复变量无网格流形方法研究
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摘要
无网格方法是近年来发展起来的一种新兴的数值方法,因其不需要网格,只需要节点信息,具有前处理简单、计算精度高等特点,已成为目前科学和工程计算方法的研究热点之一。
无网格流形方法是在无网格方法中引入数值流形方法的思想而形成的无网格方法。本文针对目前无网格流形方法计算量大等问题,提出了复变量无网格流形方法,然后将其应用于弹性力学、瞬态热传导、断裂力学和弹性动力学等问题。在复变量理论的基础上,采用一维基函数建立二维问题的试函数,结合弹性力学的数值流形方法,提出了弹性力学的复变量数值流形方法,推导了相应的计算公式。
针对无网格流形方法配点过多、计算速度慢、容易形成病态方程组等缺点,本文将复变量移动最小二乘法与无网格流形方法相结合,提出了弹性力学的复变量无网格流形方法,推导了相应的计算公式。
利用裂纹尖端解析解将复变量移动最小二乘法的基函数进行扩展,推导了相应的逼近函数。从最小势能原理出发建立了断裂力学的复变量无网格流形方法,推导了相应的复变量无网格流形方法的求解方程,并与传统的无网格流形方法进行了比较。
采用复变量无网格流形方法构造场点温度逼近函数,对时间域采用传统的两点差分法离散,空间域的离散采用复变量移动最小二乘法,将罚函数法引入本质边界条件,结合瞬态热传导问题的Galerkin积分弱形式,提出了瞬态热传导问题的复变量无网格流形方法。
对时间域采用Newmark积分方法,空间域的离散采用复变量移动最小二乘法,将复变量无网格流形方法应用于求解弹性动力学问题,提出了弹性动力学的复变量无网格流形方法。
对上述提出的数值方法,本文编制了MATLAB计算程序,并进行了数值算例分析,说明了本文方法的正确性和有效性。
Meshless method is a class of new numerical methods developed in recent years. The meshless methods only need the information at nodes, and don’t discretize the domain into a mesh. The advantages of meshless methods are the simpler pre- processing and higher precision. Meshless method is a hot topic of researches on science and engineering computation.
The meshless manifold method, in which the idea of numerical manifold method is introduced, is one of the meshless methods. It has great computational cost because of a large number of nodes selected in the domain of problem.In this dissertation, for the disadvantage of great computational cost of the meshless manifold method, the complex variable meshless manifold method (CVMMM) is developed,and is applied to solve elasticity, fracture, transient heat conduction, and elastodynamics problems respectively.
On the basis of the complex variable theory, the approximation function of a 2D problem is formed with 1D basis function when the shape function is formed. The complex variable numerical manifold method (CVNMM) for elasticity is presented in this paper. The corresponding formulae of the CVNMM for elasticity are obtained in detail.
The meshless manifold method (MMM) has a great number of nodes, which results smaller computational efficiency. And the MMM can form an ill-conditioned or singular equations sometimes. For the disadvantages of the MMM, combining the complex variables moving least-square (CVMLS) approximation with the MMM, the complex variable meshless manifold method (CVMMM) for 2D elasticity is presented in this paper, and the corresponding formulae of the CVMMM are obtained.
In CVMMM, the analytical solutions of displacements at the tip of a crack are used to enrich the approximation function of the CVMLS approximation, and the formulae of the approximation function for fracture problems are obtained. On the basis of least potential energy theory, the CVMMM for fracture problems is presented, and the corresponding formulae of the enriched CVMMM are obtained. Finally, the enriched CVMNMM is compared with the traditional meshless manifold method.
For steady heat conduction problems, the CVMMM is applied to form approximation function of transient heat conduction problems. Time discretization is given by the traditional two-point differential method, and space domain discretization is given by the CVMLS approximation. The penalty method is employed to apply the essential boundary conditions. On basis of the Galerkin weak form of transient heat conduction problems, the CVMMM for transient heat conduction problems is presented, and the corresponding formulae are obtained.
The CVMMM is also used to analyze transient elastodynamics problems. The Newmark time integration method is used for time history analysis, and the CVMLS approximation is used to discretize the space domain. Then the CVMMM for elastodynamics is presented in the paper.
In order to show the efficiency of the CVMMM in the dissertation, the MATLAB codes of the methods above are written. Some numerical examples are given, and the validity and efficiency of these methods are demonstrated.
无网格流形方法是在无网格方法中引入数值流形方法的思想而形成的无网格方法。本文针对目前无网格流形方法计算量大等问题,提出了复变量无网格流形方法,然后将其应用于弹性力学、瞬态热传导、断裂力学和弹性动力学等问题。在复变量理论的基础上,采用一维基函数建立二维问题的试函数,结合弹性力学的数值流形方法,提出了弹性力学的复变量数值流形方法,推导了相应的计算公式。
针对无网格流形方法配点过多、计算速度慢、容易形成病态方程组等缺点,本文将复变量移动最小二乘法与无网格流形方法相结合,提出了弹性力学的复变量无网格流形方法,推导了相应的计算公式。
利用裂纹尖端解析解将复变量移动最小二乘法的基函数进行扩展,推导了相应的逼近函数。从最小势能原理出发建立了断裂力学的复变量无网格流形方法,推导了相应的复变量无网格流形方法的求解方程,并与传统的无网格流形方法进行了比较。
采用复变量无网格流形方法构造场点温度逼近函数,对时间域采用传统的两点差分法离散,空间域的离散采用复变量移动最小二乘法,将罚函数法引入本质边界条件,结合瞬态热传导问题的Galerkin积分弱形式,提出了瞬态热传导问题的复变量无网格流形方法。
对时间域采用Newmark积分方法,空间域的离散采用复变量移动最小二乘法,将复变量无网格流形方法应用于求解弹性动力学问题,提出了弹性动力学的复变量无网格流形方法。
对上述提出的数值方法,本文编制了MATLAB计算程序,并进行了数值算例分析,说明了本文方法的正确性和有效性。
Meshless method is a class of new numerical methods developed in recent years. The meshless methods only need the information at nodes, and don’t discretize the domain into a mesh. The advantages of meshless methods are the simpler pre- processing and higher precision. Meshless method is a hot topic of researches on science and engineering computation.
The meshless manifold method, in which the idea of numerical manifold method is introduced, is one of the meshless methods. It has great computational cost because of a large number of nodes selected in the domain of problem.In this dissertation, for the disadvantage of great computational cost of the meshless manifold method, the complex variable meshless manifold method (CVMMM) is developed,and is applied to solve elasticity, fracture, transient heat conduction, and elastodynamics problems respectively.
On the basis of the complex variable theory, the approximation function of a 2D problem is formed with 1D basis function when the shape function is formed. The complex variable numerical manifold method (CVNMM) for elasticity is presented in this paper. The corresponding formulae of the CVNMM for elasticity are obtained in detail.
The meshless manifold method (MMM) has a great number of nodes, which results smaller computational efficiency. And the MMM can form an ill-conditioned or singular equations sometimes. For the disadvantages of the MMM, combining the complex variables moving least-square (CVMLS) approximation with the MMM, the complex variable meshless manifold method (CVMMM) for 2D elasticity is presented in this paper, and the corresponding formulae of the CVMMM are obtained.
In CVMMM, the analytical solutions of displacements at the tip of a crack are used to enrich the approximation function of the CVMLS approximation, and the formulae of the approximation function for fracture problems are obtained. On the basis of least potential energy theory, the CVMMM for fracture problems is presented, and the corresponding formulae of the enriched CVMMM are obtained. Finally, the enriched CVMNMM is compared with the traditional meshless manifold method.
For steady heat conduction problems, the CVMMM is applied to form approximation function of transient heat conduction problems. Time discretization is given by the traditional two-point differential method, and space domain discretization is given by the CVMLS approximation. The penalty method is employed to apply the essential boundary conditions. On basis of the Galerkin weak form of transient heat conduction problems, the CVMMM for transient heat conduction problems is presented, and the corresponding formulae are obtained.
The CVMMM is also used to analyze transient elastodynamics problems. The Newmark time integration method is used for time history analysis, and the CVMLS approximation is used to discretize the space domain. Then the CVMMM for elastodynamics is presented in the paper.
In order to show the efficiency of the CVMMM in the dissertation, the MATLAB codes of the methods above are written. Some numerical examples are given, and the validity and efficiency of these methods are demonstrated.
引文
[1] Christopher R J. Advanced Methods in Scientific Computing. Computer Science 6220, University of Utah, Spring Semester, 2002, 13-26
[2]徐次达.固体力学加权残值法.上海:同济大学出版社,1978
[3] Zienkiewicz O C. The finite element method (Third edition). McGraw-Hill, 1977
[4]李开泰,黄艾香,黄庆怀.有限元方法及其应用(修订本).西安:西安交通大学出版社,1992
[5]嵇醒,臧跃龙,程玉民.边界元进展及通用程序.上海:同济大学出版社,1997
[6] Brebbia C A. The Boundary Element Method for Engineers. London Pentech Press, 1978
[7] Belytschko T, Krongauz Y, Organ D et al. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 3-47
[8] Li Shaofan, Liu W K. Meshless and particles methods and their applications. Applied Mechanics Review, 2002, 55(1): 1-34
[9] G.H.Shi, Manifold method of material analysis, Transaction of the Ninth Army Conference on Applied Mathematics and Computing Minneapolis, USA, 1992
[10] Jeen-Shang Lin, A mesh-based Partition of Unity Method for Discontinuity Modeling[J]. Computer Methods and Applied Mechanics in Engineering 2003(192), 1515-1532.
