Skip to main content

Application of Shakedown Analysis to Large-Scale Problems with Selective Algorithm

  • Chapter
Limit States of Materials and Structures

Abstract

Recent results obtained by using the lower-bound theorem of shakedown analysis are presented in this paper together with a new method for solving large-scale problems by using a selective algorithm. Industrially important examples from mechanical and pavement engineering are presented.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aboudi, A.J., Sloan, S.W.: A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion. Computers and Structures 54, 427–441 (1995).

    Article  Google Scholar 

  2. Akoa, F., Hachemi, A., Le Thi Hoai An, Mouhtamid, S., Pham Dinh Tao: Application of lower bound direct method to engineering structures. J. Global Optim. 37, 609–630 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  3. An Danh Nguyen: Lower-bound shakedown analysis of pavements by using the interior point method. Doctor thesis, RWTH Aachen (2007).

    Google Scholar 

  4. Ansys Release 8.0: Ansys, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317.

    Google Scholar 

  5. Cloud, R.L., Rodabaugh, E.C.: Approximate analysis of the plastic limit pressures of nozzles in cylindrical shells. Trans. ASME, J. Engrg. Power 4, 171–176 (1968).

    Google Scholar 

  6. Conn, A.R., Gould, N.I.M., Toint, Ph.L.: LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A). Berlin, Springer-Verlag (1992).

    MATH  Google Scholar 

  7. Feige, A.: Das Traglast-Berechnungsverfahren, 2. Aufl.; Verlag Stahleisen, Düsseldorf (1980).

    Google Scholar 

  8. Gokhfeld, D.A., Cherniavsky, O.F.: Limit analysis of structures at thermal cycling. Sijthoff and Noordhoff (1980).

    Google Scholar 

  9. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985).

    MATH  Google Scholar 

  10. Johnson, K.L.: The application of shakedown principles in rolling and sliding contact. Eur. J. Mech. A/Solids 11, 155–172 (1992).

    Google Scholar 

  11. Koiter, W.T.: General theorems for elastic-plastic solids. In: Sneddon, I.N., Hill, R. (eds.), Progress in Solid Mechanics. North-Holland, Amsterdam, pp. 165–221 (1960).

    Google Scholar 

  12. König, J.A.: Shakedown of elastic-plastic structures. Elsevier, Amsterdam (1987).

    Google Scholar 

  13. Le Thi Haoi An, Pham Dinh Tao: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23–46 (2005).

    Article  MathSciNet  Google Scholar 

  14. Maier, G., Pastor, J., Ponter, A.R.S., Weichert, D.: Direct Methods of Limit and Shakedown Analysis. In: De Borst, R.; Mang, H. A. (eds.), Numerical and computational methods, Chapter 12, Vol. 3. In: Milne, I., Ritchie, R. O.; Karihaloo, B. (eds.), Comprehensive Structural Integrity. Elsevier-Pergamon, Amsterdam (2003).

    Google Scholar 

  15. Martin, G.B.: Plasticity: Fundamentals and General Results. MIT Press, Cambridge, MA (1975).

    Google Scholar 

  16. Melan, E.: Zur Plastizität des räumlichen Kontinuums. Ing. Arch. 9, 116–126 (1938).

    Article  MATH  Google Scholar 

  17. Mouhtamid, S.: Anwendung direkter Methoden zur industriellen Berechnung von Grenzlasten mechanischer Komponenten. Doctor thesis, RWTH Aachen (2007).

    Google Scholar 

  18. Nayak G.C., Zienkiewicz O.C.: Conventional form of stress invariants for plasticity. J. Struct. Div., Proc. American Society Civil Engineers 98, 949–954 (1972).

    Google Scholar 

  19. Nguyen An Danh, Hachemi, A., Weichert, D.: Application of the interior-point method to shakedown analysis of pavements. Int. J. Numer. Meth. Engng. 75, 414–439 (2008).

    Article  Google Scholar 

  20. Sharp, R.W., Booker, J.R.: Shakedown of pavements under moving surface loads. J. Transp. Enrg. 110, 1–14 (1984).

    Article  Google Scholar 

  21. Vu, D.K.: Dual limit and shakedown analysis of structures. Doctor thesis, University of Liege Faculty of Applied Sciences (2001).

    Google Scholar 

  22. Wagner, W.: Festigkeitsberechnungen im Apparate- und Rohrleitungsbau. Vogel Buchverlag, Würzburg (1991).

    Google Scholar 

  23. Weichert, D., Maier, G.: Inelastic Behaviour of Structures under Variable Repeated Loads: Direct Analysis methods. CISM Courses and Lectures No. 432, International Centre for Mechanical Sciences, Springer Wien-New York (2002).

    Google Scholar 

  24. Wellinger, K, Dietmann, H.: Festigkeitsberechnung. Alfred Kröner Verlag, Stuttgart (1969).

    Google Scholar 

  25. Wächter, A., Biegler, L.T.: On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Non-linear Programming. IBM Research Report RC 23149 IBM T. J. Watson Research Center March, Yorktown Heights, NY. USA, pp. 1–28 (2004).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Hachemi, A., Mouhtamid, S., Nguyen, A., Weichert, D. (2009). Application of Shakedown Analysis to Large-Scale Problems with Selective Algorithm. In: Dieter, W., Alan, P. (eds) Limit States of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9634-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-9634-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9633-4

  • Online ISBN: 978-1-4020-9634-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics