KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Elasto-Plastic Dynamic Analysis of Solids by Using SPH without Tensile Instability

인장 불안정이 제거된 SPH을 이용한 고체의 동적 탄소성해석

  • 이경수 (인하대학교 건축공학과) ;
  • 신상섭 (한양대학교 건설환경공학과) ;
  • 박대효 (한양대학교 건설환경공학과)
  • Received : 2010.09.13
  • Accepted : 2010.12.03
  • Published : 2011.04.30
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Abstract

In this paper elasto-plastic dynamic behavior of solid is analyzed by using smoothed particle hydrodynamics (SPH) without tensile instability which caused by a clustering of SPH particles. In solid body computations, the instability may corrupt physical behavior by numerical fragmentation which, in some cases of elastic or brittle solids, is so severe that the dynamics of the system is completely wrong. The instability removed by using an artificial stress which introduces negligible errors in long-wavelength modes. Applications to several test problems show that the artificial stress works effectively. These problems include the collision of rubber cylinders, fracture and crack of plate.

본 논문은 고체의 동적 탄소성해석을 수행하기 위해 인장불안정이 제거된 SPH기법을 사용하였다. 인장불안정은 SPH 입자들이 인장력에 의해 서로 떨어져나가는 해석적 오류현상이며, 재료적 특성에 따라 해석결과에 큰 영향을 미치게 된다. 이와 같은 인장불안정을 제어하기 위한 방법으로 본 연구에서는 가상응력의 개념을 적용하였다. 본 연구에서 제시한 SPH에 의해 해석예제를 수행하여 해석법의 효율성을 검증하였으며, 해석예제로 원형 링의 충돌문제와, 절단, 균열과 같은 재료적 파괴문제를 수행하였다.