[11] Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astrophysical Journal, 1977, 8(12): 1013-1024
[12] Gingold R A, Moraghan J J. Smoothed particle hydrodynamics: theory and applications to nonspherical stars. Mon Not Roy Astrou Soc, 1977, 18: 375-389
[13] Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys, 1995, 116: 123-134
[14] Chen J K, Beraun J E, Jih C J. An improvement for tensile instability in smoothed particle hydrodynamics. Computational Mechanics, 1998, 23: 279-287
[15] Johnsons G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 2002, 53: 825-843
[16] Lancaster P, Salkauskas K. Surfaces generated by moving least square methods. Mathematics of Computation, 1981, 37: 141-158
[17] Nayroles B Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10: 307-318
[18] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin Methods. International Journal for Numerical Methods in Engineering, 1994, 37: 229-256
[19] Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Computational Mechanics, 1999, 23: 219-230
[20] Belytschko T, Krongauz Y et al. Smoothing and accelerated computations in the element free Galerkin method. J. Comput. Appl. Math., 1996, 74: 111-126
[21] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. International Journal for Numerical Methods in Engineering, 1998, 41: 1215-1233
[22] Belytschko T, Gu L, Lu Y Y. Fracture and crack growth by element free Galerkin methods. Modlling Simul. Mater. Sci. Eng.. 1994, 2: 519-534
[23] Lu Y Y, Belytschko T. Element-free Galerkin methods for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Engineering, 1995, 126: 131-153
[24] Krysl P, Belytschko T. ESFLIB: A library to compute the element free Galerkin shape functions. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 2181-2205
[25] Krysl P, Belytschko T. Analysis of thin shells by element-free Galerkin method. Computational Mechanics, 1995, 17: 26-35
[26] Belytschko T, Lu Y Y, Gu L, Tabbara M. Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures, 1995, 32: 2547-2570
[27] Sukumar N, Moran B, Black T, Belytschko T. An element-free Galerkin method for three-dimensional fracture mechanics. Computational Mechanics, 1997, 20: 170-175
[28] 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
[29] Xu Y, Saigal S. An Element Free Galerkin analysis of steady dynamic growth of a mode I crack in elastic-plastic materials. International Journal of sounds and structures, 1999, 36: 1045-1079
[30] Kargarmovin M H, Toussi H E, Faribotz S J. Elasto-plastic element-free Galerkin method. Computational Mechanics, 2004, 33(3): 206-214
[31] Bouillard Ph, Seleau S. Element-free Galerkin solutions for Helmholtz problems: formulation and numerical assessment of the pollution effect. Computer Methods in Applied Mechanics and Engineering, 1998, 162: 317-335
[32] Lee S H, Yoon Y C. An improved crack analysis technique by element-free Galerkin. International Journal for Numerical Methods in Engineering, 2003, 56: 1291-1314
[33] Rao B N and Rahman S. An enriched meshless method for non-linear enriched fracture mechanics. International Journal for Numerical Methods in Engineering, 2004, 59: 197-223
[34] Fleming M, Chu Y A, Moran B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, 1997, 40: 1483-1504
[35] Beissel S, Belytschko T. Nodal integration of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 49-74
[36] Smolinski P, Palmer T. Procedures for multi-time step integration of element free Galerkin methods for diffusion problems. Comput. Struct., 2000, 77: 171-183
[37] Mukherjee Y X, Mukherjee S. On boundary conditions in the element-free Galerkin method. Computational Mechanics, 1997, 19: 264-270
[38] Alves M K, Rossi R. A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function. International Journal for Numerical Methods in Engineering, 2003, 57: 1523-1552
[39] Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering, 1997, 40: 2953-2974
[40] Ponthot J P, Belytschko T. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1998, 152: 19-46
[41] Liew K M, Ren J and Kitipornchai S. Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method. Engineering Analysis with Boundary Elements, 2004, 28: 497-507
[42] Liu G R, Gu Y T. Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Computational Mechanics, 2000, 26: 166-173
[43] Belytschko T, Organ D, Krongauz Y. A coupled finite element- element free Galerkin method. Computational Mechanics, 1995, 17: 186-195
[44] Krysl P, Belytschko T. Element-free Galerkin method convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering, 1997, 148: 257-277
[45] Chung H J, Belytschko T. An error estimate in the EFG menthod. Computational Mechanics,1998, 21: 91-100
[46] Gavete L, Falcon S, Ruiz A. An error indicator for the element free Galerkin method. Eur. J. Mech. A/Solids, 2001, 20, 327-341
[47] Liu W K, Jun S, Zhang Y F. Reproducing kernel partical methods. International Journal for Numerical Methods in Fluid, 1995, 20: 1081-1106
[48] Voth T E, Christon M A. Discretization errors associated with reproducing kernel methods: one-dimensional domains. Computer Methods in Applied Mechanics and Engineering, 1996, 190: 2429-2446
[49] Han W, Meng X. Error analysis of the reproducing kernel particle method. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 6157-6181
[50] Chen J S, Pan C, Wu C T, Liu W K. Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 195-227
[51] Liew K M, Ng T Y, Wu Y C. Meshfree method for large deformation analysis–a reproducing kernel particle approach. Engineering structures, 2002, 24: 543-551
[52] Li S, Liu W K. Moving least-square reproducing kernel method (I) Methodology and Convergence. Computer Methods in Applied Mechanics and Engineering, 1997, 143: 113-154
[53] Li S, Liu W K. Moving least-square reproducing kernel method Part II Fourier analysis. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 159-193
[54] Chen J S, Yoon S, Wang H P, Liu W K. An improved reproducing kernel particle method for nearly incompressible finite elasticity. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 117-145
[55] Danielson K T, Hao S, Liu W K et al. Parallel computation of meshless methods for explicit dynamic analysis. International Journal for Numerical Methods in Engineering, 2000, 47: 1323-1341
[56] Chen J S, Han W, You Y, Meng X. A reproducing kernel method with nodal interpolation property. International Journal for Numerical Methods in Engineering, 2003, 56: 935-960
[57] Liu W K, Chen Y, Uras R A, Chang C T. Generalized multiple scale reproducing kernel particle. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 91-157
[58] Liu W K, Chen Y J. Wavelet and multiple scale reproducing kernel methods. International Journal of Numerical Methods in Fluids, 1995, 21: 901-931
[59] Uras R A, Cheng C T, Chen Y et al. Multiresolution reproducing kernel particle methods in acoustics. J. Comput. Acoust., 1997, 5: 71-94
[60] Liu W K, Jun S et al. Multiresolution reproducing kernel particle methods for computational fluid dynamics. International Journal for Numerical Methods in Fluid, 1997, 24: 1391-1415
[61] Liu W K, Jun S. Multiple-scale reproducing kernel particle methods for large deformation problem. International Journal for Numerical Methods in Engineering, 1998, 41: 1339-1362
[62] Duarte C A, Oden J T. Hp clouds - a meshless method to solve boundary-value problems. Technical Report 95-05. Texas Institute for Computational and Applied Mathematics, University of Texas at Austin, 1995
[63] Duarte A, Oden J T. Hp clouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12: 673-705
[64] Duarte M, Oden J T. An h-p adptive method using clouds. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 237-262
[65] Oden J T, Duarte A, Zienkiewicz O C. A new cloud-based hp finite element method. International Journal for Numerical Methods in Engineering, 1998, 50: 160-170
[66] Babuska I, Melenk J M. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 289-314
[67] Strouboulis T, Babuska I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 43-69
[68] Onate E, Idelsohn S, Zienkiewicz O C et al. A finite point method in computational mechanics. Applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering, 1996, 39: 3839-3866
[69] Onate E, Idelsohn S. A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Computational Mechanics, 1998, 21: 283-292
[70] Atluri S N, Zhu T. A new Meshless local Petrov-Galerkin(MLPG) approach in computational mechanics. Computational Mechanics, 1998, 22(2): 117-127
[71] Atluri S N, Zhu T L. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25: 169-179
