金属塑性成形过程无网格伽辽金方法及其关键技术研究
|
摘要
金属塑性成形技术在金属零件的制造过程中起着十分重要的作用。它不仅具有生产效率高、产品质量稳定、原材料消耗少的优点，而且还可以有效地改善工件的组织性能。随着计算机技术的发展和数值计算方法的日益完善，有限元方法在工程实际中得到了广泛的应用。但是，当工件变形到一定程度时，有限元网格将产生畸变现象，此时，这种以单元作为基本概念的有限元方法面临着一些难以处理的问题。无网格方法基于离散节点的近似，避免了有限元方法对于网格的依赖，在涉及到网格畸变的大变形问题分析中具有一定的优势，并且在数据准备和后处理方面也比有限元方法灵活简单。
无网格方法作为一种较为新颖的数值方法，经过十余年的发展，已经逐渐应用于金属塑性成形过程的模拟，并且取得了一定的成果。但是对于非稳态大变形金属塑性成形问题，由于成形过程的复杂性，许多关键应用技术还有待于研究。尤其当金属流动比较剧烈或变形比较复杂时由于节点分布的非均匀性增强和变形域形状更加复杂，速度场的近似精度和变形域的积分精度会有所下降，进而导致数值模拟出现错误。因此，本文针对非稳态大变形成形过程，主要研究了基于刚(粘)塑性材料假设的无网格伽辽金方法、关键处理技术及其在金属塑性成形过程分析中的应用。
基于无网格近似方案，结合伽辽金离散方法，提出了刚(粘)塑性无网格伽辽金方法。速度场采用经过变换法修正处理的最小二乘近似和再生核质点近似或者直接采用径向基函数插值进行近似。采用反正切摩擦模型描述摩擦接触边界条件。对于模具形状任意的塑性成形过程，在局部坐标系下施加摩擦力边界条件，给出了局部坐标系和整体坐标系的变换矩阵，解决了模具形状任意的二维塑性成形过程分析中的摩擦接触边界条件施加问题。在此基础上推导建立了金属塑性成形过程无网格方法分析刚度矩阵方程。进而采用直接迭代法获得初始速度场，利用Newton-Raphson迭代方法求解刚度方程。最后给出了模拟等温塑性成形问题的分析步骤。
针对非稳态金属塑性成形过程的复杂性、数学处理上的困难性和在成形过程模拟分析模型建立以及分析程序的通用化方面存在的不足，研究了刚(粘)塑性无网格伽辽金方法应用于金属塑性成形过程分析的关键处理技术。对于任意边界形状的二维金属塑性成形过程的无网格伽辽金方法分析，建立了诸如任意形状模具描述方法、迭代收敛判据、接触脱离判断等问题的处理方法，实现了非稳态任
The technology of metal forming processing plays an important role in metal part manufacturing. Its advantages are not only in its high productivity, stable quality, and low cost of raw and processed materials, but also in its characteristics of improving the microstructure performance dramatically. With the development of computer technology and computational methods, the finite element method (FEM) gained great achievement and was applied wildly in many engineering fields. Although great success in the metal forming process numerical simulation is achieved by FEM, the mesh distortion will be inevitable for the accumulation of the metal deformation. Then many difficulties will be occurred in FEM analysis for dependence of the approximation precision on the mesh. Compared with FEM, the meshless approximation based on discrete point information has advantages in the simulation of large deformation problems with mesh distortion for getting rid of the reliance on the mesh. Simultaneously, meshless method is more flexible and simpler than FEM in data prepare for the problem simulation and post-process of simulation results.
The meshless method, a newly developed numerical method, was used to the simulation of metal forming process after decade's development, and some progresses were obtained. But there are still many key techniques, which need more attention for the complexity of the metal deformation in unsteady metal forming process. Especially when the deformation is more severe or metal flow is more complex, the approximation precision of the velocity field and integration precision of deformation domain will be deteriorated for the severe un-uniformity of the metal flow and complexity of the deformation zone. Thus simulation error will be occurred. So, the study focused on the development of the rigid-visco plastic meshless Galerkin method and its key techniques for unsteady large deformation metal forming process.
The meshless Galerkin method is introduced into the analysis of the metal forming processes. Under the hypothesis of the rigid-visco plastic material, a rigid-visco plastic meshless Galerkin method is developed. The velocity field is approximated by Moving Least Square (MLS) method, Reproducing Kernel Producing Method (RKPM) and Radial Basis Function (RBF) in which MLS and RKPM is modified by the transformation method in order to employ the essential boundary condition directly. An arctangent frictional model is used to describe the frictional boundary condition. For the
无网格方法作为一种较为新颖的数值方法，经过十余年的发展，已经逐渐应用于金属塑性成形过程的模拟，并且取得了一定的成果。但是对于非稳态大变形金属塑性成形问题，由于成形过程的复杂性，许多关键应用技术还有待于研究。尤其当金属流动比较剧烈或变形比较复杂时由于节点分布的非均匀性增强和变形域形状更加复杂，速度场的近似精度和变形域的积分精度会有所下降，进而导致数值模拟出现错误。因此，本文针对非稳态大变形成形过程，主要研究了基于刚(粘)塑性材料假设的无网格伽辽金方法、关键处理技术及其在金属塑性成形过程分析中的应用。
基于无网格近似方案，结合伽辽金离散方法，提出了刚(粘)塑性无网格伽辽金方法。速度场采用经过变换法修正处理的最小二乘近似和再生核质点近似或者直接采用径向基函数插值进行近似。采用反正切摩擦模型描述摩擦接触边界条件。对于模具形状任意的塑性成形过程，在局部坐标系下施加摩擦力边界条件，给出了局部坐标系和整体坐标系的变换矩阵，解决了模具形状任意的二维塑性成形过程分析中的摩擦接触边界条件施加问题。在此基础上推导建立了金属塑性成形过程无网格方法分析刚度矩阵方程。进而采用直接迭代法获得初始速度场，利用Newton-Raphson迭代方法求解刚度方程。最后给出了模拟等温塑性成形问题的分析步骤。
针对非稳态金属塑性成形过程的复杂性、数学处理上的困难性和在成形过程模拟分析模型建立以及分析程序的通用化方面存在的不足，研究了刚(粘)塑性无网格伽辽金方法应用于金属塑性成形过程分析的关键处理技术。对于任意边界形状的二维金属塑性成形过程的无网格伽辽金方法分析，建立了诸如任意形状模具描述方法、迭代收敛判据、接触脱离判断等问题的处理方法，实现了非稳态任
The technology of metal forming processing plays an important role in metal part manufacturing. Its advantages are not only in its high productivity, stable quality, and low cost of raw and processed materials, but also in its characteristics of improving the microstructure performance dramatically. With the development of computer technology and computational methods, the finite element method (FEM) gained great achievement and was applied wildly in many engineering fields. Although great success in the metal forming process numerical simulation is achieved by FEM, the mesh distortion will be inevitable for the accumulation of the metal deformation. Then many difficulties will be occurred in FEM analysis for dependence of the approximation precision on the mesh. Compared with FEM, the meshless approximation based on discrete point information has advantages in the simulation of large deformation problems with mesh distortion for getting rid of the reliance on the mesh. Simultaneously, meshless method is more flexible and simpler than FEM in data prepare for the problem simulation and post-process of simulation results.
