A simple rigid body algorithm for structural dynamics programs
D. J. Benson
University of California, Lawrence Livermore National Laboratory, Livermore, California. U.S.A.
Search for more papers by this authorJ. O. Hallquist
University of California, Lawrence Livermore National Laboratory, Livermore, California. U.S.A.
Search for more papers by this authorD. J. Benson
University of California, Lawrence Livermore National Laboratory, Livermore, California. U.S.A.
Search for more papers by this authorJ. O. Hallquist
University of California, Lawrence Livermore National Laboratory, Livermore, California. U.S.A.
Search for more papers by this authorAbstract
The analysis of low velocity impacts is necessary for designing everything from safe automobiles to safe shipping casks for nuclear material. Although great strides have been made in reducing the cost of impact analysis, the cost must be reduced even more before impact analysis becomes a routine design tool. One approach replaces the mesh outside of the impact zone with a rigid body.
References
- 1 W. F. Noh, ‘ Numerical methods in hydrodynamical calculations’, Rept. UCRL-52112, Univ. of California, Lawrence Livermore National Laboratory (1976).
- 2 D. J. Benson, ‘ The simulation of deformable mechanical systems using vector processors’, diss., Univ. of Michigan (1983).
- 3
J. T. Oden and
J. N. Reddy,
Variational Methods in Theoretical Mechanics,
2nd edn,
Springer-Verlag,
New York,
1983.
10.1007/978-3-642-68811-9 Google Scholar
- 4 J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, 1983.
- 5 K. Washizu, Variational Methods in Elasticity and Plasticity, 3rd edn. Pergamon Press, New York, 1982.
- 6 L. E. Malvern, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, 1969.
- 7 K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, 1982.
- 8 O. C. Zienkiewicz, The Finite Element Method, McGraw-Hill, London, 1979.
- 9 L. E. Elsgolc, Calculus of Variations, Addison Wesley, New York, 1961.
- 10 L. Meirovitch, Methods of Analytical Dynamics, McGraw-Hill, New York, 1970.
- 11 N. Orlandea, ‘ Node-analogous sparsity-oriented methods for the simulation of mechanical system’, diss., The Univ. of Michigan (1973).
- 12 P. E. Nikravesh and I. S. Chung, ‘Application of Euler parameters to the dynamic analysis of three dimensional constrained systems’, ASME J. Mech. Design, 104, 785–791 (1982).
- 13
B. J. de Veubeke,
‘The dynamics of flexible bodies’,
J. Eng. Sci.,
14,
895–913
(1976).
10.1016/0020-7225(76)90102-6 Google Scholar
- 14
T. R. Kane and
D. A. Levinson,
‘Formulation of equations of motion for complex spacecraft’,
J. Guid. Control,
3,
99–112
(1980).
10.2514/3.55956 Google Scholar
- 15
T. R. Hughes and
W. K. Liu,
‘Nonlinear finite element analysis of shells: Part I’,
J. Comp. Meths. Appl. Mech. Eng.,
26,
331–362
(1981).
10.1016/0045-7825(81)90121-3 Google Scholar
- 16 M. A. Chace and D. A. Smith, ‘ DAMN—a digital computer program for the dynamic analysis of generalized mechanical systems’, SAE Paper 710244 (1971).
- 17 P. N. Sheth, ‘ A digital computer based simulation procedure for multiple degree of freedom mechanical systems with geometrical constrains’, diss, Univ. of Wisconsin (1972).
- 18 J. R. Canavin and P. W. Likins, ‘Floating reference frames for flexible spacecraft’, J. Spacecract, 14, 724–732 (1977).
- 19 F. Buckens, ‘ The influence of elastic components on the attitude stability of a satellite’, Proc. Fifth Int. Symp. of Space Technology and Science, pp. 193–203 (1963).
- 20 T. J. Wielenga, ‘ Simplifications in the simulation of mechanisms containing flexible members’, diss. Univ. of Michigan (1984).
- 21 W. C. Hurty, ‘Dynamic analysis of structural systems using component modes’, A.I.A.A.J., 3, 678–685 (1965).
- 22 G. L. Goudreau and J. O. Hallquist, ‘Recent development in large scale finite element Lagrangian hydrocode technology’, J. Comp. Meths. Appl. Mechs. Eng., 33, 725–757 (1982).
- 23 J. O. Hallquist, ‘ Theoretical manual for DYNA3D’, Rept. UCID-19401, Univ. of California, Lawrence Livermore National Laboratory (1982).
- 24 T. J. R. Hughes and E. Carnoy, ‘ Nonlinear finite element shell formulation accounting for large membrane strains’, in Nonlinear Finite Element Analysis of Plates and Shells, AMD-Vol. 48, American Society of Mechanical Engineers, pp. 193–208 (1981).
- 25
T. J. R. Hughes,
W. K. Liu and
I. Levit,
‘ Nonlinear dynamics finite element analysis of shells’, in
Nonlinear Finite Element Analysis in Structural Mechanics:
( W. Wunderlich,
E. Stein and
K. J. Bathe, Eds.),
Springer-Verlag,
Berlin,
1981.
pp. 151–168.
10.1007/978-3-642-81589-8_9 Google Scholar
- 26 T. J. R. Hughes and J. Winget, ‘Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis’, Int. j. numer. methods eng., 15, 1862–1867 (1980).
- 27 J. O. Hallquist, ‘ NIKE2D: an implicit, finite-deformation, finite-element code for analyzing the static and dynamic response of two-dimensional solids’, Rept. UCRL-52678, Univ. of California, Lawrence Livermore National Laboratory (1979).