[72] Atluri S N, Zhu T L. New concepts in meshless methods. International Journal for Numerical Method in Engineering, 2000, 47: 537-556
[73] Atluri S N, Kim H G et al. A critical assessment of the truly meshless local Petrov-Galerkin(MLPG), and local boundary integral equation (LBIE)methods. Computational Mechanics 1999, 24: 348-372
[74] Atluri S N, Cho J Y, Kim H G.. Analysis of thin beam, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Computational Mechanics, 1999, 24: 334-347
[75] Lin H, Atluri S N. The Meshless Local Petrov-Galerkin(MLPG) Method for Solving Incompressible Navier-Stokes Equations. Computer Modeling in Engineering & Sciences(CMES), 2001, 2: 117-142
[76] Tang Z, Shen S, Atluri S N. Analysis of materials with strain gradient effects: A Meshless Local Petrov-Galerkin(MLPG) approach, with nodal displacements only. Computer Modeling in Engineering & Sciences(CMES), 2003, 4(1): 177-196
[77] Atluri S N, Shen S P. The Meshless Local Petrov-Galerkin(MLPG): a simple & less-costly alternative to the finite element and boundary element methods. CMES: Computer modeling in Engineering and Sciences, 2002, 3(1), 11-51
[78] Raju I S, Phillips D R, Krishnamurthy T. A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems. Computational Mechanics, 2004, 34: 464-474
[79]蔡永昌,朱合华,王建华.基于Voronoi结构的无网格局部Petrov-Galerkin方法.力学学报,2003,35(2):187-193
[80] Xiao J R. Local Heaviside weighted MLPG meshless methods for two-dimensional solids using compactly supported radial basis functions. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 117-138
[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] 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
[83] Liu G R, GuY T. A matrix triangularization algorithm for point interpolation method. Computer Methods in Applied Mechanics and Engineering, 2003, 28(1): 2269-2295
[84]吴宗敏.径向基函数、散乱数据拟和与无网格偏微分方程数值解.工程数学学报,2002,19(2):1-11
[85] Buhmann M D. Radial Basis Functions. Acta Numerica, 2000, 9: 1-38
[86] Wu Z M, Hon Y C. Convergence error estimate in solving free boundary diffusion problem by radial basis functions method. Engineering Analysis with Boundary Elements, 2003, 27: 73-79
[87] Wendland H. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematices, 1995, 4: 389-396
[88] Schaback R. Error estimation and condition number for radial basis function interpolation. Preprint, 1993
[89] Kansa E J. Multiquadrics-a scatered data approximation scheme with applications to computational fluid dynamics-I. Comp. Math. Applic., 1990, 19(8/9): 127-145
[90] Frink R. Scattered data interpolation: test of some methods. Mathematics of Computation, 1972, 38: 181-199
[91] Wong S M, Hon Y C, Li T S et al. Multizone decomposition of time-dependent problems using the multiquadric schem. Comput. Math. Applic., 1999, 37(8): 23-43
[92] Wu Z M. Multivariate compactly supported positive definite radial functions. Advances in Computational Mathematics, 1995, 4: 283-292
[93] Buhmann M D. Radial functions on compact support. Proceedings of the Edinburgh Mathematical Society, 1998, 41: 3-46
[94]张雄,刘岩.无网格法.北京,清华大学出版社,2004
[95] Song Kangzu, Zhang xiong, Lu Mingwan. Collocation with Modified Compactly Supported Radial Basis Function. Proceedings of International Conference on Computational Engineering & Sciences, August 19-25, 2001, Puerto Vallarta
[96] Wang J G, Liu G R. On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 2611-2630
[97] Wendland H. Meshless Galerkin method using radial basis functions. Math. Comput., 1999, 68(228): 1521-1531
[98]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
[99] Zhang X, Liu X H, Song K Z et al. Least-square collocation meshless method. International Journal for Numerical Methods in Engineering, 2001, 51(9): 1089-1100
[100]潘小飞,张雄,陆明万. Meshless Galerkin least square method.工程与科学中的计算力学,北京,2003
[101] Wu Z M. Solving PDE with radial basis functions and error estimation. In: Chen Z, Li Y,Micchelli CA et al. Advances in Computational Mathematics, Lecture Notes on Pure and Applied Mathematics, GuangZhou, 1998, 202
[102] Wu Z M, Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA Journal of Numerical Analysis, 1993, 13: 13-27
[103] Franke C, Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput., 1998, 93: 73-82
[104] Idelsohn S R, Onate E, Calvo N, Del P F. The meshless finite element method. International Journal for Numerical Methods in Engineering, 2003, 58: 893-912
[105] Sukumar N, Moran T, Belytschko T. The natural element method in solid mechanics. International Journal for Numerical Methods in Engineering, 1998, 43(5): 839-887
[106] Braun J, Sambridge. A numerical method for solving partial differential equation highly irregular evolving gride. Natural, 1995, 376: 655-660
[107]王兆清,冯伟.自然单元法研究进展.力学进展,2004,34(4):437-445
[108] Cueto E, Sukumar N, Calvol B et al. Overview and recent advances in natural neighbour Galerkin methods. Archives of Computational Methods in Engineering, 2003, 10(4): 307-384
[109]程玉民,彭妙娟,李九红.复变量移动最小二乘法及其应用.力学学报,2005,37(6):719-723
[110]程玉民,李九红.弹性力学的复变量无网格法.物理学报,2005,54(10):4463-4471
[111]程玉民,李九红.断裂力学的复变量无网格方法.中国科学G辑,2005,35(5):548-560
[112] Chati M K. Meshless standard and hypersingular boundary node method---applications in three dimensional potential theory and linear elasticity. Ph.D. thesis, Cornell Univversity, Ithaca, NY, 1999
[113] Mukherjee Y X, Mukherjee S. The boundary node method for potential problems. Internatioal Journal for Numerical Methods in Engineering, 1997, 40: 797-815
[114] Kothnur V S, Mukherjee S, Mukherjee Y X. Two dimensional linear elasticity by the boundary node method. International Journal of Solids and Structures, 1999, 36(8): 1129-1147
[115] Chati M K, Mukherjee S, Mukherjee Y X. The boundary node method for three-dimensional linear elasticity. International Journal for Numerical Methods in Engineering, 1999, 190: 1163–1184
[116] Chati M K and Mukherjee S. The boundary node method for three-dimensional problems in potential theory. International Journal for Numerical Methods in Engineering, 2000, 47:1523-1547
[117] Hwang W S. A boundary node method method for airfoils based on the Dirichlet condition. Computer Methods in Applied Mechanics and Engineering, 2000, 190: 1679-1688
[118] Zhu T, Zhang J, Atluri S N. A local boundary integral equation(LBIE) method in computational mechanics and a meshless discretization approach. Computational Mechanics, 1998, 21: 223-235
[119] Atluri S N, Sladek J, Sladek V et al. The local boundary integral equation(LBIE) and it’s meshless implementation for linear elasticity. Computational Mechanics. 2000, 25: 180-198
[120] Zhu T, Zhang J, Atluri S N. A local boundary integral equation(LBIE) method for solving nonlinear problems. Computational Mechanics, 1998, 22: 174-186
[121] Sladek V, Sladek J, Atluri S N et al. Numerical integration of singularities in meshless implementation of local boundary integral equations. Computational Mechanics, 2000, 25: 394-403
[122] Zhu Tulong. Meshless Methods in Computational Mechanics. Ph.d thesis, Georgia Institute of Techanology, 1998
[123] Sladek J, Sladek V, Atluri S N. Application of the local boundary integral equation(LBIE) method to boundary-value problems. International Applied Mechanics, 2002, 38(9): 1025-1047
[124]程玉民,陈美娟.弹性力学的一种边界无单元法.力学学报,2003,35(2):181-186
[125]程玉民,彭妙娟.弹性动力学的边界无单元法.中国科学,2005,35(4):435-448
[126]秦义校,程玉民.弹性力学的重构核离子边界无单元法.物理学报,2006,55(7):3215-22
[127] Zhang Jianming, Yao Zhenhan, Li Hong. A hybrid boundary node method. International Journal for Numerical Methods in Engineering, 2002, 53: 751-763
[128] Liu G R, Gu Y T. Boundary meshless methods based on the boundary point interpolation methods. Engineering Analysis with Boundary Elements, 2004, 28: 475-487
[129] Gu Y T, Liu G R. A boundary point interpolation method for stress analysis of solids. Computational Mechanics, 2002, 28(1): 47-54
[130] Huerta A, Fernandez-Mendez S. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering, 2000, 48: 1615-1636
[131] Wagner G J, Liu W K Hierarchical enrichment for bridging scales and mesh-free boundary conditions. International Journal for Numerical Methods in Engineering, 2001, 50: 507-524
[132] Hegen D. Element-free Galerkin methods in combination with finite element approaches. Computer Methods in Applied Mechanics and Engineering, 1996, 135: 143-166
[133] Attaway S, Heinstein M, Swegle J. Coupling of smooth particle hydrodynamics with the finite element method. Nucl. Eng. Des., 1994, 150:199–205
[134]李九红.复变量无网格方法及其应用研究.博士学位论文,西安理工大学,2004
[135] Park H, Liu W K. An introduction and tutorial on multiple-scale analysis in solids. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 1733-1772
