Unconditionally stable mid-point time integration in elastic-plastic dynamics

Alberto Corigliano; Umberto Perego

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 4, page 367-376
  • ISSN: 1120-6330

Abstract

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The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional stability of the adopted integration method is proved according to two nonlinear stability

How to cite

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Corigliano, Alberto, and Perego, Umberto. "Unconditionally stable mid-point time integration in elastic-plastic dynamics." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.4 (1990): 367-376. <http://eudml.org/doc/244074>.

@article{Corigliano1990,
abstract = {The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional stability of the adopted integration method is proved according to two nonlinear stability},
author = {Corigliano, Alberto, Perego, Umberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Dynamics; Time integration; Elastoplasticity; Stability; Newton-Raphson iterative scheme},
language = {eng},
month = {12},
number = {4},
pages = {367-376},
publisher = {Accademia Nazionale dei Lincei},
title = {Unconditionally stable mid-point time integration in elastic-plastic dynamics},
url = {http://eudml.org/doc/244074},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Corigliano, Alberto
AU - Perego, Umberto
TI - Unconditionally stable mid-point time integration in elastic-plastic dynamics
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/12//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 4
SP - 367
EP - 376
AB - The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional stability of the adopted integration method is proved according to two nonlinear stability
LA - eng
KW - Dynamics; Time integration; Elastoplasticity; Stability; Newton-Raphson iterative scheme
UR - http://eudml.org/doc/244074
ER -

References

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  5. COMI, C. - MAIER, G. - PEREGO, U., Generalized variables finite element modelling and extremum theorems in stepwise holonomic elastoplasticity with internal variables. 1990, to appear. Zbl0761.73107MR1162380DOI10.1016/0045-7825(92)90133-5
  6. HUGHES, T. J. R., Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics. Computer and Structures, 6, 1976, 313-324. Zbl0351.73102MR455775
  7. HUGHES, T. J. R. - CAUGHEY, T. K. - LIU, W. K., Finite element methods for nonlinear elastodynamics which conserve energy. ASME J. of App. Mech., 45, 1978, 366-370. Zbl0392.73075
  8. BELYTSCHKO, T. - SCHOEBERLE, D. F., On the unconditional stability of an implicit algorithm for non-linear structural dynamics. ASME J. of App. Mech., 17, 1975, 865-869. 
  9. HUGHES, T. J. R., A note on the stability of Newmark's algorithm in nonlinear structural dynamics. Int. J. for Num. Meth. in Eng., 11, 1977, 383-386. Zbl0363.73079
  10. SIMO, J. C. - GOVINDJEE, S., Nonlinear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity. 1990, to appear. Zbl0825.73959MR1087203DOI10.1002/nme.1620310109
  11. SIMO, J. C. - WONG, K. K., Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy. Int. J. for Num. Meth. in Eng., 1990, to appear. Zbl0825.73960
  12. NGUYEN, Q. S., On the elastic plastic initial boundary value problem and its numerical integration. Int. J. for Num. Meth. in Eng., 11, 1977, 817-823. Zbl0366.73034MR446041
  13. COMI, C. - CORIGLIANO, A. - MAIER, G., Extremum properties of finite step solutions in elastoplasticity with nonlinear mixed hardening. Int. J. of Solids and Structures, 1990, to appear. Zbl0734.73024MR1085612DOI10.1016/0020-7683(91)90094-V

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