The meshless method, a newly developed numerical method, was used to the simulation of metal forming process after decade's development, and some progresses were obtained. But there are still many key techniques, which need more attention for the complexity of the metal deformation in unsteady metal forming process. Especially when the deformation is more severe or metal flow is more complex, the approximation precision of the velocity field and integration precision of deformation domain will be deteriorated for the severe un-uniformity of the metal flow and complexity of the deformation zone. Thus simulation error will be occurred. So, the study focused on the development of the rigid-visco plastic meshless Galerkin method and its key techniques for unsteady large deformation metal forming process.
The meshless Galerkin method is introduced into the analysis of the metal forming processes. Under the hypothesis of the rigid-visco plastic material, a rigid-visco plastic meshless Galerkin method is developed. The velocity field is approximated by Moving Least Square (MLS) method, Reproducing Kernel Producing Method (RKPM) and Radial Basis Function (RBF) in which MLS and RKPM is modified by the transformation method in order to employ the essential boundary condition directly. An arctangent frictional model is used to describe the frictional boundary condition. For the
引文
1.彭颖红.金属塑性成形仿真技术 . 上海: 上海交通大学出版社, 1999
2. P. V. Marcal, I. P. King. Elastic-plastic Analysis of Two-dimensional Stress Systems by the Finite Element Method. International Journal of Mechanical Sciences. 1967,9:143-150
3. C. H. Lee, S. Kobayashi. New Solutions to Rigid-plastic Deformation Problems Using a Matrix Method. Trans. ASME, Journal of Engineer for Industry, 1973, 95: 865-878
4. O. C. Zienkiewicz, P. N. Godbole. Flow of Plastic and Viscoplastic Solids with Special Reference to Extrusion and Forming Process. International Journal for Numerical Methods in Engineering, 1974, 8: 3-15
5. Kobayashi S, Oh S I, Altan T. Metal forming and the finite element method. Oxford University Press, New York
6. Liszka T, Orkisz J. Finite Difference Method for Arbitrary Irregular Meshes in Nonlinear Problems of Applied Mechanics. IV SMiRt, San Francisco, 1977
7. Perrone N, Kao R. A general finite difference method for arbitrary meshes. Computers and Structures, 1975,5:45-57
8. Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astronomy J, 1977,8(12): 1013-1024
9. Monaghan J J. Introduction to SPH. Computer Physics Communications, 1987,48 (1): 89-96
10. Swegle J W, Hick s D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. Journal of Computational Physics, 1995, 116(1): 123-134
11. Dyka C T, Randies P W, Ingel R P. Stress points for tension instability in SPH. International Journal for Numerical Methods in Engineering, 1997, 40 (13): 2325-2341
12. Chen J K, Beraun J E, Jih C J. Improvement for tensile instability in smoothed particle hydrodynamics. Computational Mechanics, 1999, 23: 279-287
13. Vignjevic R, Campbell J, Libersky L. A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Computer Methods in Applied Mechanics and Engineering, 2000, 184:67-85
14. Johnson, Gordon R, Stryk, et al. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 347-373
15. Chen J K, Beraun J E. Generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering, 2000, 139: 225-239
16. Randies P W, Libersky L D. Smoothed particle hydrodynamics: some recent improvements and applications Source: Computer Methods in Applied Mechanics and Engineering, 1996, 139: 375-408
17. Abadi M G, Lambas D G, Tissera P B. Cosmological Simulations with Smoothed Particle Hydrodynamics. International Astronomical Union-Symposium, 1996, 168: 577
18. Morris, Joseph P. Simulating surface tension with smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 2000, 33: 333-353
19. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10: 307-318
20. Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37 (2): 229-256
21. Chung H J, Belytschko T. Error estimate in the EFG method. Computational Mechanics, 1998, 21:91-100
22. Lu Y Y, Belytschko T, Tabbara M. Element-free Galerkin method for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Engineering, 1995, 126: 131-153
23. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1996, 39: 923-938
24. Belytschko T, Organ D, Gerlach C. Element-free Galerkin methods for dynamic fracture in concrete. Computer Methods in Applied Mechanics and Engineering, 2000, 187: 385-399
25. Belytschko T, Krysl P, Krongauz Y. Three-dimensional explicit element-free Galerkin method. International Journal for Numerical Methods in Fluids, 1997, 24 (12): 1253-1270
26. Belytschko T, Organ D, Krongauz Y. Coupled finite element element-free Galerkin method. Computational Mechanics, 1995, 17(3): 186-195
27. Liu W K, Chen Y, Jun S et al. Overview and applications of reproducing kernel particle methods. Archives of Computation Methods in Engineering, State of the Art Review, 1996 , 3 : 3-80
28. 周进雄, 李梅娥, 张红艳. 再生核质点法研究进展. 力学进展, 2002,32 (4) :535-544
29. Liu W K, Jun S, Li S, et al. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, 1995, 38 (10): 1655-1679
30. Liu W K, Jun S, Sihling D T, et al. Multiresolution reproducing kernel particle method for computational fluid dynamics. International Journal for Numerical Methods in Fluids, 1997, 24 (12): 1391～1415