[136] Abraham F F, Broughton J Q, Bernstein N et al. Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhysics Letters, 1998, 44(6): 783-787
[137] Qian D, Wagner G J, Liu W K. A multiscale projection method for the analysis of carbon nanotubes. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 1603-1632
[138] Xiao S P and Yang W X. A Nanoscale Meshfree Particle Method with the Implementation of Quasicontinuum Method. International Journal of Computational Methods, 2005, 2(3): 293-313
[139] Xiao S P, Yang W X. Temperature-related Cauchy-Born rule for multiscale modeling of crystalline solids. Computational Materials Science, 2006, 37: 374-379
[140] Liu M B, Liu G R, Lam K Y. Constructing smoothing functions in smoothed particle hydrodynamics applications. Journal of Computational and Applied Mathematics, 2003, 155(2): 263–284
[141] Quinlan N J, Basa M and Lastiwka M. Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering, 2006, 66: 2064-2085
[142] Maria G Armentano and Ricardo G Duran. Error estimates for moving least square approximations. Applied Numerical Mathematics, 2001, 37: 397-416
[143] Carlos Z. Good quality point sets and error estimates for moving least square approximations. Applied Numerical Mathematics, 2003, 47: 575-585
[144] Chung H J, Belytschko T. An error estimate in the EFG menthod. Computational Mechanics, 1998, 21: 91-100
[145] Krysl Petr and Belytschko T. Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering, 1997, 148: 257-277
[146] Liu G R, Tu Z H. An adaptive procedure based on background cells for meshless methods.Computer Methods in Applied Mechanics and Engineering, 2002, 191: 1923-1943
[147] Enrique P. Convergence and accuracy of the path integral approach for elastostatics. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 2191-2219
[148] Franke C, Schaback R. Convergence order estimates of the meshless collocation methods using radial basis functions. Advances in Computational Mathematics, 1998, 8: 381-399
[149] Wu Z, Hon Y C. Convergence error estimates in solving free boundary diffusion problem by radial basis functions. Engineering Analysis with Boundary Elements, 2003, 27, 73-79
[150] Gu Y T. Development of Meshless techniques for computational mechanics. Ph D thesis, National University of Singapore, 2002
[151] Atluri S N, Kim H G. Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin(MLPG) method. Computer Modeling in Engineering & Science, 2002: 1(3): 11-32
[152]张雄,宋康祖,陆明万.无网格法研究进展及其应用.计算力学学报,2003,20(6):731-741
[153]姜弘道,曹国金.无单元法研究和应用现状及动态.力学进展,2002,34(4):526-534
[154]李九红,程玉民.无网格方法的研究进展与展望.力学季刊,2006,27(1):143-152
[155]娄路亮,曾攀.影响无网格方法求解精度的因素分析.计算力学学报,2003,20(3):313-319
[156]刘欣,朱德懋,陆明万等.平面裂纹问题的h, p, hp型自适应无网格方法研究.力学学报,2000,32(3):308-318
[157] Wang M Z, Sun S L. The local boundary integral equation and mean value theorem in the theory of elasticity. Journal of Elasticity, 2002, 67: 51-59
[158] Song K Z, Zhang X. Meshless method based on collocation for elasto-plastic analysis. Proceedings of Internal Conference on Computational Engineering & Science. August, 20-25, 2000, Los Angeles, USA
[159]张雄,宋康祖,陆明万.紧支试函数加权残值法.力学学报,2003,35(1):43-49
[160]周进雄,李梅娥,张红艳,张陵.再生核质点法研究进展.力学进展,2002,32(4):535-544
[161]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
[162]史宝军,袁明武,舒东伟.基于核重构的最小二乘配点法求解Helmholtz方程.力学学报,2006,38(1):125-129
[163]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
[164]张见明,姚振汉.一种新型无网格法-杂交边界点法.中国计算力学大会,2001会议论文集,广州,2001,339-343
[165] Zhang X, Lu M W. A 2-D meshless model for jointed rock structures. Int. J. Numer. Methods Engrg., 2000, 47(10): 1649-1661
[166]寇晓东,周维垣.应用无单元法近似计算拱坝开裂.水利学报,2000,10:28-35
[167]张伟星,庞辉.弹性地基板计算的无单元法.工程力学,2000,17(3):138-144
[168]庞作会,葛修润.无网格伽辽金法在边坡开挖问题中的应用.岩土力学,1999,20(1):61-64
[169]陈建,吴林志,杜善义.采用无单元计算含边沿裂纹功能梯度材料板的应力强度因子.工程力学,2000,17(5):139-144
[170]曾清红,卢德唐.无网格方法求解稳定渗流问题.计算力学学报, 2003,20(4):440-445
[171]郭隽,陶智.非线性问题的MPS无网格算法.北京航空航天大学学报,2003,29(1):83-86
[172]张延军,王思敬.有限元与无网格伽辽金耦合法分析二相连续多孔介质.计算物理,2003,20(2):142-146
[173]娄路亮,曾攀等.应力高梯度问题的无网格分析.应用力学学报,2002,19(2):121-124
[174]袁振,李子然等.无网格法模拟复合型疲劳裂纹的扩展.工程力学,2002,19(1):25-28
[175]龙述尧.用无网格局部Petrov—Galerkin法分析非线性地基梁.力学季刊,2002,23(4):547-551
[176]李卧东,谭国焕等.无网格法在弹塑性问题中的应用.固体力学学报,2001,22(4):361-367
[177] Atluri S N, Shen P. The Meshless Local Petrov-Galerkin(MLPG) method. California: Tech Science Press, 2002
[178] Liu G R. Mesh Free Methods: Moving Beyond the Finite Method. CRC Press, 2002
[179] Liu G R, Liu M B Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific, 2003
[180] Li S F, Liu W K. Meshfree Particle Methods. Berlin Heidelberg: Springer-Verlag, 2004
[181] Chen G., Miki S., and Ohnishi Y, Automatic creation of mathematical meshes in manifold method of material analysis, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 105-126
[182] T.C.Ke, Artificial joint-based on manifold method, Working Forum on the Manifold ofMaterial Analysis, California, USA, 1995, 1: 21-38
[183] J.S.Lin, Continuous and discontinuous analysis using the manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 1-20
[184]王芝银,王思敬,杨志法,岩体大变形分析的流形方法,岩石力学与工程学报,1997,16(5):199-404
[185]朱以文,曾又林,岩石大变形分析的增量流形方法,岩石力学与工程学报,1999,18(1):1-5
[186]周维垣,杨若琼,剡公瑞,流形元法及其在工程中的应用,岩石力学与工程学报,1996,15(3):211-218
[187] G.H.Shi, Modeling rock joints and blocks by manifold method, Proceedings of 32nd U.S. Symposium on Rock Mechanics, 1992, Santa Fe. New Mexico, 639-648
[188]莫海鸿,陈尤雯,流形法在岩石力学研究中的应用,华南理工大学学报,1998,26(9):48-53
[189]王书法等,考虑侧向影响的数值流形方法及其工程应用,岩石力学与工程学报,2001,20(3):297-300
[190] J.Ghaboussi, Fully deformable discrete element analysis using a finite element approach, International Journal of Computers and Geotechnics, 1997, 5: 175-195
[191] G.H.Shi, Numerical manifold method, Proc. of the Second International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997, 1-35
[192] C.T.Lin, Extensions to the discontinuous deformation analysis for jointed rock masses and other blocky systems, Ph.D. University of Colorado, 1995
[193] G.H.Shi, R.E.Goodman, Generalization of two-dimensional discontinuous deformation analysis for forward modeling, International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13: 359-380
[194] J.S.Lin and D.H.Lee, Manifold method using polynomial basis function of any order, In: Proc. of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Berkeley, CA, 1996: 365-372
[195] Guangqi Chen, Yuzo Ohnishi and Takahiro Ito, Development of high order manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 132-154
[196] G.Q.Chen, Y.Ohnishi, T.Ito, Development of high order manifold method, InternationalJournal for Numerical Methods in Engineering, 1998, 43: 685-712
[197] Wang Shuilin, Ge Xiurun and Zhangguang, Manifold method with complete first order displacement function on physical cover, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[198]蔡永昌,张湘伟,数值流形方法在连续体数值分析中的应用,力学与实践,1999,21(6):53-54
[199]田荣,连续与非连续变形分析的有限覆盖无单元方法及其应用研究,博士论文,大连:大连理工大学,2000
[200]田荣,栾茂田等,高阶流形方法及其应用,工程力学,2001,18(2):21-26
[201] Shyu K., Salami M.R., Manifold method with four-node isoperimetric finite element method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 165-182
[202] Hideomi Ohtsubo, Katsuyuki Suzuki, etc, Utilization of finite covers in the manifold method for accuracy control, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 317-322
[203] Wang Shuilin, Ge Xiurun, Manifold method with four physical covers forming an element and its application, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[204] X.J.Qiu, Manifold method without use of penalty springs, In: Proc. of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Berkeley, CA, 1996: 205-249
[205] T.C.Ke, Artificial joint-based on manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 21-38
[206]曹文贵,速宝玉,流形元覆盖系统自动形成方法之研究,岩土工程学报,2001,23(2):187-190
[207]蔡永昌,张湘伟,流形方法的矩形覆盖系统及其全自动生成算法,重庆大学学报,2001,24(1):42-46
[208] J.Sheng, M.H.Chen, C.C.Chuang, Approximation theories for the manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 61-86
[209]骆少明,张湘伟,蔡永昌,数值流形方法的变分原理与应用,应用数学和力学,2001,22(6):587-592
[210]骆少明,张湘伟,蔡永昌,非线性数值流形方法的变分原理与应用,应用数学和力学,2000,21(12):1265-1270
[211] Sasaki T, Morikawa S, Ishii D and Yuzo O, Elastic-plastic analysis of jointed rock models by manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 309-316
[212]王书法,岩体弹塑性分析的数值流形方法,岩石力学与工程学报,2002,21(6):900-904
[213]王芝银等,数值流形方法中的几点改进,岩土工程学报,1998,20(6):33-36
[214] Te-Chih Ke and Jyh-Haw Tang, Modeling of solid-fluid interaction using the manifold method, Proceeding of 2nd North American Rock Mechanics Symposium. Montreal, Quebec. Canada, 1996: 1815-1822
