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Linear instability or buckling problems for mechanical and coupled thermomechanical extreme conditions

  • Ibrahimbegovic, Adnan (Laboratoire de mecanique et technologie, Ecole Normale Superieure) ;
  • Hajdo, Emina (Laboratoire de mecanique et technologie, Ecole Normale Superieure) ;
  • Dolarevic, Samir (Faculty of Civil Engineering, University of Sarajevo)
  • 투고 : 2014.01.30
  • 심사 : 2014.03.12
  • 발행 : 2013.12.25

초록

In this work we propose a novel procedure for direct computation of buckling loads for extreme mechanical or thermomechanical conditions. The procedure efficiency is built upon the von Karmann strain measure providing the special format of the tangent stiffness matrix, leading to a general linear eigenvalue problem for critical load multiplier estimates. The proposal is illustrated on a number of validation examples, along with more complex examples of interest for practical applications. The comparison is also made against a more complex computational procedure based upon the finite strain elasticity, as well as against a more refined model using the frame elements. All these results confirm a very satisfying performance of the proposed methodology.

키워드

과제정보

연구 과제 주관 기관 : French Ministry of Foreign Affairs

참고문헌

  1. Bathe, K.J. (1996), Finite Element procedures, Prentice-Hall, Englewood Cliffs, NJ, USA.
  2. Dujc, J., Brank, B. and Ibrahimbegovic, A. (2010), "Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling", Comp. Meth. Appl. Mech. Eng., 199(21-22), 1371-1385. https://doi.org/10.1016/j.cma.2009.09.003
  3. Ericsken, J. (1998), Introduction to the Thermodynamics of Solids, Springer, Berlin, Germany.
  4. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Springer, Berlin, Germany.
  5. Ibrahimbegovic, A. and Al Mikdad, M. (2000), "Quadratically convergent direct calculation of critical points for 3d structures undergoing finite rotations", Comp. Meth. Appl. Mech. Eng., 189(1), 107-120. https://doi.org/10.1016/S0045-7825(99)00291-1
  6. Ibrahimbegovic, A. and Chorfi, L. (2000), "Viscoplasticity model in finite deformations with combined isotropic and kinematic hardening", Comput. Struct., 77(5), 509-525. https://doi.org/10.1016/S0045-7949(99)00232-1
  7. Ibrahimbegovic, A. and Chorfi, L. (2002), "Covariant principal axis formulation of associated coupled thermoplasticity at finite strains and its numerical implementation", Int. J. Solids. Struct., 39(2), 499-528. https://doi.org/10.1016/S0020-7683(01)00221-9
  8. Ibrahimbegovic, A. and Wilson, E.L. (1990), "Automated truncation of Ritz vector basis in modal transformation", J. Eng. Mech. - ASCE, 116(11), 2506-2520. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:11(2506)
  9. Ibrahimbegovic, A., Chen, H.C., Wilson, E.L. and Taylor, R.L. (1990), "Ritz method for dynamic analysis of linear systems with non-proportional damping", Earthq. Eng. Struct. D., 19(6), 877-889. https://doi.org/10.1002/eqe.4290190608
  10. Ibrahimbegovic, A., Chorfi, L. and Gharzeddine, F. (2001), "Thermomechanical coupling at finite elastic strain: Covariant formulation and numerical implementation", Numer. Meth., 17(4), 275-289.
  11. Ibrahimbegovic, A., Colliat, J.B. and Davenne, L. (2005), "Thermomechanical coupling in folded plates and non-smooth shells", Comp. Meth. Appl. Mech. Eng., 194(21-24), 2686-2707. https://doi.org/10.1016/j.cma.2004.07.052
  12. Ibrahimbegovic, A., Shakourzadeh, H., Batoz, J.L., Al Mikdad, M. and Guo, Y.Q. (1996), "On the role of geometrically exact and second order theories in buckling and post-buckling analysis of three-dimensional beam structures", Comput. Struct., 61(6), 1101-1114. https://doi.org/10.1016/0045-7949(96)00181-2
  13. Ngo, V.M., Ibrahimbegovic, A. and Brancherie, D. (2013), "Model for localized failure with thermo-plastic coupling: Theoretical formulation and ED-FEM implementation", Comput. Struct., 127, 2-18. https://doi.org/10.1016/j.compstruc.2012.12.013
  14. Timoshenko, S.P. and Gere, J.M. (1962), Theory of Elastic Stability, (2nd Edition), McGraw-Hill Co., New York, USA.
  15. Yang, Y.B., Lin, T.J., Leu, L.J. and Huang, C.W. (2008), "Inelastic postbuckling response of steel trusses under thermal loadings", J. Constr. Steel. Res., 64(12), 1394-1407. https://doi.org/10.1016/j.jcsr.2008.01.004
  16. Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method, Vols. I, II, III, Elsevier, Oxford, UK.

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