31. Liu W K, Hao S, Belytschko T, et al. Multiple scale meshfree methods for damage fracture and localization. Computational Materials Science, 1999, 16:197～205
32. Xiong S W, Liu W K, Gao J, et al. Simulation of bulk metal forming processes using the reproducing kernel particle method. Computers and Structures, 2005, 83:574～587
33. Jun S, Liu W K, Belytschko T. Explicit Reproducing Kernel Particle Methods for large deformation problems. International Journal for Numerical Methods in Engineering, 1998, 41 (1): 137～166
34. Liu W K, Jun S. Multiple-scale Reproducing Kernel Particle Methods for large deformation problems. International Journal for Numerical Methods in Engineering, 1998, 41 (7): 1339～1362
35. Chen J S, Roque C, Pan C, et al. Analysis of metal forming process based on meshless method. Journal of Materials Processing Technology, 1998, 80～81 (3) : 642～646
36. Xiong S W, Liu W K, Cao J, et al. On the utilization of reproducing kernel particle method for the numerical simulation of plane strain rolling. International Journal of Machine Tools & Manufacture, 2003, 43 (1): 89～102
37. Aluru N R. Point collocation method based on reproducing kernel approximations. International Journal for Numerical Methods in Engineering, 2000, 47 (6): 1083～1121
38．史宝军，袁明武，李君．基于核重构思想的最小二乘配点型无网格方法．力学学报，2003，35(6)：697～706
39．史宝军，袁明武，孙树立，陈斌．基于核重构思想的配点型无网格方法的研究——一维问题．计算力学学报，2004，21(1)：97～103
40. E. Onate, E Perazzo, J. Miquel. A finite point method for elasticity problems. Computers and Structures. 2001, 79, 2151～2163
41. Xiaozhong Jin, Gang Li, N. R. Aluru. Positivity conditions in meshless collocation methods. Computer methods in applied mechanics engineering. 2004, 193: 1171～1202
42. Xiaozhong Jin, Gang Li, N. R. Aluru. New approximations and collocation schemes in the finite cloud method. Computers and Structures, 2005, 83: 1336～1385
43. G. R. Liu, Y. L. Wu, H. Ding. Meshfree weak-strong form method and its application to incompressible flow problems. International Journal for numerical method in fluids. 2004, 46: 1025～1047
44. Duarte C A, Oden J T. Hp clouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12 (6): 673～705
45. Duarte C A, Oden J T. An h-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering, 1996, 139:237～262
46. Oden J T, Duarte C A M. New cloud-based hp finite element method. Computer Methods in Applied Mechanics and Engineering, 1998, 153:117～126
47. Garcia O, Fancello E A, et al. Hp-clouds in Mindlin's thick plate model. International Journal for Numerical Methods in Engineering, 2000, 47 (8): 1381～1400
48．刘欣，朱德懋，陆明万，张雄．平面裂纹问题的h，p，hp型白适应无网格方法的研究．力学学报，2000，32(3)：308～318
49. Liszka T J, Duarte C A M, Tworzydlo W W. Hp-meshless cloud method. Computer Methods in Applied Mechanics and Engineering, 1996, 139:263～288
50. Melenk J M, Babuska, I. Partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139:289～314
51. Babuska, I, Melenk J M. Partition of unity method. International Journal for Numerical Methods in Engineering, 1997, 40 (4): 727～758
52. Duarte C A, Hamzeh O N, Liszka T J, et al. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Computer Methods in Applied Mechanics and Engineering, 2001, 190:2227～2262
53. Dolbow J, Moes N, Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36 (3): 235～260
54. Alves M K, Rossi R. An extension of the partition of unity finite element method. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2005, 27 (3): 209～216
55. Gasser T C, Holzapfel G A. Modeling 3-D crack propagation in unreinforced concrete using PUFEM. Computer Methods in Applied Mechanics and Engineering, 2005, 194:2859～289
56. Atluri S N, Zhu T L. A new local meshless local Petorv—Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998,22 (2) : 117～127
57. Atluri S N, Zhu T L. Meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25: 169～179
58. Gu Y T, Liu G R. A local point interpolation method for static and dynamic analysis of thin beams. Comput Methods Appl Mech Engrg, 2001, 190:5518～5528
59．龙述尧．弹性力学问题局部Petorv—Galerkin的方法．力学学报，2001，33(4)：508～518
60．熊渊博，龙述尧．薄板的局部Petrov—Galerkin方法．应用数学和力学，2004，28(2)：189～196
61．龙述尧，刘凯远．动态断裂力学问题中的局部Petrov-Galerkin无网格方法．暨南大学学报 (自然科学版)．2005，26(1)：57～59
62. Kai Wang, Shenjie Zhou, Guojun Shah. The natural neighbour Petrov-Galerkin method for elasto-statics. International Journal for Numerical Methods in Engineering. 2005, 63 (8), 1126～1145
63. Zhu T, Zhang J D, Atluri S N. A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach. Computational Mechanics, 1998, 21:183～195
64. Zhu Tu long, Zhang Jin dong, Atluri S N. A meshless local boundary integrated equation (LBIE) method for solving nonlinear problems. Computational Mechanics, 1998, 22:174～186
65．张见明，姚振汉，李宏．二维势问题的杂交边界点法．重庆建筑大学学报，2000，22(6)：105～107
66. Zhang X, Song K Z, Lu M W. Meshless methods based on collocation with radial basis function. Comput Mech, 2000, 26 (4) : 333～343
67. Zhang X, Song K Z, L M W. Hermite type collocation with radial basis functions. Proceedings of Internal Conference on Computational Engineering & Science. Los Angeles, USA, August, 2000:20～25
68．曾清红，卢德唐．耦合径向基函数与多项式基函数的无网格方法．计算物理，2005，22(1)：43～50
69．孔亮，高学军，王燕昌．基于紧支径向基函数的点插值无网格方法．岩土力学，2004，25(2)：117～120
70. Duan Y. Meshless Galerkin method using radial basis functions based on domain decomposition. Applied Mathematics and Computation, 2006, 2(15): 750-762