[215]王水林,葛修润,受压状态下裂纹扩展的数值分析,岩土力学与工程学报,1999,18(6):671-675
[216] Ohnishi Yuzo, Tanaka Makoto, Koyama Tomofumi, Manifold method in saturated- unsaturated groundwater flow analysis, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[217] Guoxin Zhang, Yasuhito Sugiura and Hiroo Hasegawa, Crack propagation and thermal fracture analysis by manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 282-297
[218] Yaw-Jeen Chiou, Ren-Jow Tsay and Wailin Chuang, Crack propagation using manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 298-308
[219] Ren-Jow Tsay, Yaw-Jeen Chiou, and Wailin Chuang, Crack growth prediction by manifold method, Journal of Engineering Mechanics, 1999, 125(8): 884-890
[220] Yaw-Jeen Chiou, Yu-Min Lee, Ren-Jow Tsay, Mixed mode fracture propagation by manifold method, International Journal of Fracture, 2002, 114: 327-347
[221] D.M.Park, A stiffness derivative finite element technique for determination of crack tip stress intensity factor, International Journal of Fracture, 1974, 10: 487-502
[222] T.K.Hellen, On the method of virtual crack extensions, International Journal for Numerical Methods in Engineering, 1975, 9: 187-207
[223] L.Demkowicz, J.T.Oden, W.Rachowicz and O.Hardy, Toward a universal h-p adaptive finite element strategy, Part I. Constrained approximation and data structure, Computer Methods in Applied Mechanics and Engineering, 1989, 77: 79-112
[224]王水林,葛修润,流形方法在模拟裂纹扩展中的应用,岩石力学与工程学报,1997,16(5):405-410
[225]李树忱,程玉民,裂纹扩展分析的无网格流形方法,岩石力学与工程学报,2005,24(7):1187-1195
[226] S. C. Li, S. C. Li and Y. M. Cheng. Enriched meshless manifold method for two-dimensional crack modeling, Theoretical and Applied Fracture Mechanics, 2005, 44(3): 201-346
[227]李树忱,程玉民,李术才.扩展的无网格流形方法,岩石力学与工程学报,2005,24(12):2065-2073
[228] Lin Dezhang, Mo Haihong, Manifold method of material analysis, The University of Oklahoma, 1994
[229] Zhou Weiyuan, Qiang Yang and Xiaodong Kou, Manifold method and its applications to engineering, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 274-281
[230] Zhou Weiyuan, Xiaodong Kou and Yang Ruoqiong, Crack propagation by manifold method coupled with element free method, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[231]刘欣等,基于流形覆盖思想的无网格方法研究,计算力学学报,2001,18(1):21-27
[232]栾茂田,张大林,田荣,有限覆盖无单元法在裂纹扩展数值分析问题中的应用,岩土工程学报,2003,25(5):527-531
[233]栾茂田,田荣等,有限覆盖无单元法在岩土类弱拉型材料摩擦接触问题中的应用,岩土工程学报,2002,24(2):137-141
[234]李树忱,断续节理岩体的无网格流形方法和实验研究,[博士论文],上海:上海大学,2004
[235]李树忱,程玉民,基于单位分解法的无网格流形方法,力学学报,2004,36(4):496-500
[236]李树忱,程玉民.数值流形方法及其在岩石力学中的应用,力学进展,2004, 34(4):446-454
[237]高洪芬,程玉民,弹性力学的复变量数值流形方法,力学学报,2009,41(3):480-488
[238] S. Li, Y. Cheng, Y.-F. Wu. Numerical manifold method based on the method of weighted residuals, Computational Mechanics, 2005, 35(6): 470-480
[239]李树忱,程玉民.考虑裂纹尖端场的数值流形方法,土木工程学报,2005,38(7):96-101
[240]李树忱,程玉民,李术才.动态断裂力学的无网格流形方法,物理学报,2006,55(9):4760-4766
[241]陈丽,程玉民.瞬态热传导问题的复变量重构核粒子法,物理学报,2008,57(10):6047-6055
[242]程荣军,程玉民.势问题的无单元Galerkin方法的误差估计,物理学报,2008,57(10):6037-6046
[243]秦义校,程玉民.温度场分析的重构核粒子边界无单元法,机械工程学报,2008,44(6):95-100
[244]秦义校,程玉民.势问题的重构核粒子边界无单元法,力学学报,2009, 41(6): 898-905
[245] Chen Y M,Wilkins M L. Numerical analysis of dynamic crack problems. In: G C Sih Ed Mechanics ofFracture, Volume 4 [C], Leyden: Noordhoff, 1977
[246] Aliabadi M H. Boundary element formulations in fracture mechanics. AppL Mech, Rev., 1997, 50(2): 83-96
[247] Sladek J. Dynamics stress intensity fracturs studied by boundary integro-differential equations. Int. J. NumerMethods Engng, 1986; 23(5): 919-928
[248]程玉民,嵇醒,臧跃龙. Fourier本征变换在断裂动力学边界元法中的应用,同济大学学报,1996,24(3):251-256
[249] Cheng Yumin, Ji Xing. An Investigation on a New Integral Transform Boundary Element Methods for Elastodynamics. Acta Meehanica Solida Sinica, l 997; 10(3): 26-29
[250]程玉民,嵇醒.动态断裂力学的无限相似边界元法.力学学报,2004;36(1):43-48
[2]徐次达.固体力学加权残值法.上海:同济大学出版社,1978
[3] Zienkiewicz O C. The finite element method (Third edition). McGraw-Hill, 1977
[4]李开泰,黄艾香,黄庆怀.有限元方法及其应用(修订本).西安:西安交通大学出版社,1992
[5]嵇醒,臧跃龙,程玉民.边界元进展及通用程序.上海:同济大学出版社,1997
[6] Brebbia C A. The Boundary Element Method for Engineers. London Pentech Press, 1978
[7] Belytschko T, Krongauz Y, Organ D et al. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 3-47
[8] Li Shaofan, Liu W K. Meshless and particles methods and their applications. Applied Mechanics Review, 2002, 55(1): 1-34
[9] G.H.Shi, Manifold method of material analysis, Transaction of the Ninth Army Conference on Applied Mathematics and Computing Minneapolis, USA, 1992
[10] Jeen-Shang Lin, A mesh-based Partition of Unity Method for Discontinuity Modeling[J]. Computer Methods and Applied Mechanics in Engineering 2003(192), 1515-1532.
[11] Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astrophysical Journal, 1977, 8(12): 1013-1024
[12] Gingold R A, Moraghan J J. Smoothed particle hydrodynamics: theory and applications to nonspherical stars. Mon Not Roy Astrou Soc, 1977, 18: 375-389
[13] Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys, 1995, 116: 123-134
[14] Chen J K, Beraun J E, Jih C J. An improvement for tensile instability in smoothed particle hydrodynamics. Computational Mechanics, 1998, 23: 279-287
[15] Johnsons G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 2002, 53: 825-843
[16] Lancaster P, Salkauskas K. Surfaces generated by moving least square methods. Mathematics of Computation, 1981, 37: 141-158
[17] Nayroles B Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10: 307-318
[18] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin Methods. International Journal for Numerical Methods in Engineering, 1994, 37: 229-256
[19] Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Computational Mechanics, 1999, 23: 219-230
[20] Belytschko T, Krongauz Y et al. Smoothing and accelerated computations in the element free Galerkin method. J. Comput. Appl. Math., 1996, 74: 111-126
[21] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. International Journal for Numerical Methods in Engineering, 1998, 41: 1215-1233
[22] Belytschko T, Gu L, Lu Y Y. Fracture and crack growth by element free Galerkin methods. Modlling Simul. Mater. Sci. Eng.. 1994, 2: 519-534
[23] Lu Y Y, Belytschko T. Element-free Galerkin methods for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Engineering, 1995, 126: 131-153
[24] Krysl P, Belytschko T. ESFLIB: A library to compute the element free Galerkin shape functions. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 2181-2205
[25] Krysl P, Belytschko T. Analysis of thin shells by element-free Galerkin method. Computational Mechanics, 1995, 17: 26-35
[26] Belytschko T, Lu Y Y, Gu L, Tabbara M. Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures, 1995, 32: 2547-2570
[27] Sukumar N, Moran B, Black T, Belytschko T. An element-free Galerkin method for three-dimensional fracture mechanics. Computational Mechanics, 1997, 20: 170-175
[28] 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
[29] Xu Y, Saigal S. An Element Free Galerkin analysis of steady dynamic growth of a mode I crack in elastic-plastic materials. International Journal of sounds and structures, 1999, 36: 1045-1079
[30] Kargarmovin M H, Toussi H E, Faribotz S J. Elasto-plastic element-free Galerkin method. Computational Mechanics, 2004, 33(3): 206-214
[31] Bouillard Ph, Seleau S. Element-free Galerkin solutions for Helmholtz problems: formulation and numerical assessment of the pollution effect. Computer Methods in Applied Mechanics and Engineering, 1998, 162: 317-335
[32] Lee S H, Yoon Y C. An improved crack analysis technique by element-free Galerkin. International Journal for Numerical Methods in Engineering, 2003, 56: 1291-1314
[33] Rao B N and Rahman S. An enriched meshless method for non-linear enriched fracture mechanics. International Journal for Numerical Methods in Engineering, 2004, 59: 197-223
[34] Fleming M, Chu Y A, Moran B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, 1997, 40: 1483-1504
[35] Beissel S, Belytschko T. Nodal integration of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 49-74
[36] Smolinski P, Palmer T. Procedures for multi-time step integration of element free Galerkin methods for diffusion problems. Comput. Struct., 2000, 77: 171-183
[37] Mukherjee Y X, Mukherjee S. On boundary conditions in the element-free Galerkin method. Computational Mechanics, 1997, 19: 264-270
[38] Alves M K, Rossi R. A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function. International Journal for Numerical Methods in Engineering, 2003, 57: 1523-1552
[39] Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering, 1997, 40: 2953-2974
[40] Ponthot J P, Belytschko T. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1998, 152: 19-46
