A singular cell-based smoothed radial point interpolation method for fracture problems

Computers and Structures

Volumn 89, Issue 13-14, 2011, Pages 1378-1396

  Liu, G R ^a   Jiang, Y ^b   Chen, L ^b   Zhang, G Y ^c   Zhang, Y W ^d  

^a 705 Engineering Research Center   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^d INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

Author keywords

CS RPIM; Fracture; Meshfree method; Numerical methods; Singularity; Stress intensity factors

Indexed keywords

CELL-BASED; CS-RPIM; MESHFREE METHOD; RADIAL POINT INTERPOLATION METHOD; SHAPE FUNCTIONS; SINGULAR ELEMENTS; SINGULARITY; WEAK FORMULATION;

CRACK TIPS; FRACTURE; INTERPOLATION; STIFFNESS MATRIX;

COMPUTATIONAL MECHANICS;

EID: 79956093183     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2011.03.009     Document Type: Article

References (49)

1. O.C. Zienkiewicz, and R.L. Taylor The finite element method fifth ed. 2000 Butterworth Heinemann Oxford, UK
2. G.R. Liu, and S.S. Quek The finite element method: a practical course 2003 Butterworth Heinemann Oxford
3. S.C. Brenner, and L.R. Scott The mathematical theory of finite element methods 1994 Spring-Verlag
4. B. Dietrich Finite elements: theory, fast solvers, and applications in solid mechanics 2007 Cambridge University Press
5. A.A. Samarskii, P.N. Vabishchevich, and L.G. Vulkov Finite difference methods: theory and applications 1999 Nova Science Publishers New York
6. G.E. Forsythe, and W.R. Wasow Finite-difference methods for partial differential equations 1960 Cambridge University Press, Wiley New York
7. R.J. Leveque Finite volume methods for hyperbolic problems 2002 Cambridge University Press New York
8. R.H. Li, Z.Y. Chen, and W. Wu Generalized difference methods for differential equations: numerical analysis of finite volume methods 2000 Marcel Dekker New York
9. T. Belytschko, and T. Black Elastic crack growth in finite elements with minimal remeshing Int J Numer Methods Eng 45 5 1999 601 620
10. N. Moes, J. Dolbow, and T. Belytschko A finite element method for crack growth without remeshing Int J Numer Methods Eng 46 1 1999 131 150 (Pubitemid 30508928)
11. S. Bordas, T. Rabczuk, N.X. Hung, V.P. Nguyen, S. Natarajan, and T. Bog Strain smoothing in FEM and XFEM Comput Struct 2010 88 10.1016/j.compstruc.2008. 07.006 [Chapter 23-24 1419-1443]
12. A. Menk, and S. Bordas Numerically determined enrichment functions for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals Int J Numer Methods Eng 83 2010 805 828
13. T. Belytschko, R. Gracie, and G. Ventura A review of extended/generalized finite element methods for material modeling Model Simul Mater Sci Eng 2009 10.1088/0965-0393/17/4/043001
14. J. Chessa, Hw Wang, and T. Belytschko On the construction of blending elements for local partition of unity enriched finite elements Int J Numer Methods Eng 57 2003 1015 1038 (Pubitemid 36832723)
15. Q.Z. Xiao, and B.L. Karihaloo Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery Int J Numer Methods Eng 66 9 2006 1378 1410 (Pubitemid 43811114)
16. T. Rabczuk, S. Bordas, and G. Zi On three-dimensional of crack growth using partition of unity methods Comput Struct 88 2010 1391 1411
17. T. Rabczuk, S. Bordas, and G. Zi A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics Comput Mech 40 3 2007 473 495 ISBN/ISSN: 0178-7675, doi:10.1007.s00466-006-0122-1 (Pubitemid 46972355)
18. E. Wyart, D. Coulon, M. Duflot, T. Pardoen, J.F. Remacle, and F. Lani A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures Int J Numer Methods Eng 72 2007 757 779 (Pubitemid 47618155)
19. S.P.A. Bordas, J.G. Conley, B. Moran, J. Gray, and E. Nichols A simulation-based design paradigm for complex cast components Eng Comput 23 1 2007 25 37 (Pubitemid 46189947)
20. S. Bordas, and B. Moran Enriched finite elements and level sets for damage tolerance assessment of complex structures Eng Fract Mech 73 9 2006 1176 1201
21. B.L. Karihaloo, and Q.Z. Xiao Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity Eng Fract Mech 68 2001 1609 1630 (Pubitemid 32926096)
22. Q.Z. Xiao, and B.L. Karihaloo An overview of a hybrid crack element and determination of its complete displacement field Eng Fract Mech 74 2007 1107 1117 (Pubitemid 46296559)
23. G.R. Liu A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods Int J Comput Methods 5 2008 199 236
24. Xuan ZC, Lassila T, Rozza G, Quarteroni A. On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method. Int J Numer Methods Eng; 2010. doi:10.1002/nme.2825.
25. H. Nguyen-Xuan, S. Bordas, and H. Nguyen-Dang Smooth finite element methods: convergence, accuracy and properties Int J Numer Methods Eng 74 2 2008 175 208 (Pubitemid 351523304)
26. Nguyen Vinh Phu, T. Rabczuk, S. Bordas, and M. Duflot Meshless methods: A review and computer implementation aspects Mathematics and Coputers in Simulation 79 2008 763 813
27. G.R. Liu On G space theory Int J Comput Methods 6 2 2009 257 289
28. J.S. Chen, C.T. Wu, and Y. Yoon A stabilized conforming nodal integration for Galerkin mesh-free methods Int J Numer Methods Eng 50 2001 435 466
29. G.R. Liu, and G.Y. Zhang A normed G space and weakened weak formulation of a cell-based smoothed point interpolation method Int J Comput Methods 6 1 2009 147 179
30. 2) form for a unified formulation of compatible and incompatible methods, Part I: Theory and Part II: Applications to solid mechanics problems Int J Numer Methods Eng 81 9 2010 1093 1156
31. G.R. Liu Meshfree methods: moving beyond the finite element method 2nd ed. 2009 Taylor & Francis/CRC Press Boca Raton
32. G.R. Liu, and T.T. Nguyen Smoothed finite element method 2010 Taylor & Francis/CRC Press Boca Raton
33. G.R. Liu, and G.Y. Zhang Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM) Int J Numer Methods Eng 74 7 2008 1128 1161 (Pubitemid 351689224)
34. Liu GR, Chen L, Nguyen TT, Zeng KY, Zhang GY. A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracute problems. Int J Numer Methods Eng. doi:10.1002/nme.2868.
35. G.R. Liu A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods Int J Comput Methods 5 2 2008 199 236
36. H. Nguyen-Xuan, and G.R. Liu An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates Comput Methods Appl Mech Eng 199 2010 471 489
37. G.R. Liu, G.Y. Zhang, K.Y. Dai, Y.Y. Wang, Z.H. Zhong, and G.Y. Li A linearly conforming point interpolation method (LC-PIM) for 2D mechanics problems Int J Comput Methods 2 4 2005 645 665
38. G.Y. Zhang, G.R. Liu, Y.Y. Wang, H.T. Huang, Z.H. Zhong, and G.Y. Li A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems Int J Numer Methods Eng 72 2009 1524 1543 (Pubitemid 350268735)
39. Chen L, Nguyen HX, Nguyen TT, Zeng KY, Wu SC. Assessment of smoothed point interpolation methods for elastic mechanics. Commun Numer Methods Eng doi:10.1002/cnm.1251.
40. G.R. Liu, and Y.T. Gu A point interpolation method for two-dimensional solids Int J Numer Methods Eng 50 2001 937 951 (Pubitemid 32192399)
41. G.R. Liu, K.Y. Dai, K.M. Lim, and Y.T. Gu A point interpolation meshfree method for static and frequency analysis of two-dimensional piezoelectric structures Comput Mech 29 6 2002 510 519
42. G.R. Liu, and Y.T. Gu An introduction to meshfree methods and their programming 2005 Springer Dordrecht, the Netherlands
43. J.G. Wang, and G.R. Liu A point interpolation meshless method based on radial basis functions Int J Numer Mech Eng 54 11 2002 1623 1648 (Pubitemid 34842350)
44. J.G. Wang, and G.R. Liu On the optimal shape parameters of radial basis functions used for 2-D meshless methods Comput Methods Appl Mech Eng 191 2002 2611 2630 (Pubitemid 34452176)
45. L. Chen, L. Liu, N.N. Nourbakhsh, and K. Zeng A singular edge-based smoothed finite element method (ES-FEM) for biomaterial interface cracks Comput Mech 45 2010 109 125
46. R.L. Hardy Theory and applications of the multiquadrics - biharmonic method (20 years of discovery 1968-1988) Comput Math Appl 19 1990 163 208 (Pubitemid 20668366)
47. M.A. Golberg, C.S. Chen, and H. Bowman Some recent results and proposals for the use of radial basis functions in the BEM Eng Anal Bound Elem 23 1999 285 296
48. R.S. Barsoum On the use of isoparametric finite elements in linear fracture mechanics Int J Numer Methods Eng 10 1976 551 564
49. R.S. Barsoum Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements Int J Numer Methods Eng 11 1977 85 98