71. Sukumar N, Moran B, Belytschko T. The natural element method in solid mechanics. International Journal for Numerical methods in Engineering. 1998,43(5), 839～887
72. Bueche D, Sukumar N, Moran B. Dispersive properties fo the natural element method. Computational Mechanics. 2000, 25(2-3): 207～219
73. Sukumar N, Moran B, Semenov A Y, Belikov V V. Natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering. 2001, 50(1): 1～27
74. E Cueto, J Cegonino, B Calvo, M Doblare. On the imposition of essential boundary conditions in natural neighbour Galerkin methods. Communications in Numerical Methods in Engineering. 2003, 19(5): 361～376
75. Cuto E, Doblar M, Gracia L. Imposing essential boundary conditions in the natural element method by means of density-scaled alpha shapes. International Journal for Numerical Methods in Engineering. 2000, 49(4): 519-546
76. Gonzalez D, Cueto E, Martinez M A, Doblar M. Numerical integration in Natrual Neighbour Galerkin Methods. International Journal for Numerical Methods in Engineering. 2004, 60(12): 2077-2104
77. Yoo J W, Moran B, Chen J S. Stabilized conforming nodal integration in the natural-element method. International Journal for Numerical Methods in Engineering. 2004, 60(5): 861-890
78. Liu W K, Jun S, Zhang Y F. Reproducing Kernel Particle methods. International Journal for numerical method in fluids, 1995,20: 1081-1106
79. Micchelli C A. Interpolation of scattered date: distance matrices and conditionally positive definite functions. Constr. Approx., 1986, 2: 11-22
80. Wang J G, Liu G R. A point Interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering. 2002, 54:1623-1648
81. Liu G R, Gu Y T. A point Interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering. 2001, 50: 937-951
82. Liu R R, Gu Y T. A matrix triangularization algorithm for point Interpolation method. Proceeding of the Asia-pacific vibration conference, 2001, hangzhou, China, Edited by Wen Bangchun, Nov. 18-31:2001
83. Sibson R. A vector identity for the Dirichlet tessellation. Mathematical proceedings of the Cambridge philosophical society. 1980, 87: 151-155
84. Belikov, V V Semenov A Y. Non-Sibsonian Interpolation on arbitrary system of points in Euclidean space and adaptive isoline generation. Applied Numerical Mathematics, 2003, 4(4): 371-384
85. 张雄, 胡炜, 潘小飞等. 加权最小二乘无网格法. 力学学报, 2003. 35(4): 425-431
86. Kwon K C, Park S H, Youn S K. The least-squares meshfree method for elasto-plasticity and its application to metal forming analysis. International Journal for Numerical methods in Engineering. 2005, 64: 751-788
87. Chen J S, Pan C, Roque C et al. Lagrangian reproducing kernel particle method for metal forming analysis. Computational Mechanics, 1998, 22 (3): 289-307
88. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Methods in Engineering, 2000, 47 (6): 1189-1214
89. Li G Y, Belytscko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations, 2001, 18 (1): 62-78
90. Xiong S W, Rodrigues J M C, Martins P A F. Application of the element free Galerkin method to the simulation of plane strain rolling. European Journal of Mechanic A/Solids, 2004, 23: 77～93
91. Xiong S W, Li C S, Rodrigues J M C et al. Steady and non-steady state analysis of bulk forming processes by the reproducing kernel particle method. Finite Elements in Analysis and Design, 2005, 41 (6): 599～614
92. Guo Y M, Nakanishi K. A backward extrusion analysis by the rigid-plastic integralless-meshless method. Journal of Materials Processing Technology, 2003, 140 (1-3): 19～24
93. Guo Y M, Nakanishi K, Yokouchi Y. A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method. Advances in Engineering Software, 2005, 36 (4): 234～242
94. Alfaro I, Yvonnet J, Cueto E, Chinesta F, Doblare M. Meshless methods with application to metal forming. Computer methods in applied mechanics and engineering. 2006, in press
95. Alfaro I, Bel D, Cueto E, Doblare M, Chinesta F. Three-dimentional simulation of aluminium extrusion by the α-shape based natural element method. Computer methods in applied mechanics and engineering. 2006, in press
96．娄路亮，曾攀，方刚．无网格法及其在体积成形中的应用．塑性工程学报，2001，8(3)：1～5
97．赵国群，王卫东，栾贻国．完全变换法在无网格伽辽金方法中的应用．计算力学学报，2004，21(1)：104～108
98．赵国群，王卫东，栾贻国．金属塑性成形过程无网格伽辽金法数值模拟技术研究．机械工程学报，2004，40(11)：13～16
99．王卫东，赵国群，栾贻国．混合变换法在无网格伽辽金方法中的应用．应用力学学报，2004，21(1)：142～145
100．吴欣，赵国群，管延锦，王卫东．金属成形过程中的无网格热力耦合分析，锻压技术，2005，30(增刊)：189～193
101．卿启湘，李光耀，刘潭玉．棒材拉拔问题的弹塑性无网格法分析．机械工程学报，2004，40(1)：85～89
102．李长生，熊尚武，Rodrigues J．金属塑性加工过程无网格数值模拟方法．沈阳，东北大学出版社，2004
103．崔青玲，刘相华，王国拣，熊尚武．无网格RKPM法及其在体积成型中的应用．东北大学学报，2004，25(9)：855～858
104．崔青玲，李长生，刘相华，王国栋，熊尚武．无网格R KPM法模拟平板轧制过程．应用力 学学报，2005，22(2)：243～247
105．崔青玲，李长生，刘相华，王国栋，熊尚武．无网格法及其在金属塑性成形中的应用．塑性工程学报，2005，12(1)：38～42
106．王凯．自然临近无网格法的理论与应用研究．博士论文，济南：山东大学，2006／1．
107. Li S, Liu W K. Meshfree particle methods and their applications. Applied Mechanics Reviews. 2002.55(1): 1～34
108. Monaghan J J, Gingold R A. Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of Astronomical Socity. 1977. 181 : 575～389
109. P Lancaster, K Salkauskas. Surfaces generated by moving least squares method. Mathematics of Computation, 1981, 37(155): 141～158
110. Jin X, Li G, Aluru N R. On the equivalence between least-squares and kernel approximation in meshless methods. Computer modeling in Engineering and Sciences, 2001, 2, 447～462
111. T Belytschko, Krongauz Y, D Organ, F Fleming, P Krysl. Meshless methods: An overview and resent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139:3～47
112．宋康祖，陆明万，张雄．固体力学中的无网格方法．力学进展，2000，30(1)：55～65
113．周小平．对进一步发展无单元法的几点设想．福州大学学报．2001，29(3)：84～87
114．刘欣，朱德懋，陆明万，张雄．基于流形覆盖思想的无网格方法的研究．计算力学学报，2001，18(1)：21～27
115. Liu W K, Chen Y, Aziz UR et at. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 91～157
116. Chen J S, Pan C, Wu C T, Liu W K. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computational Methods in Applied Mechanics and Engineering, 1996, 139:195～227
117. Chen J S, Wang H P. New boundary condition treatments in meshfree computation of contract problems. Computer Methods in Applied Mechanics and Engineering, 2000, 187: 441～468
118. Monaghan J J. Why particle methods work. SIAM Journal on Scientific and Statistical Computing, 1982, 3(4): 422～433
119. Wu Z M. Compactly supported positive definite radial functions. Advances in Computational Mathematics. 1995,4:283～292
120. Buhmann M D. Radial functions on compact support. Prlceedings of the Edinburgh Mathematical Socity. 1998,41: 3-46
121. Wendland H. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degrees. Advances in Computational Mathematics. 1995,4, 389～396
122. Powell M J D. The theory of radial basis function approximation in 1990. Advances in Numerical Analysis. 1992, 2: 105-210
123. Zuppa C. Good quality point sets and error estimates for moving least square approximations, Applied Numerical Mathematics, 2003, 47: 575-585
124. Kansa E J, Carlson R E. Improved accuracy of multiquadric Interpolation using variable shape parameters. Computers and Mathematics with Applications. 1992, 24(12): 99-120
125. Carlson R E. The parameter in multiquadric Interpolation. Computers and Mathematics with Applications. 1991, 21 (9), 29-442
126.张雄, 刘岩. 无网格法. 1ed. 北京: 清华大学出版社.2004
127. Chen J S, Satyamurthy K, Hirschfelt L R. Consistent finite element procedure for nonlinear rubber elasticity with a higher order strain energy function. Computers & Structures, 1994, 50: 715-727
128. Dolbow J, Belytschko T. Volumetric locking in the element free Galerkin method, International Journal for Numerical Method in Engineering 1999, 46: 925-942
129. Chen J S, Yoon S, Wang H P, et al. An improved reproducing kernel particle method for nearly incompressible finite elasticity. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 117-145
130. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering. 1996, 139: 49-74
131. Zhang X, Lu M W, Wegner J L. A 2-D meshless model for jointed rock structures. International Journal for Numerical Methods in Engineering, 2000,47(10): 1649-1661
132. Borromand B, Tabatabaei A A, Onate E. Simple modifications for stabilization of the finite point method. International journal for mummerical methods in engineering. 2005; 63: 351-379
133. Yada H, Senuma T. Resistance to hot deforming of steel. J. JSTP, 1986, 27:34-44
134. Kopp R, Cal M L et al. Multi-level simulation of metal forming process. Pro. 2~(nd) ICTP, Stuttgart, Germany, 1987: 1129-1234
135. C M Sellars. Computer Modeling of hot-working process. Mater. Sci. Tech., 1985,1:325-332
136. C M Sellars. Modeling Microstructural development during hot rolling, of hot-working process. Mater. Sci. Tech., 1985,1:325-332
137. Rebelo N, Kobayashi S. A coupled analysis of viscoplastic deformation and heat transfer. International journal of Mechanical Science, 1980, 22:688～705
138．马新武．体积成形过程数值模拟与优化技术及其系统开发研究[博士学位论文]．济南：山东大学，2002．
2. P. V. Marcal, I. P. King. Elastic-plastic Analysis of Two-dimensional Stress Systems by the Finite Element Method. International Journal of Mechanical Sciences. 1967,9:143-150
3. C. H. Lee, S. Kobayashi. New Solutions to Rigid-plastic Deformation Problems Using a Matrix Method. Trans. ASME, Journal of Engineer for Industry, 1973, 95: 865-878
4. O. C. Zienkiewicz, P. N. Godbole. Flow of Plastic and Viscoplastic Solids with Special Reference to Extrusion and Forming Process. International Journal for Numerical Methods in Engineering, 1974, 8: 3-15
5. Kobayashi S, Oh S I, Altan T. Metal forming and the finite element method. Oxford University Press, New York
6. Liszka T, Orkisz J. Finite Difference Method for Arbitrary Irregular Meshes in Nonlinear Problems of Applied Mechanics. IV SMiRt, San Francisco, 1977
7. Perrone N, Kao R. A general finite difference method for arbitrary meshes. Computers and Structures, 1975,5:45-57
8. Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astronomy J, 1977,8(12): 1013-1024
9. Monaghan J J. Introduction to SPH. Computer Physics Communications, 1987,48 (1): 89-96
10. Swegle J W, Hick s D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. Journal of Computational Physics, 1995, 116(1): 123-134
11. Dyka C T, Randies P W, Ingel R P. Stress points for tension instability in SPH. International Journal for Numerical Methods in Engineering, 1997, 40 (13): 2325-2341
12. Chen J K, Beraun J E, Jih C J. Improvement for tensile instability in smoothed particle hydrodynamics. Computational Mechanics, 1999, 23: 279-287
13. Vignjevic R, Campbell J, Libersky L. A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Computer Methods in Applied Mechanics and Engineering, 2000, 184:67-85
14. Johnson, Gordon R, Stryk, et al. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 347-373
15. Chen J K, Beraun J E. Generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering, 2000, 139: 225-239
