Completeness of corrective smoothed particle method for linear elastodynamics

Computational Mechanics

Volumn 24, Issue 4, 1999, Pages 273-285

  Chen, J K ^a   Beraun, J E ^a   Jih, C J ^b  

^a AIR FORCE RESEARCH LABORATORY   (United States)

^b FORD RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010712183     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050516     Document Type: Article

References (32)

1. ABAQUS/STANDARD (1998) User's Manual, Version 5.7. Hibbitt, Karlsson and Sorenson, Pawtucket, RI
2. Belytschko T, Krongauz Y, Dolbow J, Gerlach C (1998) On the completeness of meshfree particle methods. Int. J. Num. Meth. Eng. 43:785-819
3. Black T, Belytschko T (1999) Convergence of corrected derivative methods for second-order linear partial differential equations. Int. J. Numer. Meth. Eng. 44:177-203
4. Chen JK, Allahdadi FA, Carney TC (1997) High-velocity impact of graphite/epoxy composite laminates. Comp. Sci. Technol. 57:1369-1379
5. Chen JK, Beraun JE (1999) A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng. (revised)
6. Chen JK, Beraun JE, Carney TC (1999a) A corrective smoothed particle method for boundary value problems in heat conduction. Int. J. Num. Meth. Eng. (in press)
7. Chen JK, Beraun JE, Jih CJ (1999b) An improvement for tensile instability in smoothed particle hydrodynamics. Comput. Mech. 23:279-287
8. Dalpino EMD, Ceroqueira AH (1996) 3-D sph simulations of hd and mhd jets. Astrophys. Letters & Commun. 34:303-308
9. Fulk DA, Quinn DW (1996) An analysis of 1-D smoothed particle hydrodynamics kernels. J. Comput. Phys. 126:165-180
10. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to nonspherical stars. Mon. Not. Roy. Astr. Soc. 181:275-389
11. Gutfraind R, Savage SB (1998) Flow of fractured ice through wedge-shaped channels: smoothed particle hydrodynamics and discrete-element simulations. Mech. of Materials 29:1-17
12. Johnson GR, Beissel SR (1996) Normalized smoothed functions for sph impact computations. Int. J. Num. Meth. Eng. 39:2725-2741
13. Krongauz Y, Belytschko T (1997) Consistent pseudo-derivatives in meshless methods. Comput. Meth. Appl. Mech. Eng. 146:371-386
14. Li S, Liu WK (1996) Moving least-square reproducing kernel method part II: Fourier analysis. Comput. Meth. Appl. Mech. Eng. 139:159-193
15. Li S, Liu WK (1998) Synchronized reproducing kernel interpolant via multi wavelet expansion. Comput. Mech. 21:28-47
16. Libersky LD, Petschek AG, Carny TC, Hipp JR, Allahdadi FA (1993) High strain Lagrangian hydrodynamics, a three-dimensional sph code for dynamic material response. J. Comput. Phys. 109:67-75
17. Liu WK, Adee J, Jun S, Belytschko T (1993) Reproducing kernel particle methods for elastic and plastic problems. B.J. Benson and R.A. Asaro (eds), in Advanced Computational Methods for Material Modeling, Vol. AMD 180 and PVP 268, ASME, New York, pp. 175-190
18. Liu WK, Chen Y, Chang CT, Belytschko T (1996a) Advances in multiple scale reproducing kernel methods. Comput. Mech. 18:73-111
19. Liu WK, Chen Y, Uras RA, Chang CT (1996b) Generalized multiple scale reproducing kernel methods. Comput. Meth. Appl. Mech. Eng. 139:91-157
20. Liu WK, Jun S, Li S, Adee J, Belytschko T (1995a) Reproducing kernel particle methods for structural dynamics. Int. J. Num. Meth. Eng. 38:1655-1679
21. Liu WK, Jun S, Zhang Y (1995b) Reproducing kernel particle methods. Int. J. Num. Meth. Fluids 20:1081-1106
22. Liu WK, Li S, Belytschko T (1997) Moving least-square reproducing kernel particle methods (I) Methodology and Convergence. Comput. Meth. Appl. Mech. Eng. 143:113-154
23. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron. J. 82:1013-1020
24. Monaghan JJ (1988) An introduction to sph. Comput. Phys. Commun. 48:89-96
25. Monaghan JJ, Gingold RA (1983) Shock simulation by the particle method sph. J. Comput. Phys. 52:374-389
26. Morris JP, Fox PJ, Zhu Y (1997) Modeling low Reynolds number incompressible flows using sph. J. Comput. Phys. 136:214-226
27. Posch HA, Hoover WG, Kum O (1995) Steady-state shear flows via nonequilibrium molecular dynamics and smooth-particle applied mechanics. Phys. Rev. E. 52:1711-1719
28. Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput. Meth. Appl. Mech. Eng. 139:375-408
29. Swegle JW, Attaway SW (1995) On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations. Comput. Mech. 17:151-168
30. Takeda HT, Miyama SM, Sekiya M (1994) Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progr. Theoret. Phys. 92:939-960
31. Zhu T, Atluri SN (1998) A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech. 21:211-222
32. Zhu TL, Zhang JD, Atluri SN (1999) A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and nonlinear boundary value problems. Engineering Analysis with Boundary Elements 23:375-389