Stabilized updated Lagrangian corrected SPH for explicit dynamic problems

International Journal for Numerical Methods in Engineering

Volumn 69, Issue 13, 2007, Pages 2687-2710

  Vidal, Yolanda ^a   Bonet, J ^b   Huerta, Antonio ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Corrected smooth particle hydrodynamics; Large distortions; Meshfree methods; SPH; Updated Lagrangian formulation

Indexed keywords

DYNAMICAL SYSTEMS; EULER EQUATIONS; LAGRANGE MULTIPLIERS;

EXPLICIT DYNAMIC PROBLEMS; MESHFREE METHODS; SMOOTH PARTICLE HYDRODYNAMICS;

NUMERICAL METHODS;

DYNAMICAL SYSTEMS; EULER EQUATIONS; LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

EID: 33947669410     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1859     Document Type: Article

References (33)

1. Attaway SW, Heinstein MW, Swegle JW. Coupling of smoothed particle hydrodynamics with the finite element method. Nuclear Engineering and Design 1994; 150(2-3):199-205.
2. Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method. Computational Mechanics 1995; 17(3):186-195.
3. Johnson GR, Stryk RA, Beissel SR. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):347-373.
4. Liu WK, Uras RA, Chen Y. Enrichment of the finite element method with the reproducing kernel particle method. Journal of Applied Mechanics (ASME) 1997; 64:861-870.
5. Huerta A, Fernandez-Mendez S. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering 2000; 48(11):1615-1636.
6. Fernandez-Mendez S, Bonet J, Huerta A. Continuous blending of SPH with finite elements. Computers and Structures 2005; 83(17-18):1448-1458.
7. Swegle JW, Hicks DL, Attaway SW. Smoothed particle hydrodynamics stability analysis. Journal of Computational Physics 1995; 116(1):123-134.
8. Belytschko T, Guo Y, Liu WK, Xiao SP. A unified stability analysis of meshless particle methods. International Journal for Numerical Methods in Engineering 2000; 48(9):1359-1400.
9. Huerta A, Belytschko T, Fernandez-Mendez S, Rabczuk T. Meshfree methods. In Encyclopedia of Computational Mechanics (Chapter 10, Fundamentals), Stein E, de Borst R, Hughes TJR (eds), vol. 1. Wiley: Chichester, 2004; 279-309.
10. Liu MB, Liu GR, Lam KY. Constructing smoothing functions in smoothed particle hydrodynamics with applications. Journal of Computational and Applied Mathematics 2003; 155(2):263-284.
11. Johnson GR, Beissel SR. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering 1996; 39(16):2725-2741.
12. Chen JK, Beraun JE, Carney TC. A corrective smoothed particle method for boundary value problems in heat conduction. International Journal for Numerical Methods in Engineering 1999; 46(2):231-252.
13. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Methods in Engineering 2000; 47(6):1189-1214.
14. Chen J-S, Wu C-T, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50(2):435-466.
15. Monaghan JJ. Why particle methods work. SIAM Journal on Scientific and Statistical Computing 1982; 3(4): 422-433.
16. Bonet J, Kulasegaram S. Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods. International Journal for Numerical Methods in Engineering 2001; 52(11): 1203-1220.
17. Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA. High strain Lagrangian hydrodynamics. A three-dimensional SPH code for dynamic material response. Journal of Computational Physics 1993; 109(1):67-75.
18. Johnson GR, Petersen EH, Stryk RA. Incorporation of an SPH option into the EPIC code for a wide-range of high-velocity impact computations. International Journal of Impact Engineering 1993; 14(1-4):385-394.
19. Stellingwerf R, Wingate C. Impact modeling with smooth particle hydrodynamics. International Journal of Impact Engineering 1993; 14(1-4):707-718.
20. Gray J, Monaghan J, Swift R. SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering 2001; 190(49-50):6641-6662.
21. Randles PW, Libersky LD. Normalized SPH with stress points. International Journal for Numerical Methods in Engineering 1996; 48(10):1445-1462.
22. Vignjevic R, Campbell J, Libersky L. A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Computer Methods in Applied Mechanics and Engineering 2000; 184(1):67-85.
23. Bonet J, Wood RD. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press: Cambridge, 1997.
24. Lucy L. Numerical approach to testing of the fission hypothesis. Astronomical Journal 1977; 82(12):1013-1024.
25. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20(8-9):1081-1106.
26. Randles PW, Libersky LD. Smoothed particle hydrodynamics: some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):375-408.
27. Krongauz Y, Belytschko T. Consistent pseudo-derivatives in meshless methods. Computer Methods in Applied Mechanics and Engineering 1997; 146(3-4):371-386.
28. Vila JP. On particle weighted methods and smooth particle hydrodynamics. Mathematical Models and Methods in Applied Sciences 1999; 9(2):161-209.
29. Fernandez-Mendez S, Huerta A. Imposing essential boundary conditions in mesh-free methods. Computer Methods in Applied Mechanics and Engineering 2004; 193(12-14):1257-1275.
30. Huerta A, Casadei F. New ALE applications in non-linear fast-transient solid dynamics. Engineering Computations 1994; 11(4):317-345.
31. Rodriguez-Ferran A, Casadei F, Huerta A. ALE stress update for transient and quasistatic processes. International Journal for Numerical Methods in Engineering 1998; 43(2):241-262.
32. Dyka CT, Ingel RP. An approach for tension instability in smoothed particle hydrodynamics (SPH). Computers and Structures 1995; 57(4):573-580.
33. Belytschko T, Xiao S. Stability analysis of particle methods with corrected derivatives. Computers and Mathematics with Applications 2002; 43(3-5):329-350.