16. Randies P W, Libersky L D. Smoothed particle hydrodynamics: some recent improvements and applications Source: Computer Methods in Applied Mechanics and Engineering, 1996, 139: 375-408
17. Abadi M G, Lambas D G, Tissera P B. Cosmological Simulations with Smoothed Particle Hydrodynamics. International Astronomical Union-Symposium, 1996, 168: 577
18. Morris, Joseph P. Simulating surface tension with smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 2000, 33: 333-353
19. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10: 307-318
20. Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37 (2): 229-256
21. Chung H J, Belytschko T. Error estimate in the EFG method. Computational Mechanics, 1998, 21:91-100
22. Lu Y Y, Belytschko T, Tabbara M. Element-free Galerkin method for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Engineering, 1995, 126: 131-153
23. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1996, 39: 923-938
24. Belytschko T, Organ D, Gerlach C. Element-free Galerkin methods for dynamic fracture in concrete. Computer Methods in Applied Mechanics and Engineering, 2000, 187: 385-399
25. Belytschko T, Krysl P, Krongauz Y. Three-dimensional explicit element-free Galerkin method. International Journal for Numerical Methods in Fluids, 1997, 24 (12): 1253-1270
26. Belytschko T, Organ D, Krongauz Y. Coupled finite element element-free Galerkin method. Computational Mechanics, 1995, 17(3): 186-195
27. Liu W K, Chen Y, Jun S et al. Overview and applications of reproducing kernel particle methods. Archives of Computation Methods in Engineering, State of the Art Review, 1996 , 3 : 3-80
28. 周进雄, 李梅娥, 张红艳. 再生核质点法研究进展. 力学进展, 2002,32 (4) :535-544
29. Liu W K, Jun S, Li S, et al. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, 1995, 38 (10): 1655-1679
30. Liu W K, Jun S, Sihling D T, et al. Multiresolution reproducing kernel particle method for computational fluid dynamics. International Journal for Numerical Methods in Fluids, 1997, 24 (12): 1391～1415
31. Liu W K, Hao S, Belytschko T, et al. Multiple scale meshfree methods for damage fracture and localization. Computational Materials Science, 1999, 16:197～205
32. Xiong S W, Liu W K, Gao J, et al. Simulation of bulk metal forming processes using the reproducing kernel particle method. Computers and Structures, 2005, 83:574～587
33. Jun S, Liu W K, Belytschko T. Explicit Reproducing Kernel Particle Methods for large deformation problems. International Journal for Numerical Methods in Engineering, 1998, 41 (1): 137～166
34. Liu W K, Jun S. Multiple-scale Reproducing Kernel Particle Methods for large deformation problems. International Journal for Numerical Methods in Engineering, 1998, 41 (7): 1339～1362
35. Chen J S, Roque C, Pan C, et al. Analysis of metal forming process based on meshless method. Journal of Materials Processing Technology, 1998, 80～81 (3) : 642～646
36. Xiong S W, Liu W K, Cao J, et al. On the utilization of reproducing kernel particle method for the numerical simulation of plane strain rolling. International Journal of Machine Tools & Manufacture, 2003, 43 (1): 89～102
37. Aluru N R. Point collocation method based on reproducing kernel approximations. International Journal for Numerical Methods in Engineering, 2000, 47 (6): 1083～1121
38．史宝军，袁明武，李君．基于核重构思想的最小二乘配点型无网格方法．力学学报，2003，35(6)：697～706
39．史宝军，袁明武，孙树立，陈斌．基于核重构思想的配点型无网格方法的研究——一维问题．计算力学学报，2004，21(1)：97～103
40. E. Onate, E Perazzo, J. Miquel. A finite point method for elasticity problems. Computers and Structures. 2001, 79, 2151～2163
41. Xiaozhong Jin, Gang Li, N. R. Aluru. Positivity conditions in meshless collocation methods. Computer methods in applied mechanics engineering. 2004, 193: 1171～1202
42. Xiaozhong Jin, Gang Li, N. R. Aluru. New approximations and collocation schemes in the finite cloud method. Computers and Structures, 2005, 83: 1336～1385
43. G. R. Liu, Y. L. Wu, H. Ding. Meshfree weak-strong form method and its application to incompressible flow problems. International Journal for numerical method in fluids. 2004, 46: 1025～1047
44. Duarte C A, Oden J T. Hp clouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12 (6): 673～705
45. Duarte C A, Oden J T. An h-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering, 1996, 139:237～262
46. Oden J T, Duarte C A M. New cloud-based hp finite element method. Computer Methods in Applied Mechanics and Engineering, 1998, 153:117～126
47. Garcia O, Fancello E A, et al. Hp-clouds in Mindlin's thick plate model. International Journal for Numerical Methods in Engineering, 2000, 47 (8): 1381～1400
48．刘欣，朱德懋，陆明万，张雄．平面裂纹问题的h，p，hp型白适应无网格方法的研究．力学学报，2000，32(3)：308～318
49. Liszka T J, Duarte C A M, Tworzydlo W W. Hp-meshless cloud method. Computer Methods in Applied Mechanics and Engineering, 1996, 139:263～288
50. Melenk J M, Babuska, I. Partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139:289～314
51. Babuska, I, Melenk J M. Partition of unity method. International Journal for Numerical Methods in Engineering, 1997, 40 (4): 727～758
52. Duarte C A, Hamzeh O N, Liszka T J, et al. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Computer Methods in Applied Mechanics and Engineering, 2001, 190:2227～2262
53. Dolbow J, Moes N, Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36 (3): 235～260
54. Alves M K, Rossi R. An extension of the partition of unity finite element method. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2005, 27 (3): 209～216