[41] Liew K M, Ren J and Kitipornchai S. Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method. Engineering Analysis with Boundary Elements, 2004, 28: 497-507
[42] Liu G R, Gu Y T. Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Computational Mechanics, 2000, 26: 166-173
[43] Belytschko T, Organ D, Krongauz Y. A coupled finite element- element free Galerkin method. Computational Mechanics, 1995, 17: 186-195
[44] Krysl P, Belytschko T. Element-free Galerkin method convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering, 1997, 148: 257-277
[45] Chung H J, Belytschko T. An error estimate in the EFG menthod. Computational Mechanics,1998, 21: 91-100
[46] Gavete L, Falcon S, Ruiz A. An error indicator for the element free Galerkin method. Eur. J. Mech. A/Solids, 2001, 20, 327-341
[47] Liu W K, Jun S, Zhang Y F. Reproducing kernel partical methods. International Journal for Numerical Methods in Fluid, 1995, 20: 1081-1106
[48] Voth T E, Christon M A. Discretization errors associated with reproducing kernel methods: one-dimensional domains. Computer Methods in Applied Mechanics and Engineering, 1996, 190: 2429-2446
[49] Han W, Meng X. Error analysis of the reproducing kernel particle method. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 6157-6181
[50] Chen J S, Pan C, Wu C T, Liu W K. Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 195-227
[51] Liew K M, Ng T Y, Wu Y C. Meshfree method for large deformation analysis–a reproducing kernel particle approach. Engineering structures, 2002, 24: 543-551
[52] Li S, Liu W K. Moving least-square reproducing kernel method (I) Methodology and Convergence. Computer Methods in Applied Mechanics and Engineering, 1997, 143: 113-154
[53] Li S, Liu W K. Moving least-square reproducing kernel method Part II Fourier analysis. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 159-193
[54] Chen J S, Yoon S, Wang H P, Liu W K. An improved reproducing kernel particle method for nearly incompressible finite elasticity. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 117-145
[55] Danielson K T, Hao S, Liu W K et al. Parallel computation of meshless methods for explicit dynamic analysis. International Journal for Numerical Methods in Engineering, 2000, 47: 1323-1341
[56] Chen J S, Han W, You Y, Meng X. A reproducing kernel method with nodal interpolation property. International Journal for Numerical Methods in Engineering, 2003, 56: 935-960
[57] Liu W K, Chen Y, Uras R A, Chang C T. Generalized multiple scale reproducing kernel particle. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 91-157
[58] Liu W K, Chen Y J. Wavelet and multiple scale reproducing kernel methods. International Journal of Numerical Methods in Fluids, 1995, 21: 901-931
[59] Uras R A, Cheng C T, Chen Y et al. Multiresolution reproducing kernel particle methods in acoustics. J. Comput. Acoust., 1997, 5: 71-94
[60] Liu W K, Jun S et al. Multiresolution reproducing kernel particle methods for computational fluid dynamics. International Journal for Numerical Methods in Fluid, 1997, 24: 1391-1415
[61] Liu W K, Jun S. Multiple-scale reproducing kernel particle methods for large deformation problem. International Journal for Numerical Methods in Engineering, 1998, 41: 1339-1362
[62] Duarte C A, Oden J T. Hp clouds - a meshless method to solve boundary-value problems. Technical Report 95-05. Texas Institute for Computational and Applied Mathematics, University of Texas at Austin, 1995
[63] Duarte A, Oden J T. Hp clouds: a h-p meshless method. Numerical Methods for Partial Differential Equations, 1996, 12: 673-705
[64] Duarte M, Oden J T. An h-p adptive method using clouds. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 237-262
[65] Oden J T, Duarte A, Zienkiewicz O C. A new cloud-based hp finite element method. International Journal for Numerical Methods in Engineering, 1998, 50: 160-170
[66] Babuska I, Melenk J M. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 289-314
[67] Strouboulis T, Babuska I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering, 2000, 181: 43-69
[68] Onate E, Idelsohn S, Zienkiewicz O C et al. A finite point method in computational mechanics. Applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering, 1996, 39: 3839-3866
[69] Onate E, Idelsohn S. A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Computational Mechanics, 1998, 21: 283-292
[70] Atluri S N, Zhu T. A new Meshless local Petrov-Galerkin(MLPG) approach in computational mechanics. Computational Mechanics, 1998, 22(2): 117-127
[71] Atluri S N, Zhu T L. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, 2000, 25: 169-179
[72] Atluri S N, Zhu T L. New concepts in meshless methods. International Journal for Numerical Method in Engineering, 2000, 47: 537-556
[73] Atluri S N, Kim H G et al. A critical assessment of the truly meshless local Petrov-Galerkin(MLPG), and local boundary integral equation (LBIE)methods. Computational Mechanics 1999, 24: 348-372
[74] Atluri S N, Cho J Y, Kim H G.. Analysis of thin beam, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Computational Mechanics, 1999, 24: 334-347
[75] Lin H, Atluri S N. The Meshless Local Petrov-Galerkin(MLPG) Method for Solving Incompressible Navier-Stokes Equations. Computer Modeling in Engineering & Sciences(CMES), 2001, 2: 117-142
[76] Tang Z, Shen S, Atluri S N. Analysis of materials with strain gradient effects: A Meshless Local Petrov-Galerkin(MLPG) approach, with nodal displacements only. Computer Modeling in Engineering & Sciences(CMES), 2003, 4(1): 177-196
[77] Atluri S N, Shen S P. The Meshless Local Petrov-Galerkin(MLPG): a simple & less-costly alternative to the finite element and boundary element methods. CMES: Computer modeling in Engineering and Sciences, 2002, 3(1), 11-51
[78] Raju I S, Phillips D R, Krishnamurthy T. A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems. Computational Mechanics, 2004, 34: 464-474
[79]蔡永昌,朱合华,王建华.基于Voronoi结构的无网格局部Petrov-Galerkin方法.力学学报,2003,35(2):187-193
[80] Xiao J R. Local Heaviside weighted MLPG meshless methods for two-dimensional solids using compactly supported radial basis functions. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 117-138
[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] 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
[83] Liu G R, GuY T. A matrix triangularization algorithm for point interpolation method. Computer Methods in Applied Mechanics and Engineering, 2003, 28(1): 2269-2295
[84]吴宗敏.径向基函数、散乱数据拟和与无网格偏微分方程数值解.工程数学学报,2002,19(2):1-11
[85] Buhmann M D. Radial Basis Functions. Acta Numerica, 2000, 9: 1-38
[86] Wu Z M, Hon Y C. Convergence error estimate in solving free boundary diffusion problem by radial basis functions method. Engineering Analysis with Boundary Elements, 2003, 27: 73-79
[87] Wendland H. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematices, 1995, 4: 389-396
[88] Schaback R. Error estimation and condition number for radial basis function interpolation. Preprint, 1993
[89] Kansa E J. Multiquadrics-a scatered data approximation scheme with applications to computational fluid dynamics-I. Comp. Math. Applic., 1990, 19(8/9): 127-145
[90] Frink R. Scattered data interpolation: test of some methods. Mathematics of Computation, 1972, 38: 181-199
[91] Wong S M, Hon Y C, Li T S et al. Multizone decomposition of time-dependent problems using the multiquadric schem. Comput. Math. Applic., 1999, 37(8): 23-43
[92] Wu Z M. Multivariate compactly supported positive definite radial functions. Advances in Computational Mathematics, 1995, 4: 283-292
[93] Buhmann M D. Radial functions on compact support. Proceedings of the Edinburgh Mathematical Society, 1998, 41: 3-46
[94]张雄,刘岩.无网格法.北京,清华大学出版社,2004
[95] Song Kangzu, Zhang xiong, Lu Mingwan. Collocation with Modified Compactly Supported Radial Basis Function. Proceedings of International Conference on Computational Engineering & Sciences, August 19-25, 2001, Puerto Vallarta
[96] Wang J G, Liu G R. On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 2611-2630
[97] Wendland H. Meshless Galerkin method using radial basis functions. Math. Comput., 1999, 68(228): 1521-1531
[98]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
[99] Zhang X, Liu X H, Song K Z et al. Least-square collocation meshless method. International Journal for Numerical Methods in Engineering, 2001, 51(9): 1089-1100
[100]潘小飞,张雄,陆明万. Meshless Galerkin least square method.工程与科学中的计算力学,北京,2003
