An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

Engineering Fracture Mechanics

Volumn 78, Issue 1, 2011, Pages 175-190

  Gu, Y T ^a   Wang, W ^a   Zhang, L C ^b   Feng, X Q ^c  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

^c TSINGHUA UNIVERSITY   (China)

Author keywords

Crack tip; Enriched RPIM; Fracture mechanics; Meshfree method; RBF

Indexed keywords

CONDITION NUMBERS; CRACK ANALYSIS; CRACK TIP FIELDS; ENRICHED RPIM; INTERPOLATION MATRIX; LINEAR FRACTURE MECHANICS; MESH-FREE METHOD; MESHFREE; POLYNOMIAL SURFACE; RADIAL POINT INTERPOLATION METHOD; RBF; SHAPE FUNCTIONS; SIMULATION TOOL; SURFACE FITTING; SYSTEM OF EQUATIONS; TRIGONOMETRIC BASIS FUNCTIONS;

COMPUTATIONAL MECHANICS; CRACK TIPS; FRACTURE MECHANICS; FUNCTION EVALUATION; INTERPOLATION; NUMBER THEORY;

RADIAL BASIS FUNCTION NETWORKS;

EID: 78650274667     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2010.10.014     Document Type: Article

References (36)

1. Liu G.R. On G space theory. Int J Comput Methods 2009, 6(2):257-289.
2. Liu G.R., Gu Y.T. An introduction to meshfree methods and their programming 2005, Springer Press, Berlin.
3. Liu G.R. Mesh free methods: moving beyond the finite element method 2009, CRC press, USA. 2nd ed.
4. Zhang X., Liu X.H., Song K.Z., Lu M.W. Least-squares collocation meshless method. Int J Numer Methods Engng 2001, 51(9):1089-1100.
5. Gingold R.A., Moraghan J.J. Smooth particle hydrodynamics: theory and applications to non spherical stars. Mon Not Roy Astron Soc 1977, 181:375-389.
6. Belytschko T., Lu Y.Y., Gu L. Element-fee Galerkin methods. Int J Numer Methods Engng 1994, 37:229-256.
7. Liu W.K., Jun S., Zhang Y. Reproducing kernel particle methods. Int J Numer Methods Engng 1995, 20:1081-1106.
8. Liu G.R., Gu Y.T. A point interpolation method for two-dimensional solids. Int J Numer Methods Engng 2001, 50(4):937-951.
9. Atluri S.N., Zhu T. A new meshfree local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 1998, 22:117-127.
10. Liu G.R., Gu Y.T. A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J Sound Vib 2001, 246(1):29-46.
11. Mukherjee Y.X., Mukherjee S. Boundary node method for potential problems. Int J Numer Methods Engng 1997, 40:797-815.
12. Gu Y.T., Liu G.R. A boundary point interpolation method for stress analysis of solids. Comput Mech 2002, 28:47-54.
13. Gu Y.T., Liu G.R. A boundary radial point interpolation method (BRPIM) for 2-D structural analyses. Struct Engng Mech 2003, 15(5):535-550.
14. Liu G.R., Zhang G.Y. Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM). Int J Numer Methods Engng 2008, 74:1128-1161.
15. Liu G.R., Gu Y.T., Dai K.Y. Assessment and applications of point interpolation methods for computational mechanics. Int J Numer Methods Engng 2004, 59(10):1373-1397.
16. Wang J.G., Liu G.R. A point interpolation meshless method based on radial basis functions. Int J Numer Methods Engng 2002, 54:1623-1648.
17. Liu G.R. A G space and weakened weak (W2) form for a unified formulation of compatible and incompatible methods, part I - theory and part II - application to solid mechanics problems. Int J Numer Methods Engng 2008.
18. Liu G.R., Dai K.Y., Nguyen T.T. A smoothed finite element method for mechanics problems. Comput Mech 2007, 39:859-877.
19. Liu G.R., Nourbakhshnia N., Chen L., Zhang Y.W. A novel general formulation for singular stress field using the ES-FEM method for the analysis of mixed-mode cracks. Int J Comput Methods 2010, 7(1):191-214.
20. Chen L., Liu G.R., Nourbakhsh-Nia N., Zeng K. A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks. Comput Mech 2010, 45(2-3):109-125.
21. Fleming M., Chu Y., Moran B., Belytschko T. Int J Numer Methods Engng 1997, 40:1483-1504.
22. Lu Y.Y., Belytschko T., Tabbara M. Element-free Galerkin method for wave propagation and dynamic fracture. Comput Methods Appl Mech Engng 1995, 126:131-153.
23. Gu Y.T., Zhang L.C. Coupling of the meshfree and finite element methods for determination of the crack tip fields. Engng Fract Mech 2008, 75(5):986-1004.
24. Liu G.R., Zhang G.Y., Gu Y.T., et al. A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput Mech 2005, 36(6):421-430.
25. Gdoutos E.E. Fracture mechanics: an introduction 1993, Kluwer Academic Publishers.
26. Ching H.K., Batra R.C. Determination of crack tip fields in linear elastostatics by the meshfree local Petrov-Galerkin (MLPG) method. CMES 2001, 2(2):273-289.
27. Schaback R., Wendland H. Characterization and construction of radial basis functions. Multivariate approximation and applications 2000, Cambridge University Press. N. Dyn, D. Leviatan, D. Levin, A. Pinkus (Eds.).
28. Gu Y.T. Meshfree methods and their comparison. Int J Comput Methods 2005, 2(4):477-515.
29. Kansa E.J. Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. Computers Math Applic 1990, 19(8/9):127-145.
30. Liu G.R., Gu Y.T., Dai K.Y. Assessment and applications of point interpolation methods for computational mechanics. Int J Numer Methods Engng 2004, 59(10):1373-1397.
31. Liu G.R., Tu Z.H. An adaptive procedure based on background cells for meshfree methods. Comput Methods Appl Mech Engng 2002, 191:1923-1943.
32. Rice J.N. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Comput Meth 1968, 35:379-386.
33. Irwin G.R. Analysis of stress and strains near the end of a crack traversing a plate. J Appl Mech 1957, 24:361-364.
34. Yau, et al. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 1980, 47:335-341.
35. Shih, Asaro Elastic-plastic analysis of cracks on bimaterial interfaces: part I - small scale yielding. J Appl Mech 1988, 55:299-316.
36. Rao B.N., Rahman S. Probabilistic fracture mechanics by Galerkin meshless methods - part 1: rates of stress intensity factors. Comput Mech 2002, 28:351-364.