Keywords

References

  1. 김남형, 고행식(2007) SPH 기법을 이용한 물기둥 붕괴의 수치 모의, 대한토목학회논문집, 대한토목학회, 제27권, 제3B호, pp. 313-318.
  2. 김유일, 남보우, 김용환(2007) SPH기법의 계산인자 민감도에 대한 연구, 대한조선학회논문집, 대한조선학회, 제44권, 제4호, pp. 398-407.
  3. 서송원, 이재훈, 민옥기(2005) 임의 형상의 강체면 탄소성 접촉 해석을 위한 SPH 알고리즘, 대한기계학회논문집 A권, 대한기계학회, 제29권 제1호, pp. 30-37.
  4. 윤성기, 이상호(2003) 무요소법의 이론과 적용, 제28-2회 전산구조공학회 기술강습회, 한국전산구조공학회.
  5. 이재훈, 서송원, 민옥기(2004) SPH기법을 이용한 복합 적층판의 초고속 충돌 해석, 2004년도 대한기계학회 추계학술대회 논문집, 대한기계학회, pp. 331-336.
  6. Atluri, S.N. and Zhu, T. (2000) A new meshless local petrov galerkin (MLPG) approach in computational mechanics, Computational Mechanics, Vol. 22, pp. 117-127.
  7. Belytschko, T., Lu, Y.Y., and Gu, L. (1994) Element-free galerkin methods, International Journal for Numerical methods in Engineering, Vol. 37, pp. 229-256. https://doi.org/10.1002/nme.1620370205
  8. Belytschko, T. and Xiao, S. (2002) Stability analysis of particle methods with corrected derivatives, Computers and Mathematics with Applications, Vol. 43, pp. 329-350. https://doi.org/10.1016/S0898-1221(01)00290-5
  9. Bonet, J. and Kulasegaram, S. (2000) Correction and stabilization of smoothed particle hydrodynamics methods with applications in metal forming simulations, Internat. J. Numer. Methods Engrg, Vol. 47, pp. 1189-1214. https://doi.org/10.1002/(SICI)1097-0207(20000228)47:6<1189::AID-NME830>3.0.CO;2-I
  10. Bonet, J., Kulasegaram, S., Rodriguez-Paz, M.X., and Profit, M. (2004) Variational formulation for the smoothe particle hydrodynamics(SPH) simulation of fluid and solid problems, Comput. Methods Appl. Mech. Engrg, Vol. 193, pp. 1245-1256. https://doi.org/10.1016/j.cma.2003.12.018
  11. Century Dynamics (2004) AUTODYN User's manual
  12. Chen, J.K., Beraun, J.E., and Jih, C.J. (1999) An improvement for tensile instability in smoothed particle hydrodynamics, Comput. Mech, Vol. 23, pp. 279-287. https://doi.org/10.1007/s004660050409
  13. Dilts, G.A. (1999) Moving least squares hydrodynamics: Consistency and stability, Internat. J. Numer. Methods Engrg, Vol. 44, pp. 1115-1155. https://doi.org/10.1002/(SICI)1097-0207(19990320)44:8<1115::AID-NME547>3.0.CO;2-L
  14. Dyka, C.T., Randles, P.W., and Ingel, R.P. (1997) Stress points for tension instability in SPH, Internat. J. Numer. Methods Engrg, Vol. 40, pp. 2325-2341. https://doi.org/10.1002/(SICI)1097-0207(19970715)40:13<2325::AID-NME161>3.0.CO;2-8
  15. Engelmann, B.E. (1991) NIKE2D User's Manual
  16. Gingold, R.A. and Monaghan, J.J. (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices Royal Astronomical Society, Vol. 181, pp. 375-389. https://doi.org/10.1093/mnras/181.3.375
  17. Gray, J.P., Monaghan, J.J., and Swift, R.P. (2001) SPH elastic dynamics, Comput. Methods Appl. Mech. Engrg, Vol. 190, pp. 6641- 6662. https://doi.org/10.1016/S0045-7825(01)00254-7
  18. Johnson, G.R. and Holmquist, T.J. (1988) Evaluation of cylinderimpact test data for constitutive model constants, J. Appl. Phys. Vol. 64, No. 8, pp. 3901-3910. https://doi.org/10.1063/1.341344
  19. Libersky, L.D. and Randles, P.W. (1998) Boundary conditions in a meshless staggered particle code, Technical Report LA-UR-98- 590, Los Alamos National Laboratory, Los Alamos, NM.
  20. Liu W. L., Jun S., Li S., Adee J., and Belytschko T. (1995) Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, Vol. 38, pp. 1655-1679. https://doi.org/10.1002/nme.1620381005
  21. Lucy, L.B. (1977) A numerical approach to the testing of fusion process, Astronomical Journal, Vol. 88, pp. 1013-1024.
  22. Maker, B.N., (1995) NIKE3D User's Manual.
  23. Monaghan, J.J. (2000) SPH without tensile instability, J. Comput. Phys. Vol. 159, pp. 290-311. https://doi.org/10.1006/jcph.2000.6439
  24. Morris, J.P., Fox, P.J., and Zhu, Y. (1997) Modeling low reynolds number incompressible flows using SPH, J. Comput. Phys. Vol. 136, pp. 214-226. https://doi.org/10.1006/jcph.1997.5776
  25. Phillips, G. and Monaghan, J.J. (1985) A numerical method for three-dimensional simulations of collapsing, isothermal, magnetic gas clouds, Mon. Not. R. Astron. Soc, Vol. 216, pp. 883- 895. https://doi.org/10.1093/mnras/216.4.883
  26. Randles, P.W. and Libersky, L.D. (2000) Normalized SPH with stress pointss, Int. J. Numer. Meth. Engng, Vol. 48, pp. 1445- 1462. https://doi.org/10.1002/1097-0207(20000810)48:10<1445::AID-NME831>3.0.CO;2-9
  27. Schussler, M. and Schmitt. D. (1981) Comments on smoothed particle hydrodynamics, Astron. Astrophys, Vol. 97, pp. 373-379.
  28. Sigalotti, L.D.G., Lopez, H., Donoso, A., Sira, E., and Klapp, J. (2006) A shock-capturing SPH scheme based on adaptive kernel estimation, J. Comput. Phys, Vol. 212, pp. 124-149. https://doi.org/10.1016/j.jcp.2005.06.016
  29. Sigalotti, L.D.G. and Lopez, H. (2008) Adaptive kernel estimation and SPH tensile instability, I. J. Computers and Mathematics with applications, Vol. 55, pp. 23-50. https://doi.org/10.1016/j.camwa.2007.03.007
  30. Swegle, J.W., SPH in Tension, Memo. (Sandia National Laborarories, 1992).
  31. Swegle, J.W., Hicks, D.L., and Attaway, S.W. (1995) Smoothed particle hydrodynamics stability analysis, J. Comput. Phys, Vol. 116, pp. 123-134. https://doi.org/10.1006/jcph.1995.1010
  32. Vidal, Y., Bonet, J., and Huerta1, A. (2007) Stabilized updated Lagrangian corrected SPH for explicit dynamic problems, Int. J. Numer. Meth. Engng, Vol. 69, pp. 2687-2710. https://doi.org/10.1002/nme.1859