[101] Wu Z M. Solving PDE with radial basis functions and error estimation. In: Chen Z, Li Y,Micchelli CA et al. Advances in Computational Mathematics, Lecture Notes on Pure and Applied Mathematics, GuangZhou, 1998, 202
[102] Wu Z M, Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA Journal of Numerical Analysis, 1993, 13: 13-27
[103] Franke C, Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput., 1998, 93: 73-82
[104] Idelsohn S R, Onate E, Calvo N, Del P F. The meshless finite element method. International Journal for Numerical Methods in Engineering, 2003, 58: 893-912
[105] Sukumar N, Moran T, Belytschko T. The natural element method in solid mechanics. International Journal for Numerical Methods in Engineering, 1998, 43(5): 839-887
[106] Braun J, Sambridge. A numerical method for solving partial differential equation highly irregular evolving gride. Natural, 1995, 376: 655-660
[107]王兆清,冯伟.自然单元法研究进展.力学进展,2004,34(4):437-445
[108] Cueto E, Sukumar N, Calvol B et al. Overview and recent advances in natural neighbour Galerkin methods. Archives of Computational Methods in Engineering, 2003, 10(4): 307-384
[109]程玉民,彭妙娟,李九红.复变量移动最小二乘法及其应用.力学学报,2005,37(6):719-723
[110]程玉民,李九红.弹性力学的复变量无网格法.物理学报,2005,54(10):4463-4471
[111]程玉民,李九红.断裂力学的复变量无网格方法.中国科学G辑,2005,35(5):548-560
[112] Chati M K. Meshless standard and hypersingular boundary node method---applications in three dimensional potential theory and linear elasticity. Ph.D. thesis, Cornell Univversity, Ithaca, NY, 1999
[113] Mukherjee Y X, Mukherjee S. The boundary node method for potential problems. Internatioal Journal for Numerical Methods in Engineering, 1997, 40: 797-815
[114] Kothnur V S, Mukherjee S, Mukherjee Y X. Two dimensional linear elasticity by the boundary node method. International Journal of Solids and Structures, 1999, 36(8): 1129-1147
[115] Chati M K, Mukherjee S, Mukherjee Y X. The boundary node method for three-dimensional linear elasticity. International Journal for Numerical Methods in Engineering, 1999, 190: 1163–1184
[116] Chati M K and Mukherjee S. The boundary node method for three-dimensional problems in potential theory. International Journal for Numerical Methods in Engineering, 2000, 47:1523-1547
[117] Hwang W S. A boundary node method method for airfoils based on the Dirichlet condition. Computer Methods in Applied Mechanics and Engineering, 2000, 190: 1679-1688
[118] Zhu T, Zhang J, Atluri S N. A local boundary integral equation(LBIE) method in computational mechanics and a meshless discretization approach. Computational Mechanics, 1998, 21: 223-235
[119] Atluri S N, Sladek J, Sladek V et al. The local boundary integral equation(LBIE) and it’s meshless implementation for linear elasticity. Computational Mechanics. 2000, 25: 180-198
[120] Zhu T, Zhang J, Atluri S N. A local boundary integral equation(LBIE) method for solving nonlinear problems. Computational Mechanics, 1998, 22: 174-186
[121] Sladek V, Sladek J, Atluri S N et al. Numerical integration of singularities in meshless implementation of local boundary integral equations. Computational Mechanics, 2000, 25: 394-403
[122] Zhu Tulong. Meshless Methods in Computational Mechanics. Ph.d thesis, Georgia Institute of Techanology, 1998
[123] Sladek J, Sladek V, Atluri S N. Application of the local boundary integral equation(LBIE) method to boundary-value problems. International Applied Mechanics, 2002, 38(9): 1025-1047
[124]程玉民,陈美娟.弹性力学的一种边界无单元法.力学学报,2003,35(2):181-186
[125]程玉民,彭妙娟.弹性动力学的边界无单元法.中国科学,2005,35(4):435-448
[126]秦义校,程玉民.弹性力学的重构核离子边界无单元法.物理学报,2006,55(7):3215-22
[127] Zhang Jianming, Yao Zhenhan, Li Hong. A hybrid boundary node method. International Journal for Numerical Methods in Engineering, 2002, 53: 751-763
[128] Liu G R, Gu Y T. Boundary meshless methods based on the boundary point interpolation methods. Engineering Analysis with Boundary Elements, 2004, 28: 475-487
[129] Gu Y T, Liu G R. A boundary point interpolation method for stress analysis of solids. Computational Mechanics, 2002, 28(1): 47-54
[130] Huerta A, Fernandez-Mendez S. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering, 2000, 48: 1615-1636
[131] Wagner G J, Liu W K Hierarchical enrichment for bridging scales and mesh-free boundary conditions. International Journal for Numerical Methods in Engineering, 2001, 50: 507-524
[132] Hegen D. Element-free Galerkin methods in combination with finite element approaches. Computer Methods in Applied Mechanics and Engineering, 1996, 135: 143-166
[133] Attaway S, Heinstein M, Swegle J. Coupling of smooth particle hydrodynamics with the finite element method. Nucl. Eng. Des., 1994, 150:199–205
[134]李九红.复变量无网格方法及其应用研究.博士学位论文,西安理工大学,2004
[135] Park H, Liu W K. An introduction and tutorial on multiple-scale analysis in solids. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 1733-1772
[136] Abraham F F, Broughton J Q, Bernstein N et al. Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhysics Letters, 1998, 44(6): 783-787
[137] Qian D, Wagner G J, Liu W K. A multiscale projection method for the analysis of carbon nanotubes. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 1603-1632
[138] Xiao S P and Yang W X. A Nanoscale Meshfree Particle Method with the Implementation of Quasicontinuum Method. International Journal of Computational Methods, 2005, 2(3): 293-313
[139] Xiao S P, Yang W X. Temperature-related Cauchy-Born rule for multiscale modeling of crystalline solids. Computational Materials Science, 2006, 37: 374-379
[140] Liu M B, Liu G R, Lam K Y. Constructing smoothing functions in smoothed particle hydrodynamics applications. Journal of Computational and Applied Mathematics, 2003, 155(2): 263–284
[141] Quinlan N J, Basa M and Lastiwka M. Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering, 2006, 66: 2064-2085
[142] Maria G Armentano and Ricardo G Duran. Error estimates for moving least square approximations. Applied Numerical Mathematics, 2001, 37: 397-416
[143] Carlos Z. Good quality point sets and error estimates for moving least square approximations. Applied Numerical Mathematics, 2003, 47: 575-585
[144] Chung H J, Belytschko T. An error estimate in the EFG menthod. Computational Mechanics, 1998, 21: 91-100
[145] Krysl Petr and Belytschko T. Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering, 1997, 148: 257-277
[146] Liu G R, Tu Z H. An adaptive procedure based on background cells for meshless methods.Computer Methods in Applied Mechanics and Engineering, 2002, 191: 1923-1943
[147] Enrique P. Convergence and accuracy of the path integral approach for elastostatics. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 2191-2219
[148] Franke C, Schaback R. Convergence order estimates of the meshless collocation methods using radial basis functions. Advances in Computational Mathematics, 1998, 8: 381-399
[149] Wu Z, Hon Y C. Convergence error estimates in solving free boundary diffusion problem by radial basis functions. Engineering Analysis with Boundary Elements, 2003, 27, 73-79
[150] Gu Y T. Development of Meshless techniques for computational mechanics. Ph D thesis, National University of Singapore, 2002
[151] Atluri S N, Kim H G. Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin(MLPG) method. Computer Modeling in Engineering & Science, 2002: 1(3): 11-32
[152]张雄,宋康祖,陆明万.无网格法研究进展及其应用.计算力学学报,2003,20(6):731-741
[153]姜弘道,曹国金.无单元法研究和应用现状及动态.力学进展,2002,34(4):526-534
[154]李九红,程玉民.无网格方法的研究进展与展望.力学季刊,2006,27(1):143-152
[155]娄路亮,曾攀.影响无网格方法求解精度的因素分析.计算力学学报,2003,20(3):313-319
[156]刘欣,朱德懋,陆明万等.平面裂纹问题的h, p, hp型自适应无网格方法研究.力学学报,2000,32(3):308-318
[157] Wang M Z, Sun S L. The local boundary integral equation and mean value theorem in the theory of elasticity. Journal of Elasticity, 2002, 67: 51-59
[158] Song K Z, Zhang X. Meshless method based on collocation for elasto-plastic analysis. Proceedings of Internal Conference on Computational Engineering & Science. August, 20-25, 2000, Los Angeles, USA
[159]张雄,宋康祖,陆明万.紧支试函数加权残值法.力学学报,2003,35(1):43-49
[160]周进雄,李梅娥,张红艳,张陵.再生核质点法研究进展.力学进展,2002,32(4):535-544
[161]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
[162]史宝军,袁明武,舒东伟.基于核重构的最小二乘配点法求解Helmholtz方程.力学学报,2006,38(1):125-129
[163]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
[164]张见明,姚振汉.一种新型无网格法-杂交边界点法.中国计算力学大会,2001会议论文集,广州,2001,339-343
[165] Zhang X, Lu M W. A 2-D meshless model for jointed rock structures. Int. J. Numer. Methods Engrg., 2000, 47(10): 1649-1661
[166]寇晓东,周维垣.应用无单元法近似计算拱坝开裂.水利学报,2000,10:28-35
[167]张伟星,庞辉.弹性地基板计算的无单元法.工程力学,2000,17(3):138-144
[168]庞作会,葛修润.无网格伽辽金法在边坡开挖问题中的应用.岩土力学,1999,20(1):61-64
[169]陈建,吴林志,杜善义.采用无单元计算含边沿裂纹功能梯度材料板的应力强度因子.工程力学,2000,17(5):139-144
[170]曾清红,卢德唐.无网格方法求解稳定渗流问题.计算力学学报, 2003,20(4):440-445
