Stochastic dynamics of hysteretic media

  • Fabio Casciati
Parametric Stochastic Control of Non-Linear Systems and Stochastic Equivalent Linearization
Part of the Lecture Notes in Physics book series (LNP, volume 451)


Classic plasticity theory regards the yielding condition as discontinuity between elastic and plastic phases. This discontinuity leads obvious negative consequences in the mathematical features of the algorithm one uses in solving solid and structural mechanics problems.

Smoothed plasticity models are presently available in the framework of endochronic theory. This contribution discusses in particular three-dimensional tensorial smoothed idealizations of the Prager's model. Multivariate smoothed constitutive laws are also provided at a section level. Some aspect of the stochastic equivalent linearization algorithm which makes direct use of this smoothed model are discussed.


Yielding Surface Gauss Point Plastic Multiplier Hysteretic System Frame Storey 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bouc R., Modèle Mathématique d'Hysteresis (in French), Acustica, 24, 1971, pp 16–25Google Scholar
  2. 2.
    Wen Y.K., Equivalent Linearization for Hysteretic Systems under Random Excitation, J. Applied Mechanics, 47, 1980, pp. 150–154Google Scholar
  3. 3.
    Casciati F., Faravelli L., Methods of Non-linear Stochastic Dynamics for the Assessment of Structural Fragility, Nuclear Engineering and Design, 90, 1985, pp. 341–356Google Scholar
  4. 4.
    Casciati F., Faravelli L., Stochastic Linearization for 3-D Frames, accepted for publication in J. of Eng. Mech., ASCEGoogle Scholar
  5. 5.
    Casciati F., Faravelli L., Hysteretic 3-D Frames under Stochastic Excitation, accepted for publication in Res MechanicaGoogle Scholar
  6. 6.
    Ceradini G., Un legame costitutivo elasto-plastico pluridimensionale per materiali con degradazione (in Italian), in Sandro Dei Poli, A Festschrift for the 70th Birthday, Politecnico di Milano, 1985, pp.195–207Google Scholar
  7. 7.
    Casciati F., Faravelli L., Stochastic Equivalent Linearization for Dynamic Analysis of Continuous Structures, Proc. ASME/SES Meeting on Computational Probabilistic Methods, Berkeley, 1988, pp. 205–210Google Scholar
  8. 8.
    Casciati F., Faravelli L., Endochronic Theory and Nonlinear Stochastic Dynamics of 3D-Frame, ASCE Spec. Conf. on Probabilistic Methods in Civil Engineering, Blacksburg, 1988, pp. 400–403Google Scholar
  9. 9.
    Baber T.T., Wen Y.K., Stochastic Equivalent Linearization for Hysteretic Degrading Multistory Structures, UILU-ENG-80-2001, SRS 471, Univ. of Illinois, 1980Google Scholar
  10. 10.
    Bouc R., Forced Vibrations of a Mechanical System with Hysteresis, Proc. of 4th Conf. on Non-linear Oscillations, Prague, 1967Google Scholar
  11. 11.
    Casciati F., Non-Linear Stochastic Dynamics of Large Structural Systems by Equivalent Linearization, Proc. ICASPS, Vancouver, 1987, pp. 1165–1172Google Scholar
  12. 12.
    Bazant Z.P., Krizek R.J., Shieh C-L., Hysteretic Endochronic Theory for Sand, J. of Eng. Mech., ASCE, 109,1983, pp.1073–1095Google Scholar
  13. 13.
    Casciati F., Faravelli L., Singh M.P., Non-Linear Structural Response and Modeling Uncertainty on System Parameters and Seismic exxitation, Proc. 8th ECEE, Lisbon, 1986, 6.3, pp.41–48Google Scholar
  14. 14.
    Iwan W.D., Private Communication, 1988Google Scholar
  15. 15.
    Casciati F., Faravelli L., Non-Linear Stochastic Dynamics by Equivalent Linearization, in Casciati F. and Faravelli L. (eds.), Methods of Stochastic Structural Mechanics, SEAG, Pavia, 1986, pp.571–586Google Scholar
  16. 16.
    Karray M.A., Etude de l'Efficacité d'un Système d'Isolation á la Base avec Ammortissement par Plasticité (in French), Ph.D.Thesis, Univ. d'Aix-Marseille II, 1987.Google Scholar
  17. 17.
    Spanos P., Stochastic Linearization in Structural Dynamics, Appl. Mech. Rev., 34, 1981, pp 1–11Google Scholar
  18. 18.
    Casciati F., Faravelli L., Equivalent Linearization in Non Linear Random Vibration Problems, Proc. Int. Conf. on Vibration Problems in Eng., Xian, Cina, 1986, pp. 986–991Google Scholar
  19. 19.
    Baber T.T., Modal Analysis for Random Vibration of Hysteretic Frames, Earth. Eng. and Struct. Dyn., 14, 1986, pp.841–859Google Scholar
  20. 20.
    Casciati F., Faravelli L., Singh M.P., Stochastic Equivalent Linearization Algorithms and Their Applicability to Hysteretic Systems, accepted for publ. in MeccanicaGoogle Scholar
  21. 21.
    Singh M.P., Maldonado G., Heller R., Faravelli L., Modal Analysis of Nonlinear Hysteretic Structurs for Seismic Motions, in Ziegler F., Schueller G. (eds.), Non Linear Struct. Dynamics in Engineering Systems, Springer Verlag, 1988, pp. 443–454Google Scholar
  22. 22.
    Park Y.J., Wen, Y.K., Ang A.H-S., Random Vibration of Hysteretic Systems under Bi-Dimensional Ground Motion, Earth. EnR. and Struct. Dyn., 14, 1986, pp.543–557Google Scholar
  23. 23.
    Park Y.J., Ang A.H.-S., Seismic Damage Analysis of r/c Nuclear Structures, Proc. 9th SMiRT Conference, Lausanne, 1987, Vol. M, pp. 229–236Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Fabio Casciati

There are no affiliations available

Personalised recommendations