55. Gasser T C, Holzapfel G A. Modeling 3-D crack propagation in unreinforced concrete using PUFEM. Computer Methods in Applied Mechanics and Engineering, 2005, 194:2859～289
56. Atluri S N, Zhu T L. A new local meshless local Petorv—Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998,22 (2) : 117～127
57. Atluri S N, Zhu T L. Meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25: 169～179
58. Gu Y T, Liu G R. A local point interpolation method for static and dynamic analysis of thin beams. Comput Methods Appl Mech Engrg, 2001, 190:5518～5528
59．龙述尧．弹性力学问题局部Petorv—Galerkin的方法．力学学报，2001，33(4)：508～518
60．熊渊博，龙述尧．薄板的局部Petrov—Galerkin方法．应用数学和力学，2004，28(2)：189～196
61．龙述尧，刘凯远．动态断裂力学问题中的局部Petrov-Galerkin无网格方法．暨南大学学报 (自然科学版)．2005，26(1)：57～59
62. Kai Wang, Shenjie Zhou, Guojun Shah. The natural neighbour Petrov-Galerkin method for elasto-statics. International Journal for Numerical Methods in Engineering. 2005, 63 (8), 1126～1145
63. Zhu T, Zhang J D, Atluri S N. A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach. Computational Mechanics, 1998, 21:183～195
64. Zhu Tu long, Zhang Jin dong, Atluri S N. A meshless local boundary integrated equation (LBIE) method for solving nonlinear problems. Computational Mechanics, 1998, 22:174～186
65．张见明，姚振汉，李宏．二维势问题的杂交边界点法．重庆建筑大学学报，2000，22(6)：105～107
66. Zhang X, Song K Z, Lu M W. Meshless methods based on collocation with radial basis function. Comput Mech, 2000, 26 (4) : 333～343
67. Zhang X, Song K Z, L M W. Hermite type collocation with radial basis functions. Proceedings of Internal Conference on Computational Engineering & Science. Los Angeles, USA, August, 2000:20～25
68．曾清红，卢德唐．耦合径向基函数与多项式基函数的无网格方法．计算物理，2005，22(1)：43～50
69．孔亮，高学军，王燕昌．基于紧支径向基函数的点插值无网格方法．岩土力学，2004，25(2)：117～120
70. Duan Y. Meshless Galerkin method using radial basis functions based on domain decomposition. Applied Mathematics and Computation, 2006, 2(15): 750-762
71. Sukumar N, Moran B, Belytschko T. The natural element method in solid mechanics. International Journal for Numerical methods in Engineering. 1998,43(5), 839～887
72. Bueche D, Sukumar N, Moran B. Dispersive properties fo the natural element method. Computational Mechanics. 2000, 25(2-3): 207～219
73. Sukumar N, Moran B, Semenov A Y, Belikov V V. Natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering. 2001, 50(1): 1～27
74. E Cueto, J Cegonino, B Calvo, M Doblare. On the imposition of essential boundary conditions in natural neighbour Galerkin methods. Communications in Numerical Methods in Engineering. 2003, 19(5): 361～376
75. Cuto E, Doblar M, Gracia L. Imposing essential boundary conditions in the natural element method by means of density-scaled alpha shapes. International Journal for Numerical Methods in Engineering. 2000, 49(4): 519-546
76. Gonzalez D, Cueto E, Martinez M A, Doblar M. Numerical integration in Natrual Neighbour Galerkin Methods. International Journal for Numerical Methods in Engineering. 2004, 60(12): 2077-2104
77. Yoo J W, Moran B, Chen J S. Stabilized conforming nodal integration in the natural-element method. International Journal for Numerical Methods in Engineering. 2004, 60(5): 861-890
78. Liu W K, Jun S, Zhang Y F. Reproducing Kernel Particle methods. International Journal for numerical method in fluids, 1995,20: 1081-1106
79. Micchelli C A. Interpolation of scattered date: distance matrices and conditionally positive definite functions. Constr. Approx., 1986, 2: 11-22
80. Wang J G, Liu G R. A point Interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering. 2002, 54:1623-1648
81. Liu G R, Gu Y T. A point Interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering. 2001, 50: 937-951
82. Liu R R, Gu Y T. A matrix triangularization algorithm for point Interpolation method. Proceeding of the Asia-pacific vibration conference, 2001, hangzhou, China, Edited by Wen Bangchun, Nov. 18-31:2001
83. Sibson R. A vector identity for the Dirichlet tessellation. Mathematical proceedings of the Cambridge philosophical society. 1980, 87: 151-155
84. Belikov, V V Semenov A Y. Non-Sibsonian Interpolation on arbitrary system of points in Euclidean space and adaptive isoline generation. Applied Numerical Mathematics, 2003, 4(4): 371-384
85. 张雄, 胡炜, 潘小飞等. 加权最小二乘无网格法. 力学学报, 2003. 35(4): 425-431
86. Kwon K C, Park S H, Youn S K. The least-squares meshfree method for elasto-plasticity and its application to metal forming analysis. International Journal for Numerical methods in Engineering. 2005, 64: 751-788
87. Chen J S, Pan C, Roque C et al. Lagrangian reproducing kernel particle method for metal forming analysis. Computational Mechanics, 1998, 22 (3): 289-307
88. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Methods in Engineering, 2000, 47 (6): 1189-1214
89. Li G Y, Belytscko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations, 2001, 18 (1): 62-78
90. Xiong S W, Rodrigues J M C, Martins P A F. Application of the element free Galerkin method to the simulation of plane strain rolling. European Journal of Mechanic A/Solids, 2004, 23: 77～93
91. Xiong S W, Li C S, Rodrigues J M C et al. Steady and non-steady state analysis of bulk forming processes by the reproducing kernel particle method. Finite Elements in Analysis and Design, 2005, 41 (6): 599～614
92. Guo Y M, Nakanishi K. A backward extrusion analysis by the rigid-plastic integralless-meshless method. Journal of Materials Processing Technology, 2003, 140 (1-3): 19～24