[171]郭隽,陶智.非线性问题的MPS无网格算法.北京航空航天大学学报,2003,29(1):83-86
[172]张延军,王思敬.有限元与无网格伽辽金耦合法分析二相连续多孔介质.计算物理,2003,20(2):142-146
[173]娄路亮,曾攀等.应力高梯度问题的无网格分析.应用力学学报,2002,19(2):121-124
[174]袁振,李子然等.无网格法模拟复合型疲劳裂纹的扩展.工程力学,2002,19(1):25-28
[175]龙述尧.用无网格局部Petrov—Galerkin法分析非线性地基梁.力学季刊,2002,23(4):547-551
[176]李卧东,谭国焕等.无网格法在弹塑性问题中的应用.固体力学学报,2001,22(4):361-367
[177] Atluri S N, Shen P. The Meshless Local Petrov-Galerkin(MLPG) method. California: Tech Science Press, 2002
[178] Liu G R. Mesh Free Methods: Moving Beyond the Finite Method. CRC Press, 2002
[179] Liu G R, Liu M B Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific, 2003
[180] Li S F, Liu W K. Meshfree Particle Methods. Berlin Heidelberg: Springer-Verlag, 2004
[181] Chen G., Miki S., and Ohnishi Y, Automatic creation of mathematical meshes in manifold method of material analysis, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 105-126
[182] T.C.Ke, Artificial joint-based on manifold method, Working Forum on the Manifold ofMaterial Analysis, California, USA, 1995, 1: 21-38
[183] J.S.Lin, Continuous and discontinuous analysis using the manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 1-20
[184]王芝银,王思敬,杨志法,岩体大变形分析的流形方法,岩石力学与工程学报,1997,16(5):199-404
[185]朱以文,曾又林,岩石大变形分析的增量流形方法,岩石力学与工程学报,1999,18(1):1-5
[186]周维垣,杨若琼,剡公瑞,流形元法及其在工程中的应用,岩石力学与工程学报,1996,15(3):211-218
[187] G.H.Shi, Modeling rock joints and blocks by manifold method, Proceedings of 32nd U.S. Symposium on Rock Mechanics, 1992, Santa Fe. New Mexico, 639-648
[188]莫海鸿,陈尤雯,流形法在岩石力学研究中的应用,华南理工大学学报,1998,26(9):48-53
[189]王书法等,考虑侧向影响的数值流形方法及其工程应用,岩石力学与工程学报,2001,20(3):297-300
[190] J.Ghaboussi, Fully deformable discrete element analysis using a finite element approach, International Journal of Computers and Geotechnics, 1997, 5: 175-195
[191] G.H.Shi, Numerical manifold method, Proc. of the Second International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997, 1-35
[192] C.T.Lin, Extensions to the discontinuous deformation analysis for jointed rock masses and other blocky systems, Ph.D. University of Colorado, 1995
[193] G.H.Shi, R.E.Goodman, Generalization of two-dimensional discontinuous deformation analysis for forward modeling, International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13: 359-380
[194] J.S.Lin and D.H.Lee, Manifold method using polynomial basis function of any order, In: Proc. of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Berkeley, CA, 1996: 365-372
[195] Guangqi Chen, Yuzo Ohnishi and Takahiro Ito, Development of high order manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 132-154
[196] G.Q.Chen, Y.Ohnishi, T.Ito, Development of high order manifold method, InternationalJournal for Numerical Methods in Engineering, 1998, 43: 685-712
[197] Wang Shuilin, Ge Xiurun and Zhangguang, Manifold method with complete first order displacement function on physical cover, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[198]蔡永昌,张湘伟,数值流形方法在连续体数值分析中的应用,力学与实践,1999,21(6):53-54
[199]田荣,连续与非连续变形分析的有限覆盖无单元方法及其应用研究,博士论文,大连:大连理工大学,2000
[200]田荣,栾茂田等,高阶流形方法及其应用,工程力学,2001,18(2):21-26
[201] Shyu K., Salami M.R., Manifold method with four-node isoperimetric finite element method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 165-182
[202] Hideomi Ohtsubo, Katsuyuki Suzuki, etc, Utilization of finite covers in the manifold method for accuracy control, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 317-322
[203] Wang Shuilin, Ge Xiurun, Manifold method with four physical covers forming an element and its application, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[204] X.J.Qiu, Manifold method without use of penalty springs, In: Proc. of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Berkeley, CA, 1996: 205-249
[205] T.C.Ke, Artificial joint-based on manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 21-38
[206]曹文贵,速宝玉,流形元覆盖系统自动形成方法之研究,岩土工程学报,2001,23(2):187-190
[207]蔡永昌,张湘伟,流形方法的矩形覆盖系统及其全自动生成算法,重庆大学学报,2001,24(1):42-46
[208] J.Sheng, M.H.Chen, C.C.Chuang, Approximation theories for the manifold method, Working Forum on the Manifold of Material Analysis, California, USA, 1995, 1: 61-86
[209]骆少明,张湘伟,蔡永昌,数值流形方法的变分原理与应用,应用数学和力学,2001,22(6):587-592
[210]骆少明,张湘伟,蔡永昌,非线性数值流形方法的变分原理与应用,应用数学和力学,2000,21(12):1265-1270
[211] Sasaki T, Morikawa S, Ishii D and Yuzo O, Elastic-plastic analysis of jointed rock models by manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 309-316
[212]王书法,岩体弹塑性分析的数值流形方法,岩石力学与工程学报,2002,21(6):900-904
[213]王芝银等,数值流形方法中的几点改进,岩土工程学报,1998,20(6):33-36
[214] Te-Chih Ke and Jyh-Haw Tang, Modeling of solid-fluid interaction using the manifold method, Proceeding of 2nd North American Rock Mechanics Symposium. Montreal, Quebec. Canada, 1996: 1815-1822
[215]王水林,葛修润,受压状态下裂纹扩展的数值分析,岩土力学与工程学报,1999,18(6):671-675
[216] Ohnishi Yuzo, Tanaka Makoto, Koyama Tomofumi, Manifold method in saturated- unsaturated groundwater flow analysis, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[217] Guoxin Zhang, Yasuhito Sugiura and Hiroo Hasegawa, Crack propagation and thermal fracture analysis by manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 282-297
[218] Yaw-Jeen Chiou, Ren-Jow Tsay and Wailin Chuang, Crack propagation using manifold method, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 298-308
[219] Ren-Jow Tsay, Yaw-Jeen Chiou, and Wailin Chuang, Crack growth prediction by manifold method, Journal of Engineering Mechanics, 1999, 125(8): 884-890
[220] Yaw-Jeen Chiou, Yu-Min Lee, Ren-Jow Tsay, Mixed mode fracture propagation by manifold method, International Journal of Fracture, 2002, 114: 327-347
[221] D.M.Park, A stiffness derivative finite element technique for determination of crack tip stress intensity factor, International Journal of Fracture, 1974, 10: 487-502
[222] T.K.Hellen, On the method of virtual crack extensions, International Journal for Numerical Methods in Engineering, 1975, 9: 187-207
[223] L.Demkowicz, J.T.Oden, W.Rachowicz and O.Hardy, Toward a universal h-p adaptive finite element strategy, Part I. Constrained approximation and data structure, Computer Methods in Applied Mechanics and Engineering, 1989, 77: 79-112
[224]王水林,葛修润,流形方法在模拟裂纹扩展中的应用,岩石力学与工程学报,1997,16(5):405-410
[225]李树忱,程玉民,裂纹扩展分析的无网格流形方法,岩石力学与工程学报,2005,24(7):1187-1195
[226] S. C. Li, S. C. Li and Y. M. Cheng. Enriched meshless manifold method for two-dimensional crack modeling, Theoretical and Applied Fracture Mechanics, 2005, 44(3): 201-346
[227]李树忱,程玉民,李术才.扩展的无网格流形方法,岩石力学与工程学报,2005,24(12):2065-2073
[228] Lin Dezhang, Mo Haihong, Manifold method of material analysis, The University of Oklahoma, 1994
[229] Zhou Weiyuan, Qiang Yang and Xiaodong Kou, Manifold method and its applications to engineering, Proc. of the 2nd International Conference on Analysis of Discontinuous Deformation, Kyoto, Japan, 1997: 274-281
[230] Zhou Weiyuan, Xiaodong Kou and Yang Ruoqiong, Crack propagation by manifold method coupled with element free method, 3rd International Conference on Analysis of Discontinuous Deformation from Theory to Practice, Vail, Colorado, USA, 1999
[231]刘欣等,基于流形覆盖思想的无网格方法研究,计算力学学报,2001,18(1):21-27
[232]栾茂田,张大林,田荣,有限覆盖无单元法在裂纹扩展数值分析问题中的应用,岩土工程学报,2003,25(5):527-531
[233]栾茂田,田荣等,有限覆盖无单元法在岩土类弱拉型材料摩擦接触问题中的应用,岩土工程学报,2002,24(2):137-141
[234]李树忱,断续节理岩体的无网格流形方法和实验研究,[博士论文],上海:上海大学,2004
[235]李树忱,程玉民,基于单位分解法的无网格流形方法,力学学报,2004,36(4):496-500
[236]李树忱,程玉民.数值流形方法及其在岩石力学中的应用,力学进展,2004, 34(4):446-454
[237]高洪芬,程玉民,弹性力学的复变量数值流形方法,力学学报,2009,41(3):480-488
[238] S. Li, Y. Cheng, Y.-F. Wu. Numerical manifold method based on the method of weighted residuals, Computational Mechanics, 2005, 35(6): 470-480
[239]李树忱,程玉民.考虑裂纹尖端场的数值流形方法,土木工程学报,2005,38(7):96-101
[240]李树忱,程玉民,李术才.动态断裂力学的无网格流形方法,物理学报,2006,55(9):4760-4766
[241]陈丽,程玉民.瞬态热传导问题的复变量重构核粒子法,物理学报,2008,57(10):6047-6055
[242]程荣军,程玉民.势问题的无单元Galerkin方法的误差估计,物理学报,2008,57(10):6037-6046
[243]秦义校,程玉民.温度场分析的重构核粒子边界无单元法,机械工程学报,2008,44(6):95-100
[244]秦义校,程玉民.势问题的重构核粒子边界无单元法,力学学报,2009, 41(6): 898-905
[245] Chen Y M,Wilkins M L. Numerical analysis of dynamic crack problems. In: G C Sih Ed Mechanics ofFracture, Volume 4 [C], Leyden: Noordhoff, 1977
[246] Aliabadi M H. Boundary element formulations in fracture mechanics. AppL Mech, Rev., 1997, 50(2): 83-96
[247] Sladek J. Dynamics stress intensity fracturs studied by boundary integro-differential equations. Int. J. NumerMethods Engng, 1986; 23(5): 919-928
[248]程玉民,嵇醒,臧跃龙. Fourier本征变换在断裂动力学边界元法中的应用,同济大学学报,1996,24(3):251-256
[249] Cheng Yumin, Ji Xing. An Investigation on a New Integral Transform Boundary Element Methods for Elastodynamics. Acta Meehanica Solida Sinica, l 997; 10(3): 26-29
[250]程玉民,嵇醒.动态断裂力学的无限相似边界元法.力学学报,2004;36(1):43-48