Skip to main content
SpringerLink
Log in

Stress and strain fields in rotating elastic/plastic annular discs

  • Special
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The von Mises yield criterion is used in conjunction with its associated flow rule to provide the elastic/plastic stress and strain distributions within the rotating annular discs made of perfectly plastic material under plane stress conditions. The solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one. The strain solution requires a numerical technique to evaluate ordinary integrals. An example is presented to illustrate the general solution. The general method proposed can be readily extended to orthotropic and pressure-dependent yield criteria.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Gamer, U., Kollmann, F.G.: A theory of rotating elasto-plastic shrink fits. Ing. Arch. 56, 254–264 (1986)

    Article  MATH  Google Scholar 

  2. Akis, T., Eraslan, A.N.: Exact solution of rotating FGM shaft problem in the elastoplastic state of stress. Arch. Appl. Mech. 77, 745–765 (2007)

    Article  MATH  Google Scholar 

  3. Nejad, M.Z., Rastgoo, A., Hadi, A.: Exact elasto-plastic analysis of rotating disks made of functionally graded materials. Int. J. Eng. Sci. 85, 47–57 (2014)

    Article  MathSciNet  Google Scholar 

  4. Eraslan, A.N.: Stress distributions in elastic–plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria. ZAMM 85, 252–266 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Toussi, H.E., Farimani, M.R.: Elasto-plastic deformation analysis of rotating disc beyond its limit speed. Int. J. Press. Ves. Pip. 89, 170–177 (2012)

    Article  Google Scholar 

  6. Hassani, A., Hojjati, M.H., Farrahi, G.H., Alashti, R.A.: Semi-exact solution for thermo-mechanical analysis of functionally graded elastic–strain hardening rotating disks. Commun. Nonlinear Sci. Numer. Simul. 17, 3747–3762 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rees, D.W.A.: Elastic–plastic stresses in rotating discs by von Mises and Tresca. ZAMM 79, 281–288 (1999)

    Article  MATH  Google Scholar 

  8. Alexandrova, N., Alexandrov, S., Vila Real, P.: Displacement field and strain distribution in a rotating annular disk. Mech. Based Des. Struct. Mach. 32, 441–457 (2004)

    Article  Google Scholar 

  9. Aleksandrova, N.: Application of Mises yield criterion to rotating solid disk problem. Int. J. Eng. Sci. 51, 333–337 (2012)

    Article  MathSciNet  Google Scholar 

  10. Alexandrova, N., Alexandrov, S.: Elastic–plastic stress distribution in a plastically anisotropic rotating disk. Trans. ASME J. Appl. Mech. 71, 427–429 (2004)

    Article  MATH  Google Scholar 

  11. Alexandrov, S.E., Lomakin, E.V., Jeng, Y.-R.: Effect of the pressure dependency of the yield condition on the stress distribution in a rotating disk. Dokl. Phys. 55, 606–608 (2010)

    Article  Google Scholar 

  12. Timoshenko, S.P., Goodier, J.N.: Theory of elasticity, 3rd edn. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  13. Kleiber, M., Kowalczyk, P.: Sensitivity analysis in plane stress elasto-plasticity and elasto-viscoplasticity. Comput. Methods Appl. Mech. Eng. 137, 395–409 (1996)

    Article  MATH  Google Scholar 

  14. Roberts, S.M., Hall, F.R., Bael, A.V., Hartley, P., Pillinger, I., Sturgess, C.E.N., Houtte, P.V., Aernoudt, E.: Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modeling of metal forming processes. J. Mater. Process. Technol. 34, 61–68 (1992)

    Article  Google Scholar 

  15. Helsing, J., Jonsson, A.: On the accuracy of benchmark tables and graphical results in the applied mechanics literature. Trans. ASME J. Appl. Mech. 69, 88–90 (2002)

    Article  MATH  Google Scholar 

  16. Hill, R.: The Mathematical Theory of Plasticity. Clarendon Press, Oxford (1950)

    MATH  Google Scholar 

  17. Alexandrov, S., Jeng, Y.-R., Lomakin, E.: Effect of pressure-dependency of the yield criterion on the development of plastic zones and the distribution of residual stresses in thin annular disks. Trans. ASME J. Appl. Mech. 78, 031012 (2011)

    Article  Google Scholar 

  18. Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis for limit design. Q. Appl. Math. 10, 157–165 (1952)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors acknowledge financial support of this research through Grants 14-01-92002 (RFBR, Russia), 103-2923-E-194-002-MY3 (NSC, Taiwan) and NSH-1275.2014.1 (Russia).

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia, 119991

    Evgenii Lomakin

  2. A.Yu. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, Moscow, Russia, 119526

    Sergei Alexandrov

  3. Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University, Chia-Yi, 62102, Taiwan

    Yeau-Ren Jeng

Authors
  1. Evgenii Lomakin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei Alexandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yeau-Ren Jeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yeau-Ren Jeng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lomakin, E., Alexandrov, S. & Jeng, YR. Stress and strain fields in rotating elastic/plastic annular discs. Arch Appl Mech 86, 235–244 (2016). https://doi.org/10.1007/s00419-015-1101-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1101-9

Keywords

Search

Navigation