A meshfree poly-cell Galerkin (MPG) approach for problems of elasticity and fracture

CMES - Computer Modeling in Engineering and Sciences

Volumn 38, Issue 2, 2008, Pages 149-178

  Zheng, C ^a   Wu, S C ^b,c   Tang, X H ^a   Zhangl, J H ^a  

^a SICHUAN UNIVERSITY   (China)

^b HEFEI UNIVERSITY OF TECHNOLOGY   (China)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Fracture.; Improved MLS; Meshfree; Poly cell local support; Superconvergence

Indexed keywords

AIRCRAFT LANDING SYSTEMS; CRACK TIPS; ELASTICITY; FUNCTION EVALUATION;

BASIS FUNCTIONS; CRACK-TIP; ENERGY NORMS; ESSENTIAL BOUNDARY CONDITIONS; FRACTURE ANALYSIS; GALERKIN; IMPROVED MLS; J INTEGRALS; LEAST SQUARES; MATRIX INVERSIONS; MESHFREE; NUMERICAL RESULTS; POLY-CELL LOCAL SUPPORT; SHAPE FUNCTIONS; STRESS FIELDS; STRESS INTENSITIES; SUPERCONVERGENCE; SUPERCONVERGENT; THEORETICAL VALUES;

GALERKIN METHODS;

EID: 62449123066     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (43)

