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An Efficient Algorithm for Shakedown Analysis Based on Equality Constrained Sequential Quadratic Programming

  • Giovanni GarceaEmail author
  • Antonio Bilotta
  • Leonardo Leonetti
Chapter

Abstract

A new iterative algorithm to evaluate the elastic shakedown multiplier is proposed. On the basis of a three field mixed finite element, a series of mathematical programming problems or steps, obtained from the application of the proximal point algorithm to the static shakedown theorem, are obtained. Each step is solved by an Equality Constrained Sequential Quadratic Programming (EC-SQP) technique that retain all the equations and variables of the problem at the same level so allowing a consistent linearization that improves the computational efficiency. The numerical tests performed for 2D problems show the good performance and the great robustness of the proposed algorithm.

Keywords

Sequential Quadratic Programming Gauss Point Active Constraint Proximal Point Algorithm Proximal Point Method 
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.

Notes

Acknowledgments

The research leading to these results has received regional funding from the European Communitys Seventh Framework Programme FP7-FESR: “PIA Pacchetti Integrati di Agevolazione industria, artigianato e servizi” in collaboration with the Newsoft s.a.s. (www.newsoft-eng.it).

References

  1. 1.
    Bilotta A, Casciaro R (2002) Assumed stress formulation of high order quadrilateral elements with an improved in-plane bending behaviour. Comput Methods Appl Mech Eng 191(15–16):1523–1540CrossRefzbMATHGoogle Scholar
  2. 2.
    Bilotta A, Casciaro R (2007) A high-performance element for the analysis of 2d elastoplastic continua. Comput Methods Appl Mech Eng 196(4–6):818–828CrossRefzbMATHGoogle Scholar
  3. 3.
    Bilotta A, Leonetti L, Garcea G (2011) Three field finite elements for the elastoplastic analysis of 2D continua. Finite Elem Anal Des 47(10):1119–1130CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bilotta A, Leonetti L, Garcea G (2012) An algorithm for incremental elastoplastic analysis using equality constrained sequential quadratic programming. Comput Struct 102–103:97–107CrossRefGoogle Scholar
  5. 5.
    Bisbos CD, Makrodimopoulos A, Pardalos PM (2005) Second-order cone programming approaches to static shakedown analysis in steel plasticity. Optim Methods Softw 20(1):25–52CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bouby C, De Saxcé G, Tritsch J-B (2006) 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. Int J Solids Struct 43(9):2670–2692CrossRefzbMATHGoogle Scholar
  7. 7.
    Casciaro R, Garcea G (2002) An iterative method for shakedown analysis. Comput Methods Appl Mech Eng 191(49–50):5761–5792CrossRefzbMATHGoogle Scholar
  8. 8.
    Chen HF, Ponter ARS (2001) Shakedown and limit analyses for 3-d structures using the linear matching method. Int J Press Vessel Pip 78(6):443–451CrossRefGoogle Scholar
  9. 9.
    Garcea G, Leonetti L (2011) A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis. Int J Numer Methods Eng 88:1085–1111CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Garcea G, Trunfio GA, Casciaro R (1998) Mixed formulation and locking in path-following nonlinear analysis. Comput Methods Appl Mech Eng 165(1–4):247–272CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Garcea G, Armentano G, Petrolo S, Casciaro R (2005) Finite element shakedown analysis of two-dimensional structures. Int J Numer Methods Eng 63(8):1174–1202CrossRefzbMATHGoogle Scholar
  12. 12.
    Krabbenhoft K, Damkilde L (2003) A general non-linear optimization algorithm for lower bound limit analysis. Comput Methods Appl Mech Eng 56(2):165–184zbMATHGoogle Scholar
  13. 13.
    Krabbenhoft K, Lyamin AV, Sloan SW, Wriggers P (2007) An interior-point algorithm for elastoplasticity. Int J Numer Methods Eng 69(3):592–626CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Ngo NS, Tin-Loi F (2007) Shakedown analysis using the p-adaptive finite element method and linear programming. Eng Struct 29(1):46–56CrossRefGoogle Scholar
  15. 15.
    Nocedal J, Wright SJ (2000) Numerical optimization. Springer, New YorkGoogle Scholar
  16. 16.
    Pastor J, Thai TH, Francescato P (2003) Interior point optimization and limit analysis: an application. Commun Numer Methods Eng 19(10):779–785CrossRefzbMATHGoogle Scholar
  17. 17.
    Ponter ARS, Carter KF (1997) Shakedown state simulation techniques based on linear elastic solutions. Comput Methods Appl Mech Eng 140(3–4):259–279CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Simó JC, Hughes TJR (1998) Computational inelasticity mechanics and materials. Interdisciplinary applied mathematics. Springer, BerlinGoogle Scholar
  19. 19.
    Simon J-W, Weichert D (2011) Numerical lower bound shakedown analysis of engineering structures. Comput Methods Appl Mech Eng 200(41–44):2828–2839CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Simon J-W, Weichert D (2012) Shakedown analysis of engineering structures with limited kinematical hardening. Int J Solids Struct 49(15–16):2177–2186CrossRefMathSciNetGoogle Scholar
  21. 21.
    Simon J-W, Weichert D (2011) Numerical lower bound shakedown analysis of engineering structures. Comput Methods Appl Mech Eng 200(41–44):2828–2839CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Simon J-W, Kreimeier M, Weichert D (2013) A selective strategy for shakedown analysis of engineering structures. Int J Numer Methods Eng 94:985–1014CrossRefMathSciNetGoogle Scholar
  23. 23.
    Spiliopoulos KV, Panagiotou KD (2012) A direct method to predict cyclic steady states of elastoplastic structures. Comput Methods Appl Mech Eng 223–224:186–198CrossRefMathSciNetGoogle Scholar
  24. 24.
    Tran TN, Liu GR, Nguyen-Xuan H, Nguyen-Thoi T (2010) An edge-based smoothed finite element method for primal-dual shakedown analysis of structures. Int J Numer Methods Eng 82(7):917–938zbMATHMathSciNetGoogle Scholar
  25. 25.
    Vu DK, Yan AM, Nguyen-Dang H (2004) A primal-dual algorithm for shakedown analysis of structures. Comput Methods Appl Mech Eng 193(42–44):4663–4674CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Giovanni Garcea
    • 1
    Email author
  • Antonio Bilotta
    • 1
  • Leonardo Leonetti
    • 1
  1. 1.Dipartimento di Modellistica per L’IngegneriaUniversità della CalabriaCosenzaCalabria

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