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A Linear Matching Method for Shakedown Analysis

  • Alan R. S. Ponter
Part of the International Centre for Mechanical Sciences book series (CISM, volume 432)

Abstract

This article describes the Linear Matching Method for the evaluation of shakedown limits for bodies subjected to cyclic load and temperature and composed of an elastic-perfectly plastic material. The method provides a development of the Elastic Compensation and related methods that have been used as a practical design tool in industry for some time. Such methods may be developed into general upper bound methods that are capable of providing the minimum upper bound associated with a class of possible displacement fields as described, for example, by a finite element mesh. At the same time a sequence of lower bounds are generated that converge to the least upper bound. The ability to implement these methods within a standard commercial finite element code makes them particularly attractive for engineering applications.

Keywords

Yield Surface Limit Load Residual Stress Field Reverse Plasticity Strain Rate Field 
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.

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References

  1. Bree, J. (1967). Elasto-plastic behaviour of thin walled tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast reactor fuel elements. J Strain Analysis 2: 226–238.CrossRefGoogle Scholar
  2. Chen, H. F., Cen, Z. Z., Xu, B. Y. and Zhan, S. G. (1997). A numerical method for reference stress in the evaluation of structure integrity,” Int Journal of Pressure Vessel & Piping 71: 47–53.CrossRefGoogle Scholar
  3. Chen, H. and Ponter, A. R. S. (2001). A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading. Euro. Jn. Mech., A/Solids 20: 555–571.MathSciNetCrossRefMATHGoogle Scholar
  4. Chen, H. and Ponter, A. R. S. (2001). The 3-D shakedown and limit load using the elastic compensation method, Int Journal of Pressure Vessel & Piping, to appear.Google Scholar
  5. Engelhardt, M. (1999), Computational Modelling of Shakedown, Ph.D thesis, University of Leicester.Google Scholar
  6. Franco, J. R. Q. and Ponter, A. R. S. (1997). A general approximate technique for the finite element shakedown and limit load analysis of axisymmetric shells, Part 1: Theory and fundamental relationships. Int. Jn. for Num. Methods in Engrg 40: 3495–3513CrossRefMATHGoogle Scholar
  7. Franco, J. R. Q. and Ponter, A. R. S. (1997). A general approximate technique for the finite element shakedown and limit load analysis of axisymmetric shells, Part 2: Numerical applications. Int. Jn. for Num. Methods in Engrg. 40: 3515–3536.CrossRefGoogle Scholar
  8. Gokhfeld, D. A. and Cherniaysky, D.F. (1980). Limit Analysis of Structures at Thermal Cycling. Sijthoffl& Noordhoff. Alphen an Der Rijn, The Netherlands.Google Scholar
  9. Goodall, I. W., Goodman, A.M., Chell, G. C., Ainsworth, R. A., and Williams J. A. (1991). R5: An assessment procedure for the high temperature response of structures. Report, Nuclear Electric Ltd., Barnwood, Gloucester, UK.Google Scholar
  10. Hentz, S. (1998). Finite element limit state solutions, accuracy of an iterative method, Internal Report, Department of Engineering, University of Leicester.Google Scholar
  11. Koiter, W.T. (1960). General theorems of elastic-plastic solids. In Sneddon J.N. and Hill R., eds., Progress in Solid Mechanics 1: 167–221.Google Scholar
  12. König, J.A., (1987). Shakedown of Elastic-Plastic Structures, PWN-Polish Scientific Publishers, Warsaw and Elsevier, Amsterdam.Google Scholar
  13. Mackenzie, D. and Boyle, J.T. (1993). A simple method of estimating shakedown loads for complex structures Proc. ASME Pressure Vessel and Piping Conference, Denver.Google Scholar
  14. Parrinello, F. and Ponter, A. R. S. (2001). Shakedown limits based on linear solutions, for a hydrostatic pressure dependent material. Proc. 2 nd European Conference on Computational Mechanics, Cracow, Poland, June 2001, Abstracts, ISBN83–85688–68–4, 718 – 719, Institute of Computer Methods in Civil Engineering, Cracow University of Technology, Poland.Google Scholar
  15. Parrinello F, (2000). PhD thesis, University of Palermo, Italy.Google Scholar
  16. Polizzotto, C., Borino, G., Caddemi, S and Fuschi, P. (1991). Shakedown problems for materials with internal variables. Eur. J. Mech. A/ Solids 10: 621–639.MathSciNetMATHGoogle Scholar
  17. Ponter, A.R.S. and Carter, K.F. (1997). Limit state solutions, based upon linear elastic solutions with a statially varying elastic modulus. Comput. Methods Appl. Mech. Engrg. 140: 237–258.MathSciNetCrossRefMATHGoogle Scholar
  18. Ponter, A.R.S. and Carter, K.F., (1997). Shakedown state simulation techniques based on linear elastic solutions Comput. Methods Appl. Mech. Engrg. 140: 259–279.MathSciNetCrossRefMATHGoogle Scholar
  19. Ponter, A. R. S., Fuschi P. and Engelhardt, M. (2000). Limit analysis for a general class of yield conditions. European Journal of Mechanics, A/Solids 19: 401–421.CrossRefMATHGoogle Scholar
  20. Ponter, A. R. S. and Engelhardt, M. (2000). Shakedown limits for a general yield condition. European Journal of Mechanics, A/Solids 19: 423–445CrossRefMATHGoogle Scholar
  21. Ponter, A. R. S. and Chen H. (2001). A Minimum theorem for cyclic load in excess of shakedown, with applications to the evaluation of a ratchet limit. Euro. Jn. Mech., A/Solids, 20: 539–553.MathSciNetCrossRefMATHGoogle Scholar
  22. Ponter, A. R. S. (2001). Minimum theorems and iterative solution methods for creep cyclic loading problems, Meccanica, 296–8: 1–11.Google Scholar
  23. Riou, B., Ponter A.R.S., Carter K.F. and Guinovart J. (1997). Recent improvements in the ratchetting diagram method, Livolant M. ed. Trans. 14th Int. Conf. on Structural Mechanics in Reactor Technology, International Ass. for Structural Mechanics in Reactor Technology, 3:93–100.Google Scholar
  24. Seshadri, R. and Fernando, C.P.D., (1991) Limit loads of mechanical components and structures based on linear elastic solutions using the GLOSS R-Node method”, Trans ASME Pressure Vessel and Piping Conference, San Diego. 210–2: 125–134.Google Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Alan R. S. Ponter
    • 1
  1. 1.University of LeicesterLeicesterUK

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