On the analysis of dispersion property and stable time step in meshfree method using the generalized meshfree approximation

Finite Elements in Analysis and Design

Volumn 47, Issue 7, 2011, Pages 683-697

  Park, C K ^a,b   Wu, C T ^c   Kan, C D ^a,b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b George Washington University   (United States)

^c LIVERMORE SOFTWARE TECHNOLOGY CORPORATION   (United States)

Author keywords

Convex approximation; Dispersion error; Generalized meshfree approximation; Meshfree method; Non convex approximation; Stable time step

Indexed keywords

CONVEX APPROXIMATION; DISPERSION ERROR; MESH-FREE METHOD; MESHFREE; NON-CONVEX APPROXIMATION; STABLE TIME STEP;

ACOUSTIC DISPERSION; BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

DISPERSIONS;

EID: 79955470646     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2011.02.001     Document Type: Article

References (33)

1. M. Arroyo, and M. Ortiz Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods Int. J. Numer. Methods Eng. 65 2006 2167 2202
2. T. Belytschko, Y. Guo, W.K. Liu, and S.P. Xiao A unified stability analysis of meshless particle methods Int. J. Numer. Methods Eng. 48 2000 1359 1400
3. T. Belytschko, W.K. Liu, and B. Moran Nonlinear Finite Elements for Continua and Structures 2000 Wiley NY
4. T. Belytschko, Y.Y. Lu, and L. Gu Element-free Galerkin methods Int. J. Numer. Methods Eng. 37 2 1994 229 256
5. J.S. Chen, C. Pan, C.T. Wu, and W.K. Liu Reproducing kernel particle methods for large deformation analysis of non-linear structures Comput. Methods Appl. Mech. Eng. 139 1996 195 227 (Pubitemid 126382697)
6. J.S. Chen, and H.P. Wang New boundary condition treatments in meshfree computation of contact problems Comput. Methods Appl. Mech. Eng. 187 2000 441 468
7. M.A. Christon, and T.E. Voth Results of von Neumann analyses for reproducing kernel semi-discretizations Int. J. Numer. Methods Eng. 47 2000 1285 1301 (Pubitemid 30168356)
8. C.J. Cyron, M. Arroyo, and M. Ortiz Smooth, second order, non-negative meshfree approximants selected by maximum entropy Int. J. Numer. Methods Eng. 79 2009 1605 1632
9. D.P. Flanagan, and T. Belytschko Eigenvalues and stable time steps for the uniform strain hexahedron and quadrilateral J. Appl. Mech. 51 1984 35 40 (Pubitemid 14550149)
10. ® Theory Manual 2006 LSTC CA
11. M.P. Hobson, and A.N. Lasenby The entropic prior for distributions with positive and negative values Mon. Not. R. Astron. Soc. 298 1998 905 908 (Pubitemid 128503102)
12. E.T. Jaynes Information theory and statistical mechanics Phys. Rev. 106 4 1957 620 630
13. R.D. Krieg, and S.W. Key Transient shell response by numerical time integration Int. J. Numer. Methods Eng. 7 1973 273 286
14. P. Lancaster, and K. Salkauskas Surfaces generated by moving least squares methods Math. Comput. 37 1981 141 158
15. S. Li, and W.K. Liu Moving least square reproducing kernel method. Part II: Fourier analysis Comput. Methods Appl. Mech. Eng. 139 1996 159 193 (Pubitemid 126382696)
16. G.R. Liu Mesh Free Methods: Moving Beyond the Finite Element Method 2002 CRC Press NY
17. W.K. Liu, S. Jun, S. Li, J. Adee, and T. Belytschko Reproducing kernel particle methods for structural dynamics Int. J. Numer. Methods Eng. 38 1995 1655 1679
18. W.K. Liu, S. Jun, and Y.F. Zhang Reproducing kernel particle methods Int. J. Numer. Methods Fluids 20 1995 1081 1106
19. ® Keyword Users Manual, Version 971, LSTC, CA, 2007.
20. D.S. Malkus, and M.E. Plesha Zero and negative masses in finite element vibration and transient analysis Comput. Methods Appl. Mech. Eng. 59 1986 281 306
21. R. Mullen, and T. Belytschko Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation Int. J. Numer. Methods Eng. 18 1982 11 29 (Pubitemid 12507935)
22. C.K. Park, The development of a generalized meshfree approximation for solid and fracture analysis, Dissertation, The George Washington University, DC, 2009.
23. M.A. Puso, J.S. Chen, E. Zywicz, and W. Elmer Meshfree and finite element nodal integration methods Int. J. Numer. Methods Eng. 74 2008 416 446 (Pubitemid 351516704)
24. A. Renyi, On measures of entropy and information, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 1961, pp. 547561.
25. C.E. Shannon A mathematical theory of communication Bell Syst. Tech. J. 27 1948 379 423
26. D. Shepard, A two-dimensional interpolation function for irregularly-spaced data, in: Proceedings of the ACM 23rd National Conference, NY, 1968, pp. 517524, doi:10.1145/800186.810616.
27. N. Sukumar Construction of polygonal interpolants: a maximum entropy approach Int. J. Numer. Methods Eng. 61 2004 2159 2181 (Pubitemid 39622525)
28. N. Sukumar, and R.W. Wright Overview and construction of meshfree basis functions: from moving least squares to entropy approximants Int. J. Numer. Methods Eng. 70 2007 181 205 (Pubitemid 46566843)
29. A. Tagliani Existence and stability of a discrete probability distribution by maximum entropy approach Appl. Math. Comput. 110 2000 105 114
30. R. Vichnevetsky, and J.B. Bowles Fourier Analysis of Numerical Approximations of Hyperbolic Equations 1982 SIAM Philadelphia, PA
31. T.E. Voth, and M.A. Christon Discretization errors associated with reproducing kernel methods: one-dimensional domains Comput. Methods Appl. Mech. Eng. 190 2001 2429 2446 (Pubitemid 32232592)
32. C.T. Wu, C.K. Park, and J.S. Chen A generalized meshfree approximation for the meshfree analysis of solids Int. J. Numer. Methods Eng. 85 2011 693 722 doi:10.1002/nme.2991
33. Y. You, J.S. Chen, and T.E. Voth Characteristics of semi- and full discretization of stabilized Galerkin meshfree method Finite Elem. Anal. Des. 38 2002 999 1012 (Pubitemid 34545046)