Structural Engineering and Mechanics

  • 제25권1호
  • /
  • Pages.107-126
  • /
  • 2007
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bounds on plastic strains for elastic plastic structures in plastic shakedown conditions

  • Giambanco, Francesco (Dipartimento di Ingegneria Strutturale & Geotecnica (DISEG), Universita degli Studi di Palermo) ;
  • Palizzolo, Luigi (Dipartimento di Ingegneria Strutturale & Geotecnica (DISEG), Universita degli Studi di Palermo) ;
  • Caffarelli, Alessandra (Dipartimento di Ingegneria Strutturale & Geotecnica (DISEG), Universita degli Studi di Palermo)
  • 투고 : 2005.04.13
  • 심사 : 2006.08.07
  • 발행 : 2007.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

The problem related to the computation of bounds on plastic deformations for structures in plastic shakedown condition (alternating plasticity) is studied. In particular, reference is made to structures discretized by finite elements constituted by elastic perfectly plastic material and subjected to a special combination of fixed and cyclic loads. The load history is known during the steady-state phase, but it is unknown during the previous transient phase; so, as a consequence, it is not possible to know the complete elastic plastic structural response. The interest is therefore focused on the computation of bounds on suitable measures of the plastic strain which characterizes just the first transient phase of the structural response, whatever the real load history is applied. A suitable structural model is introduced, useful to describe the elastic plastic behaviour of the structure in the relevant shakedown conditions. A special bounding theorem based on a perturbation method is proposed and proved. Such theorem allows us to compute bounds on any chosen measure of the relevant plastic deformation occurring at the end of the transient phase for the structure in plastic shakedown; it represents a generalization of analogous bounding theorems related to the elastic shakedown. Some numerical applications devoted to a plane steel structure are effected and discussed.

키워드

참고문헌

  1. Benfratello, S., Cirone, L. and Giambanco, F. (2006), 'A multicriterion design of steel frames with shakedown constraints', Comput. Struct., 84, 269-282 https://doi.org/10.1016/j.compstruc.2005.09.015
  2. Capurso, M., Corradi, L. and Maier, G. (1979), 'Bounds on deformations and displacements in shakedown theory', Materiaux et structures sous chargement cyclique, Ass. amicale des ingenieurs anciens eleves de l'E.N.P.C., Paris, 231-244
  3. Corradi, L. (1983), 'A displacement formulation for the finite element elastic-plastic problem', Meccanica, 18, 77-91 https://doi.org/10.1007/BF02128348
  4. Cottle, R.W., Spang, J.S. and Stone, R.E. (1992), The Linear Complementarity Problem, Academic Press
  5. Giambanco, F. and Palizzolo, L. (1996), 'Computation of bounds on chosen measures of real plastic deformation for beams', Comput. Struct., 61(1), 171-182 https://doi.org/10.1016/0045-7949(96)00021-1
  6. Giambanco, F. and Palizzolo, L. (1997), 'Optimal bounds on plastic deformations for bodies constituted by temperature-dependent elastic hardening material', J. Appl. Mech., ASME, 64(3), 510-518 https://doi.org/10.1115/1.2788922
  7. Giambanco, F., Palizzolo, L. and Caffarelli, A. (2002), 'Optimal design of elastic plastic structures: Elastic and plastic shakedown formulations', Proc. of the 'Intensive Workshop' - Optimal Design of Materials and Structures, Paris, France
  8. Giambanco, F., Palizzolo, L. and Caffarelli, A. (2004), 'Computational procedures for plastic shakedown design of structures', J. of Structural and Multidisciplinary Optimization, 28, 317-329 https://doi.org/10.1007/s00158-004-0402-3
  9. Koiter, W.T. (1960), 'General theorem for elastic-plastic solids', In Progress in Solid Mechanics, Vol. I, Ed. I.N. Sneddon and R. Hill, North Holland, 165-219
  10. Konig, J.A. (1979), 'On upper bounds to shakedown loads', Z. Angew. Math., 59, 349-354 https://doi.org/10.1002/zamm.19790590803
  11. Konig, J.A. (1987), Shakedown of Elastic Plastic Structures, PWN-Polish Scientific Publishers, Warsaw and Elsevier, Amsterdam
  12. Maier, G. (1968), 'A quadratic programming approach for certain classes of nonlinear structural problems', Meccanica, 3, 121-130 https://doi.org/10.1007/BF02129011
  13. Melan, E. (1938a), 'Der Spannungszustand eines Hencky-Mises'shen continuum bei verandilicher Belastung', Stz. Ber. AK. Wiss Wien, 147, 73
  14. Melan, E. (1938b), 'Zur Plastzitat del raumlichen kontinuum', Ing. Arch., 9, 116 https://doi.org/10.1007/BF02084409
  15. Polizzotto, C. (1978), 'A unified approach to quasi-static shakedown problem for elastic-plastic solids with a piecewise linear yield surface', Meccanica, 13, 109-120 https://doi.org/10.1007/BF02128538
  16. Polizzotto, C. (1982), 'A unified treatment of shakedown theory and related bounding techniques', S. M. Archives, 7(1), 19-75
  17. Polizzotto, C., Borino, G. and Fuschi, P. (1990), 'On the steady-state response of elastic perfectly plastic solids to cyclic loads', In M. Kleiber, J.A. Konig (ed.), Inelastic Solids and Structures, Swansea (U.K.): Pineridge Press, 473-488
  18. Polizzotto, C. (1994a), 'On elastic plastic structures under cyclic loads', Eur. J. Mech. A/Solids, 13/4, 149-173
  19. Polizzotto, C. (1994b), 'Steady states and sensitivity analysis in elastic-plastic structures subjected to cyclic loads', Int. J. Solids Struct., 31, 953-970 https://doi.org/10.1016/0020-7683(94)90005-1
  20. Polizzotto, C., Borino, G. and Fuschi, P. (2001), 'Assessment of the elastic/plastic shakedown load boundary for structures subjected to cyclic loading', Proc. of XV Congresso Nazionale AIMETA, Taormina, Italy
  21. Ponter, A.R.S. and Haofeng, C. (2001), 'A minimum theorem for cyclic load in excess of shakedown, with application to the evaluation of a ratchet limit', Eur. J. Mech. A/Solids, 20, 539-553 https://doi.org/10.1016/S0997-7538(01)01161-5
  22. Zarka, J. and Casier, J. (1979), 'Elastic-plastic response of structure to cyclic loading: Practical rules', In S. Nemat Nasser (ed.), Mechanics Today, Oxford: Pergamon Press, 93-198
  23. Zarka, J., Frelat, J., Inglebert, G. and Kasnat-Navidi, P. (1990), 'A new approach in inelastic analysis of structure', Ecole Polytechnique Palaisau, France

피인용 문헌

  1. Discrete variable design of frames subjected to seismic actions accounting for element slenderness vol.147, 2015, https://doi.org/10.1016/j.compstruc.2014.09.016
  2. The scanning method for analysing the residual displacements of the framed structures at shakedown 2017, https://doi.org/10.1016/j.compstruc.2017.05.007
  3. Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads vol.44, pp.1, 2009, https://doi.org/10.1007/s00466-008-0350-7
  4. Minimum volume design of structures with constraints on ductility and stability vol.68, 2014, https://doi.org/10.1016/j.engstruct.2014.02.025