1. Atluri, S.N.; Zhu, T.L. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Comput. Mech, vol. 22, pp. 117-27.
2. Atluri, S.N.; Sladek, J.; Sladek, V.; Zhu, T. (2000): The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity, Computational Mechanics, vol. 25, pp. 180-198.
3. Atluri, S.N., Shen, S.P. (2002): The meshless local Petrov-Galerkin (MLPG) method: A simple & lesscostly alternative to the finite element and boundary element methods, CMES: Computer Modeling in Engineering and Sciences, 3 (1) 11-51.
4. Atluri, S.N. (2004): The Meshless Local Petrov-Galerkin (MLPG) Method for Domain & Boundary Discretizations, Tech Science Press.
5. Atluri, S.N.; Han, Z.D.; Rajendran, A.M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach, CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. 6, pp. 491-514.
6. Atluri, S.N.; Shen, S. (2005): The Meshless Local Petrov-Galerkin (MLPG) method, Tech Science Press, Encino, USA.
7. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems, CMES: Computer Modeling in Engineering & Sciences, 14 (3), 141-152.
8. Atluri, S.N.; Liu, H.T; Han, Z.D. (2006): Meshless local Petro-Galerkin (MLPG) mixed finite difference method for solid mechanics, CMES: Computer Modeling in Engineering & Sciences, vol. 15, pp. 1-16.
9. Budiansky, D.; Rice, J.R. (1973): Conservation laws and energy-release rates, J. Appl. Mech, vol. 40, pp. 201-203.
10. Belytschko, T.; Lu, Y.Y.; Gu, L. (1995): Crack propagation by element-free Galerkin methods, Eng. Fract Mech, vol. 51, pp. 295-315.
11. Belytschko, T.; Lu, Y.Y.; Gu, L. (1994): Element free Garlerkin methods, Int. J. Numer. Meth. Engng, vol. 37, pp. 229-256.
12. Beissel, S.; Belytschko, T. (1994): Nodal integration of the element-free Galerkin method, Comput. methods Appl. Mech. Engrg, vol. 139, pp. 49-74.
13. Brighenti, R. (2005): Application of the element-free Galerkin meshless method to 3D fracture mechanics problems, Eng. Fract Mech, vol. 72, pp. 2808-2820.
14. Braum, J.; Sambridge, M. (1995): A numerical method for solving partial differential equations on highly irregular evolving grids, Nature, vol. 375, pp. 665-660.
15. Ching, H.K.; Batra, R.C. (2001): Determination of crack tip fields in linear elastostatics by the meshless local Petrov-Galerkin (MLPG) method, CMES: Computer Modeling in Engineering & Sciences, vol. 12, pp. 273-289.
16. Chow,W.T.; Atluri, S.N. (1998): Stress intensity factors as the fracture parameters for determination crack growth in composite laminates, Comput. Mech, vol. 21, pp. 1-10.
17. Cui, X.Y.; Liu, G.Y.; Li, G.Y.; Zhao, X.; Nguyen, T. T.; Sun, G.Y. (2008): A smoothed finite element method (SFEM) for linear and geometrically nonlinear analysis of plates and shells, CMES: Computer Modeling in Engineering & Sciences, vol. 28, pp. 109-125.
18. Fleming, M.; Chu, Y.A.; Moran, B.; Belytschko, T. (1997): Enriched elementfree Galerkin methods for crack-tip fields, Int. J. Numer. Meth. Engng, vol. 40, pp. 1483-1504.
19. Fries, T.P.; Belytschko, T. (2008): Convergence and stabilization of stress-point integration in mesh-free and particle methods, Int. J. Numer. Meth. Engng, vol. 74, pp. 1067-1087.
20. Gu, Y.T.; Zhang, L.C. (2008): Coupling of the meshfree and finite element methods for determination of the crack tip fields, Eng. Fract Mech, vol. 75, pp. 986-1004.
21. Han, Z.D.; Atluri, S.N. (2004): Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics, CMES: Computer Modeling in Engineering & Sciences, vol. 6 no. 2, pp. 169-188.
22. Han, Z.D.; Rajendran, A.M; Atluri, S.N. (2005): Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformation and Rotation, CMES: Computer Modeling in Engineering & Sciences, vol. 10, no. 1, pp. 12.
23. Han, Z.D., Liu, H.T., Rajendran, A.M., et al. (2006): The applications of meshless local Petrov-Galerkin (MLPG) approaches in high-speed impact, penetration and perforation problems, CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 2, pp. 119-128.
24. Idelsohn, S.R.; Oñate, E.; Calvo, N.; Facundo, D.P. (2003): The meshless finite element method. Int. J. Numer. Meth. Engng, vol. 58, pp. 893-912.
25. Idelsohn, S.R.; Oñate, E. (2006): To mesh or not to mesh. That is the question. Comput. methods Appl. Mech. Engrg, vol. 195, pp. 4681-4696.
26. Lancaser, P.; Salkauskas, K. (1981): Surface generated by moving least squares methods. Math. Comp, vol. 37, pp. 141-158.
27. Li, S.F.; Liu, W.K. (2002): Meshfree and particle methods and their applications. Appl. Mech. Rev, vol. 55, pp. 1-34.
28. Li, F.Z.; Shih, F.C.A. (1985): Needleman. A comparison of methods for calculating energy release rates. Eng. Fract Mech, vol. 21, pp. 405-421.
29. Liu, G.R. (2002): Meshfree methods: Moving Beyond the Finite Element Method, CRC Press, Boca Raton, USA.
30. Liu,W.K.; Jun, S.; Zhang, Y.F. (1995): Reproducing kernel particle methods, Int. J. Numer. Meth. Fluids, vol. 20, pp. 1081-1106.
31. Liu, G.R.; Zhang, G.Y.; Wang, Y.Y.; Zhong, Z.H.; Li, G.Y.; Han, X. (2006): A nodal integration technique for meshfree radial point interpolation method (NIRPIM). Int. J. Solids Struct, vol. 44, pp. 3840-3860.
32. Lu, Y.Y.; Belytschko, T.; Gu, L. (1994): A new implementation of the Elementfree Galerkin methods. Comput. methods Appl. Mech. Engrg, vol. 113, pp. 397-414.
33. Sladek, J. ; Sladek, V.; Atluri, S.N. (2004): Meshless local Petrov-Galerkin method in anisotropic elasticity, CMES: Computer Modeling in Engn. & Sciences, vol. 6, pp. 477-489.
34. Sladek, J.; Sladek, V.; Krivacek, J.; Zhang Ch. (2005): Meshless Local Petrov-Galerkin Method for stress and crack analysis in 3-D axisymmteric FGM bodies, CMES: Computer Modeling in Engineering & Sciences, vol. 8, pp. 259-270.
35. Sonia, F.M.; Antonio, H. (2004): Imposing essential boundary conditions. Comput. methods Appl. Mech. Engrg, vol. 193, pp. 1257-1275.
36. Sukumar, N,; Moran, B.; Belytschko, T. (1998): The natural element method in solid mechanics. Int. J. Numer. Meth. Engng, vol. 43, pp. 839-887.
37. Timoshenko, S.P.; Goodier, J.N. (1970): Theory of Elasticity, third edition, McGraw, New York, USA.
38. Roark, R.J.; Young, W.C. (1975): Formulas for stress and strain, McGraw, New York, USA.
39. Wu, S.C.; Liu, G.R.; Zhang, H.O.; Zhang G.Y. (2008): A node-based smoothed point interpolation method (NS-PIM) for three-dimensional thermoelastic problems, Numerical Heat Transfer: Part A: Applications, vol. 54, pp. 1121-1147.
40. Yau, J.; Wang, S.; Corten, H. (1980): A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J. Appl. Mech, vol. 47, pp. 335-341.
41. Zheng, C.; Zhang, J.H.; Wu, S.C. (2008): A novel mesh-free poly-cell Galerkin (MPG) Method, Acta Mechanic Sinica, (in press).
42. Zienkiewicz, O.C.; Taylor, R.L. (2000): The Finite Element Method, fifth edition, Butterworth Heinemann, Oxford, UK.
43. Zhou, J.X.; Wen, J.B.; Zhang, H.Y.; Zhang, L. (2003): A nodal integration and post-processing technique based on Voronoi diagram for Galerkin meshless methods. Comput. methods Appl. Mech. Engrg, vol. 192, pp. 3831-3843.