Skip to main content
SpringerLink
Log in

General analytical shakedown solution for structures with kinematic hardening materials

  • Advanced Manufacturing and Machining Technology
  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.

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

Similar content being viewed by others

References

  1. WEICHERT D, GROß-WEEGE J. The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two-surface yield condition[J]. International Journal of Mechanical Sciences, 1988, 30(10): 757–767.

    Article  MATH  Google Scholar 

  2. STEIN E, ZHANG G, HUANG Y. Modeling and computation of shakedown problems for nonlinear hardening materials[J]. Computer Methods in Applied Mechanics and Engineering, 1993, 103(1–2): 247–272.

    Article  MathSciNet  MATH  Google Scholar 

  3. STEIN E, ZHANG G, KÖNIG J A. Shakedown with nonlinear strain-hardening including structural computation using finite element method[J]. International Journal of Plasticity, 1992, 8(1): 1–31.

    Article  MATH  Google Scholar 

  4. PHAM D C. On shakedown theory for elastic-plastic materials and extensions[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 1905–1915.

    Article  MathSciNet  MATH  Google Scholar 

  5. PHAM D C. Shakedown theory for elastic plastic kinematic hardening bodies[J]. International Journal of Plasticity, 2007, 23(7): 1240–1259.

    Article  MATH  Google Scholar 

  6. HEITZER M, POP G, STAAT M. Basis reduction for the shakedown problem for bounded kinematic hardening material[J]. Journal of Global Optimization, 2000, 17(1): 185–200.

    Article  MathSciNet  MATH  Google Scholar 

  7. ABDEL-KARIM M. Shakedown of complex structures according to various hardening rules[J]. International Journal of Pressure Vessels and Piping, 2005, 82(6): 427–458.

    Article  Google Scholar 

  8. CHEN Shenshen, LIU Yinghua, LI Jun, et al. Performance of the MLPG method for static shakedown analysis for bounded kinematic hardening structures[J]. European Journal of Mechanics A/Solids, 2011, 30(2): 183–194.

    Article  MathSciNet  MATH  Google Scholar 

  9. NAYEBI A, EL A R. Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics[J]. International Journal of Mechanical Sciences, 2008, 50(8): 1247–1254.

    Article  MATH  Google Scholar 

  10. NGUYEN Q. On shakedown analysis in hardening plasticity[J]. Journal of The Mechanics and Physics of Solids, 2003, 51(1): 101–125

    Article  MathSciNet  MATH  Google Scholar 

  11. HEITZER M, STAAT M, REINERS H, et al. Shakedown and ratchetting under tension-torsion loadings: analysis and experiments[J]. Nuclear Engineering and Design, 2003, 225(1): 11–26.

    Article  Google Scholar 

  12. BOUBY C, DE SAXCE G, TRITSCH J-B. Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening[J]. Mechanics Research Communications, 2009, 36(5): 556–562.

    Article  MATH  Google Scholar 

  13. BOUBY C, DE SAXCÉ G, TRITSCH J B. A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening[J]. International Journal of Solids and Structures, 2006, 43(9): 2670–2692.

    Article  MATH  Google Scholar 

  14. SIMON J W. Direct evaluation of the limit states of engineering structures exhibiting limited, nonlinear kinematical hardening[J]. International Journal of Plasticity, 2013, 42: 141–167.

    Article  Google Scholar 

  15. SIMON J W. Limit states of structures in n-dimensional loading spaces with limited kinematical hardening[J]. Computers & Structures, 2015, 147: 4–13.

    Article  Google Scholar 

  16. SIMON J W, WEICHERT D. Shakedown analysis of engineering structures with limited kinematical hardening[J]. International Journal of Solids and Structures, 2012, 49(15–16): 2177–2186.

    Article  MathSciNet  Google Scholar 

  17. ABDALLA H F, MEGAHED M M, YOUNAN M Y A. A simplified technique for shakedown limit load determination of a large square plate with a small central hole under cyclic biaxial loading[J]. Nuclear Engineering and Design, 2011, 241(3): 657–665.

    Article  Google Scholar 

  18. TRAN T D, LE C V, PHAM D C, et al. Shakedown reduced kinematic formulation, separated collapse modes, and numerical implementation[J]. International Journal of Solids and Structures, 2014, 51(15–16): 2893–2899.

    Article  Google Scholar 

  19. KHALIJ L, HARIRI S, VAUCHER R. Shakedown of threedimensional structures under cyclic loading with the simplified analysis[J]. Computational Materials Science, 2002, 24(3): 393–400.

    Article  MATH  Google Scholar 

  20. PHAM D C. Shakedown working limits for circular shafts and helical springs subjected to fluctuating dynamic loads[J]. Journal of Mechanics of Materials and Structures, 2010, 5(3): 447–458.

    Article  Google Scholar 

  21. LEU S Y, LI J S. Shakedown analysis of truss structures with nonlinear kinematic hardening[J]. International Journal of Mechanical Sciences, 2015, 103: 172–180.

    Article  Google Scholar 

  22. HüBEL H. Simplified Theory of plastic zones for cyclic loading and multilinear hardening[J]. International Journal of Pressure Vessels and Piping, 2015, 129–130: 19–31.

    Article  Google Scholar 

  23. NAYEBI A, TIRMOMENIN A, DAMADAM M. Elasto-plastic analysis of a functionally graded rotating disk under cyclic thermo-mechanical loadings considering continuum damage mechanics[J]. International Journal of Applied Mechanics, 2015, 7(2): 1550026, 1–16.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education, Yanshan University, Qinhuangdao, 066004, China

    Baofeng Guo, Zongyuan Zou & Miao Jin

Authors
  1. Baofeng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zongyuan Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miao Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miao Jin.

Additional information

Supported by National Science and Technology Major Project of China (Grant No. 2013ZX04003031), National Natural Science Foundation of China(Grant No. 51575474), Hebei Provincial College Innovation Team Leader Training Program of China(Grant No. LJRC012), and Hebei Provincial Natural Science Foundation of China(Grant No. E2015203223)

GUO Baofeng, born in 1958, is currently a professor at Yanshan University, China. He received his PhD degree from Yanshan University, China, in 2001. His research interests include analysis and design for the frame of hydraulic press and stamping process.

ZOU Zongyuan, born in 1986, is currently a PhD candidate at Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education, Yanshan University, China. She received her bachelor degree from Yanshan University, China, in 2009. Her main research interest is strength analysis for the frame of hydraulic press.

JIN Miao, born in 1968, is currently a professor at Yanshan University, China. He received his PhD degree from Yanshan University, China, in 2000. His research interests include analysis and design for the frame of hydraulic press and forging process.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, B., Zou, Z. & Jin, M. General analytical shakedown solution for structures with kinematic hardening materials. Chin. J. Mech. Eng. 29, 944–953 (2016). https://doi.org/10.3901/CJME.2016.0304.025

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2016.0304.025

Keywords

Search

Navigation