problems[J]. SeisanKenkyu. 1977, 29(4):204–207
[85]森川博司,冈野昌明,小林伸浩.应用离散元法的钢筋混凝土破坏分析[C].日本建筑学会大会学术讲演论文集. 1985
[86]目黑公郎,博野元彦.用粒状体模拟对混凝土结构的破坏分析[R].东京大学地质研究所汇报,第63号,第4册:409–468
[87]上田真念,毛井祟博,川井忠彦.应用离散元法解决钢筋混凝土结构的非线性问题[C].日本混凝土协会文集. 1986, 12:179–186
[88]白井孝治,依藤千浩,大沼博志.飞来物冲击条件下混凝土局部破坏分析中的离散元的适用性[C].构造工学数值专题讨论会论文集. 1991, 1:409–411
[89] Sawamoto Y, Tsubota H, et al. Analytical studies on local damage to reinforced concretestructures under impact loading by discrete element method[J]. Nuclear Engineering andDesign. 1998, 179:157–177
[90] Griffiths DV, Mustoe GGW. Modelling of elastic continua using a grillage of structuralelements based on discrete element concepts[J]. International Journal for NumericalMethods in Engineering. 2001, 50:1759–1775
[91] Liu K, Zheng W, et al. A numerical analysis for stress wave propagation of anisotropicsolids by discrete element method[J]. Hokamoto K eds Chiba A, Tanimura S, (Editor)Proceedings of the 4th International Symposium on Impact Engineering, Kumamoto,Japan: UK: Elsevier Science Ltd, 2001. 589–594
[92] Liu K, Gao L. The application of discrete element method in solving three dimensionalimpact dynamics problems[J]. Acta Mechniaca Solida. 2003, 16(3):256–261
[93] Liu K, Gao L, Tanimura S. Application of discrete element method in impact prob-lems[J]. JSME International Journal Series A. 2004, 47(2):138–145
[94] Liu K, Liu W. Application of discrete element method for continuum dynamic prob-lems[J]. Archive of Applied Mechanics. 2006, 76(3):229–243
[95] Cheng M, Liu W, Liu K. New discrete element models for elastoplastic problems[J].Acta Mechanica Sinica. 2009, 25(5):629–637
[96] Kazerani T, Zhao GF, Zhao J. Dynamic fracturing simulation of brittle material using thedistinct lattice spring method with a full rate-dependent cohesive law[J]. Rock Mechanicsand Rock Engineering. 2010:1–10
[97] Balevi?cius R, D?ziugys A, et al. Discrete element method and its application to the analy-sis of penetration into granular media[J]. Journal of Civil Engineering and Management.2004, 10(1):3–14
[98] Iwai T, Hong C.-W, Greil P. Fast Particle Pair Detection Algorithms for Particle Simula-tions[J]. International Journal of Modern Physics C. 1999, 10(5):823–837
[99] Feng YT, Owen DRJ. An augmented spatial digital tree algorithm for contact detectionin computational mechanics[J]. International Journal for Numerical Methods in Engi-neering. 2002, 55(2):159–176
[100] Williams JR, Perkins E, Cook B. A contact algorithm for partitioning N arbitrary sizedobjects[J]. Engineering Computations. 2004, 21(2-4):235–248
[101] Mio H, Shimosaka A, et al. Optimum cell size for contact detection in the algorithmof the discrete element method[J]. Journal of Chemical Engineering of Japan. 2005,38(12):969–975
[102] Mio H, Shimosaka Y, et al. Optimum cell condition for contact detection having a largeparticle size ratio in the discrete element method[J]. Journal of Chemical Engineering ofJapan. 2006, 39(4):409–416
[103] Li CF, Feng YT, Owen DRJ. SMB: Collision detection based on temporal coherence[J].Computer Methods in Applied Mechanics and Engineering. 2006, 195(19-22):2252–2269
[104] K. Han, YT Feng, DRJ Owen. Performance comparisons of tree-based and cell-basedcontact detection algorithms[J]. Engineering Computations. 2007, 24(2):165–181
[105] Akin, J.E.. Object-oriented programming via Fortran 90/95[M]. Cambridge UniversityPress, 2003
[106] Cary, S.G. Shasharina, J.C. Cummings, J.V.W. Reynders, P.J. Hinker, J.R.. Comparisonof C++ and Fortran 90 for object-oriented scientific programming[J]. Computer PhysicsCommunications. 1997, 105(1):20–36
[107] Lemmon, J.L. Schafer, D.R.. Developing statistical software in Fortran 95[M]. Springer-Verlag New York Inc, 2005
[108]彭国伦. Fortran 95程序设计[M].中国电力出版社, 2002
[109] ZP, Tang. Three-dimensional DEM theory and its application to impact mechanics[J].Science in China (Ser E). 2001, 44(6):561–571
[110] A. Munjiza, KRF Andrews. Penalty function method for combined finite–discrete ele-ment systems comprising large number of separate bodies[J]. International Journal forNumerical Methods in Engineering. 2000, 49(11):1377–1396
[111]臧孟炎,雷周,尾田十八.汽车玻璃的静力学特性和冲击破坏现象[J].机械工程学报. 2009, 45(002):268–272
[112] Xu J, Li Y, Chen X et al. Characteristics of windshield cracking upon low-speed impact:Numerical simulation based on the extended finite element method[J]. ComputationalMaterials Science. 2010, 48(3):582–588
[113] Bennett WW, Hess KM. Criminal investigation[M]. Eighth edition. Thomson Learning,Inc., 2007
[114] Bertino AJ, Bertino PN. Forensic science: fundamentals and investigations[M]. South-Western Pub, 2008