马文涛. 基于单位分解的扩展无网格法及其在岩体断裂中的应用[D]. 西安: 西安理工大学, 2013. Ma Wentao. An extended meshfree method based on partition of unity and its application in jointed rockness [D]. Xi’an: Xi’an University of Technology, 2013. (in Chinese)
[2]
Fleming M, Chu Y A, Moran B. Enriched element-free Galerkin methods for crack tip fields [J]. International Journal for Numerical Methods in Engineering, 1997, 40: 1483―1504.
[3]
Rao B N, Rahman S. A coupled meshless-finite element method for fracture analysis of cracks [J]. International Journal of Pressure Vessels and Piping, 2001, 78(9): 647―657.
[4]
Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks [J]. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316―2443.
[5]
Rabczuk T, Zi G S. A meshfree method based on the local partition of unity for cohesive cracks [J]. Computational Mechanics, 2007, 39(6): 743―760.
[6]
Nguyen V P, Rabczuk T, Bordas S, et al. Meshless methods: A review and computer implementation aspects [J]. Mathematics and Computers in Simulation, 2008, 79: 763―813.
[7]
Gu Y T, Wang W, Zhang L C, et al. An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields [J]. Engineering Fracture Mechanics, 2011, 1: 175―190.
[8]
Liew K M, CHENG Yu min, S Kitipornchai. Analyzing the 2D fracture problems via the enriched boundary element-free method [J]. International Journal of Solids and Structures, 2007, 44(11): 4220―4233.
[9]
Barbieri E, Petrinic N, Meo M, et al. A new weight-function enrichment in meshless methods for multiple cracks in linear elasticity [J]. International Journal for Numerical Methods in Engineering, 2012, 90(2): 177―195.
[10]
彭翀, 袁慧娜, 张丙印. 无网格自动加密方法及其在土体裂纹分析中的应用[J]. 工程力学, 2013, 30(6): 231―235. Peng Chong, Yuan Huina, Zhang Bingyin. Autoumatic node refinement for meshfree method and its application soil crack analysis [J]. Engineering Mechanics, 2013, 30(6): 231―235. (in Chinese)
[11]
Bowie O L. Rectangular tensile sheet with symmetric edge cracks [J]. Journal of Applied Mechanics, 1964, 31(2): 208―212.
[12]
Yan X Q. A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate [J]. Applied Mathematical Modelling, 2010, 34: 2722―2737.
[13]
Chen Y Z. General case of multiple crack problems in an infinite plate [J]. Engineering Fracture Mechanics, 1984, 20: 591―597.
[14]
买买提明·艾尼, 热合买提江·依明. 现代数值模拟方法与工程实际应用[J]. 工程力学, 2014, 31(4): 11―18. Geni Mamtimin, Imin Rahmatjian. Modern numerical simulation methods and its practical applications in engineering [J]. Engineering Mechanics, 2014, 31(4): 11―18. (in Chinese)
[15]
Daux C, Moes N, Dolbow J, et al. Arbitrary branched and intersecting cracks with the extended finite element method [J]. International Journal for Numerical Methods in Engineering, 2000, 48: 1741―1760.
[16]
Törg F U, Stefan E, Carsten K. Modelling of cohensive crack growth in concrete structures with the extended finite element method [J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196: 4087―4100.
[17]
苏静波, 范晓晨, 邵国建. 几何非线性扩展有限元法及其断裂力学应用[J]. 工程力学, 2013, 30(4): 42―46. Su Jingbo, Fan Xiaochen, Shao Guojian. Extended finite element method with nonlinear geometry and its application in fracture mechanics [J]. Engineering Mechanics, 2013, 30(4): 42―46. (in Chinese)
[18]
Muravin B, Turkel E. Multiple crack weight for solution of Multiple interacting cracks by meshless numerical methods [J]. International Journal for Numerical Methods in Engineering, 2006, 67: 1146―1159.
[19]
Singh I V, Mishra B K, Pant Mohit. A modified intrinsic enriched element free Galerkin method for multiple cracks simulation [J]. Materials and Design, 2010, 31: 628―632.
[20]
Shi J P, Ma W T, Li N. Extended meshless method based on partition of unity for solving multiple crack problems [J]. Meccanica, 2013, 48: 2263―2270.
[21]
Dolbow J E, Gosz M. On the computation of mixed-mode stress intensity factors in functionally graded materials [J]. International Journal of Solids and Structures, 2002, 39: 2557―2574.
