Steady Cyclic State of a Structure: Methods of its Direct Determination

  • D. A. Gokhfeld
  • O. S. Sadakov
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 36)


Unlike the majority of publications in which the problem in question is considered within the framework of the shakedown theory and its specific mathematical methods, another approach is here developed. The latter is based on the structural (composite, layers) rheological model by which a more realistic description of deformation behavior of elastic-visco-plastic bodies can be obtained. In accordance with this model, the steady cyclic state of any structure made of an actual material is characterized, in the general case, by alternating inelastic deformation superposed on constant strain distribution which has been derived during the previous transient stage of the process. Methods of direct determination of the hysteresis loop parameters and of total (asymptotic) accumulated strain are discussed in the paper.


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  1. 1966 Frederick, C.O. & Arm Strong, P.J., Convergent internal stresses and steady cyclic state of stress. J. Strain Anal.,1, No.2, 154.Google Scholar
  2. 1971 Mroz, Z, On the theory of steady plastic cycles in structures, Trans. 1st Intern. SMiRT Conf., Berlin, Paper L5/6.Google Scholar
  3. 1975 Halphen, B., Stress accommodation in elastic-perfectly plastic and viscoplastic structures, Mech. Res. Comm., 2, 5–6.Google Scholar
  4. 1980 Gokhfeld, D.A. & Cherniavsky, O. F., Limit analysis of structures at thermal cycling. Sijthoff & Noordhoff, The Netherlands-USA.Google Scholar
  5. 1985 Ponter,A.R.S.& Cardeniz, S., An extended shakedown theory for structures that suffer cyclic thermal loading, Part I: Theory, J. Appl. Mech., 52, pp.877–882.Google Scholar
  6. 1990 Pollizotto, C., Bornio, G. & Fueschi, P., On the steady state response of elastic-perfectly plastic solids to cyclic loads, in: M. Kleiber & J.A König (eds), Inelastic Solids and Structures (Antoni Sawczuk Memorial Volume), Pineridge Press, Swansea, U.K., pp.473–478.Google Scholar
  7. 1987 König, J.A., Shakedown of elasto-plastic structures, PWN-Elsevier, Warsaw-Amsterdam.Google Scholar
  8. 1964 Shorr, B.F. Cyclic creep of non-uniformly heated cylinders, in Russian, in: Thermal Stresses in Structural Members, 4, Naukova Dumka, Kiev.Google Scholar
  9. 1984 Gokhfeld, D.A.& Sadakov, O.S. Plasticity and creep of structural elements subjected to repeated loading, in Russian. Mashinostrojenije, Moscow.Google Scholar
  10. 1989 Gokhfeld, D.A., Kononov, K.M., Poroshin, V.B. & Sadakov, O.S., Coupled mathematical models for cyclic inelastic deformation and damage accumulation processes Trans. 10th Int. SMiRT Conf. Anaheim, Calif, USA, Paper L1/5.Google Scholar
  11. 1984 Krempl, E. & Kallianpur, V.V., Some critical uniaxial experiments for viscoplasticity at room temperature, J. Mech. Phys. Solids. 32, No.4.Google Scholar
  12. 1990 Gokhfeld D.A., & Sadakov, O.S., On the main approaches to strength and lifetime evaluation of structures under variable-repeated load and temperature, in: M. Kleiber & J.-A König (eds), Inelastic Solids and Structures (Antoni Sawczuk Memorial Volume), Pineridge Press, Swansea, U.K. pp. 415–432.Google Scholar
  13. 1952 Koiter, W.T., Some remarks on plastic shakedown theorems. Proc. 8th Intern. Congr. Appl. Mech., Istanbul, 1, 220.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • D. A. Gokhfeld
    • 1
  • O. S. Sadakov
    • 1
  1. 1.Cheliabinsk State Technical UniversityCheliabinskRussia

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