93. Guo Y M, Nakanishi K, Yokouchi Y. A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method. Advances in Engineering Software, 2005, 36 (4): 234～242
94. Alfaro I, Yvonnet J, Cueto E, Chinesta F, Doblare M. Meshless methods with application to metal forming. Computer methods in applied mechanics and engineering. 2006, in press
95. Alfaro I, Bel D, Cueto E, Doblare M, Chinesta F. Three-dimentional simulation of aluminium extrusion by the α-shape based natural element method. Computer methods in applied mechanics and engineering. 2006, in press
96．娄路亮，曾攀，方刚．无网格法及其在体积成形中的应用．塑性工程学报，2001，8(3)：1～5
97．赵国群，王卫东，栾贻国．完全变换法在无网格伽辽金方法中的应用．计算力学学报，2004，21(1)：104～108
98．赵国群，王卫东，栾贻国．金属塑性成形过程无网格伽辽金法数值模拟技术研究．机械工程学报，2004，40(11)：13～16
99．王卫东，赵国群，栾贻国．混合变换法在无网格伽辽金方法中的应用．应用力学学报，2004，21(1)：142～145
100．吴欣，赵国群，管延锦，王卫东．金属成形过程中的无网格热力耦合分析，锻压技术，2005，30(增刊)：189～193
101．卿启湘，李光耀，刘潭玉．棒材拉拔问题的弹塑性无网格法分析．机械工程学报，2004，40(1)：85～89
102．李长生，熊尚武，Rodrigues J．金属塑性加工过程无网格数值模拟方法．沈阳，东北大学出版社，2004
103．崔青玲，刘相华，王国拣，熊尚武．无网格RKPM法及其在体积成型中的应用．东北大学学报，2004，25(9)：855～858
104．崔青玲，李长生，刘相华，王国栋，熊尚武．无网格R KPM法模拟平板轧制过程．应用力 学学报，2005，22(2)：243～247
105．崔青玲，李长生，刘相华，王国栋，熊尚武．无网格法及其在金属塑性成形中的应用．塑性工程学报，2005，12(1)：38～42
106．王凯．自然临近无网格法的理论与应用研究．博士论文，济南：山东大学，2006／1．
107. Li S, Liu W K. Meshfree particle methods and their applications. Applied Mechanics Reviews. 2002.55(1): 1～34
108. Monaghan J J, Gingold R A. Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of Astronomical Socity. 1977. 181 : 575～389
109. P Lancaster, K Salkauskas. Surfaces generated by moving least squares method. Mathematics of Computation, 1981, 37(155): 141～158
110. Jin X, Li G, Aluru N R. On the equivalence between least-squares and kernel approximation in meshless methods. Computer modeling in Engineering and Sciences, 2001, 2, 447～462
111. T Belytschko, Krongauz Y, D Organ, F Fleming, P Krysl. Meshless methods: An overview and resent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139:3～47
112．宋康祖，陆明万，张雄．固体力学中的无网格方法．力学进展，2000，30(1)：55～65
113．周小平．对进一步发展无单元法的几点设想．福州大学学报．2001，29(3)：84～87
114．刘欣，朱德懋，陆明万，张雄．基于流形覆盖思想的无网格方法的研究．计算力学学报，2001，18(1)：21～27
115. Liu W K, Chen Y, Aziz UR et at. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 91～157
116. Chen J S, Pan C, Wu C T, Liu W K. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computational Methods in Applied Mechanics and Engineering, 1996, 139:195～227
117. Chen J S, Wang H P. New boundary condition treatments in meshfree computation of contract problems. Computer Methods in Applied Mechanics and Engineering, 2000, 187: 441～468
118. Monaghan J J. Why particle methods work. SIAM Journal on Scientific and Statistical Computing, 1982, 3(4): 422～433
119. Wu Z M. Compactly supported positive definite radial functions. Advances in Computational Mathematics. 1995,4:283～292
120. Buhmann M D. Radial functions on compact support. Prlceedings of the Edinburgh Mathematical Socity. 1998,41: 3-46
121. Wendland H. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degrees. Advances in Computational Mathematics. 1995,4, 389～396
122. Powell M J D. The theory of radial basis function approximation in 1990. Advances in Numerical Analysis. 1992, 2: 105-210
123. Zuppa C. Good quality point sets and error estimates for moving least square approximations, Applied Numerical Mathematics, 2003, 47: 575-585
124. Kansa E J, Carlson R E. Improved accuracy of multiquadric Interpolation using variable shape parameters. Computers and Mathematics with Applications. 1992, 24(12): 99-120
125. Carlson R E. The parameter in multiquadric Interpolation. Computers and Mathematics with Applications. 1991, 21 (9), 29-442
126.张雄, 刘岩. 无网格法. 1ed. 北京: 清华大学出版社.2004
127. Chen J S, Satyamurthy K, Hirschfelt L R. Consistent finite element procedure for nonlinear rubber elasticity with a higher order strain energy function. Computers & Structures, 1994, 50: 715-727
128. Dolbow J, Belytschko T. Volumetric locking in the element free Galerkin method, International Journal for Numerical Method in Engineering 1999, 46: 925-942
129. Chen J S, Yoon S, Wang H P, et al. An improved reproducing kernel particle method for nearly incompressible finite elasticity. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 117-145
130. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering. 1996, 139: 49-74
131. Zhang X, Lu M W, Wegner J L. A 2-D meshless model for jointed rock structures. International Journal for Numerical Methods in Engineering, 2000,47(10): 1649-1661
132. Borromand B, Tabatabaei A A, Onate E. Simple modifications for stabilization of the finite point method. International journal for mummerical methods in engineering. 2005; 63: 351-379
133. Yada H, Senuma T. Resistance to hot deforming of steel. J. JSTP, 1986, 27:34-44
134. Kopp R, Cal M L et al. Multi-level simulation of metal forming process. Pro. 2~(nd) ICTP, Stuttgart, Germany, 1987: 1129-1234
135. C M Sellars. Computer Modeling of hot-working process. Mater. Sci. Tech., 1985,1:325-332
136. C M Sellars. Modeling Microstructural development during hot rolling, of hot-working process. Mater. Sci. Tech., 1985,1:325-332
137. Rebelo N, Kobayashi S. A coupled analysis of viscoplastic deformation and heat transfer. International journal of Mechanical Science, 1980, 22:688～705
138．马新武．体积成形过程数值模拟与优化技术及其系统开发研究[博士学位论文]．济南：山东大学，2002．