10.3. References

The following references are cited in this section:

  1.  R. Courant, K. Friedrichs and H. Lewy, "On the partial difference equations of mathematical physics", IBM Journal, March 1967, pp. 215-234

  2.  Meyers, M. A., (1994) "Dynamic behaviour of materials", John Wiley & Sons, ISBN 0-471-58262-X.

  3.  Zukas, J. A., (1990) "High velocity impact dynamics", John Wiley & Sons, ISBN 0-471-51444-6.

  4.  von Neumann, J., Richtmyer, R. D. (1950)., "A Method for the Numerical Calculation of Hydrodynamic Shocks", J. App. Phys., 21, pp 232-237, 1950

  5.  Wilkins, M. L., (1980).  "Use of Artificial Viscosity in Multidimensional Fluid Dynamic Calculations", J. Comp. Phys., 36, pp 281-303, 1980

  6.  Kosloff D., Frazier G. A., (1978) "Treatment of hourglass patterns in low order finite element codes", Int. J. Num. Anal. Meth. Geomech. 2, 57-72

  7.  Flanagan D. P., Belytschko T., (1981) "A uniform strain hexahedron and Quadrilateral and Orthogonal Hourglass Control", Int. J. Num. Meth. Eng. 17, 679-706.

  8.  Wilkins, M. L., Blum, R. E., Cronshagen, E. & Grantham, P. (1974).  "A Method for Computer Simulation of Problems in Solid Mechanics and Gas Dynamics in Three Dimensions and Time." Lawrence Livermore Laboratory Report UCRL-51574, 1974

  9. Hallquist, J. O., (1982) "A theoretical manual for DYNA3D, LLNL Report UCID-19401.

  10. Zienkiewicz, O. C., Taylor, R. L., "The finite element method, Volume 1", ISBN 0-07-084174-8

  11.  Burton, A..J.. (1996) 'Explicit, Large Strain, Dynamic Finite Element Analysis with Applications to Human Body Impact Problems', PhD Thesis, University of Wales.

  12.  Wilkins, M. L., Blum, R. E., Cronshagen, E., & Grantham, P. (1974).  "A Method for Computer Simulation of Problems in Solid Mechanics and Gas Dynamics in Three Dimensions and Time." Lawrence Livermore Laboratory Report UCRL-51574, 1974

  13. Belytschko, T., et al. (1984), "Explicit algorithms for the nonlinear dynamics of shells", Comp. Meth. Appl. Mech Eng., 42, 225-251.

  14. Belytschko, T., et al. (1992), "Advances in one-point quadrature shell elements", Comp. Meth. Appl. Mech Eng., 1992, 93-107.

  15. Belytschko, T., et al. (1984), "A C0 Triangular Plate Element with One-point Quadrature", Int. J. Num. Meth. Engng., 20, 787-802, 1984.

  16. Belytschko, T. et al., 1977, "Large Displacement Analysis of Space Frames", Int. J. Num. Meth. And Anal. Mech. Engng., 11, 65-84, 1977.

  17. Godunov, S. K. (1959), "A Difference Scheme for Numerical Solution of Discontinuous Solution of Hydrodynamic Equations", Math. Sbornik, 47, 271-306, translated US Joint Publ. Res. Service, JPRS 7226, 1969.

  18. Noh, W. F. and Woodward, P., “SLIC (Simple line interface calculation),” in Lecture Notes in Physics (A. I. van der Vooren and P. J. Zandbergen, eds.), pp. 330–340, Springer-Verlag, 1976.

  19. Van Leer, B (1977). “Towards the Ultimate Conservative Difference Scheme. IV. A new Approach to Numerical Convection”, J. Comp. Phys. 23, pp 276-299, 1977.

  20. Van Leer, B (1979). “Towards the Ultimate Conservative Difference Scheme. V. A Second Order Sequel to Godunov’s Method”, J. Comp. Phys. 32, pp 101-136, 1979.

  21. Bonet J., Marriott H., Hassan O. “An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamics applications”. Communications in Numerical Methods in Engineering 2001; 17, 551-561.

  22. Puso M. A.,Solberg J. “A stabilized nodally integrated tetrahedral”. International Journal for Numerical Methods in Engineering 2006; 67, 841-867.

  23. Liu, G.R., Liu, M.B., (2003) “Smoothed particle hydrodynamics: a meshfree particle method”, World Scientific Publishing Co., ISBN 981-238-456-1.