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Analysis of dynamic stability of beam structures

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Abstract

This paper presents two numerical models (Model L and Model N) and its application in the analysis of dynamic stability of beam-type structures. Both numerical models use two-noded rotation-free finite elements and take into account the exact formulation for finite displacement, finite rotations, and finite strains. Model L was previously developed and is intended for linear elastic material behavior, whereas Model N is newly developed, considers laminar cross sections, and takes into account the nonlinear material behavior. Both models have been implemented into the open-source finite discrete element package Y-FDEM. Performance and conditions under which both numerical models can be used for the analysis of dynamic stability are presented by numerical examples which show good agreement in comparison with the analytical solutions.

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References

  1. Hoff, N.J.: The dynamics of the buckling of elastic columns. J. Appl. Mech. 18, 68–74 (1951)

    MathSciNet  MATH  Google Scholar 

  2. Erickson, B., Nardo, S.V., Patel, S.A., Hoff, N.J.: An experimental investigation of the maximum loads supported by elastic columns in rapid compression tests. Proc. Soc. Exp. Stress Anal. 14(1), 13–20 (1956)

    Google Scholar 

  3. Erickson, B., Mimura, K., Kikui, T., Nishide, N., Umeda, T., Riku, I., Hashimoto, H.: Buckling behavior of clamped and intermediately-supported long rods in the static–dynamic transition velocity region. J. Soc. Mater. Sci. 61(11), 881–887 (2012)

    Article  Google Scholar 

  4. Motamarri, P., Suryanarayan, S.: Unifed analytical solution for dynamic elastic buckling of beams for various boundary conditions and loading rates. Int. J. Mech. Sci. 56(1), 60–69 (2012)

    Article  Google Scholar 

  5. Sevin, E.: On the elastic bending of columns due to dynamic axial forces including effects of axial inertia. J. Appl. Mech. 27(1), 125–131 (1960)

    Article  MathSciNet  Google Scholar 

  6. Dym, C.L., Rasmussen, M.L.: On a perturbation problem in structural dynamics. Int. J. Non-Linear Mech. 3(2), 215–225 (1968)

    Article  Google Scholar 

  7. Elishakoff, I.: Hoff’s problem in a probabilistic setting. J. Appl. Mech. 47(2), 403–408 (1980)

    Article  Google Scholar 

  8. Kounadis, A.N., Mallis, J.: Dynamic stability of initially crooked columns under a time-dependent axial displacement of their support. Q. J. Mech. Math. 41(4), 579–596 (1988)

    Article  MathSciNet  Google Scholar 

  9. Tyler Jr., C.M.: Discussion of reference [2]. J. Appl. Mech. 18, 317 (1951)

    Google Scholar 

  10. Vaughn, D.G., Canning, J.M., Hutchinson, J.W.: Coupled plastic wave propagation and column buckling. J. Appl. Mech. 72(1), 139–146 (2005)

    Article  Google Scholar 

  11. Kuzkin, V.A., Dannert, M.M.: Buckling of a column under a constant speed compression: a dynamic correction to the Euler formula. Acta Mech. 227(6), 1645–1652 (2016)

    Article  MathSciNet  Google Scholar 

  12. Hutchinson, J.W., Budiansky, B.: Dynamic buckling estimates. AIAA J. 4(3), 525–530 (1966)

    Article  Google Scholar 

  13. Cui, S., Hao, H., Cheong, H.K.: Theoretical study of dynamic elastic buckling of columns subjected to intermediate velocity impact loads. Int. J. Mech. Sci. 44(4), 687–702 (2002)

    Article  Google Scholar 

  14. Smoljanović, H., Uzelac, I., Trogrlić, B., Živaljić, N., Munjiza, A.: A computationally efficient numerical model for a dynamic analysis of beam type structures based on the combined finite-discrete element method. Mater. Sci. Eng. Technol. 49(5), 651–665 (2018)

    Google Scholar 

  15. Munjiza, A.: The Combined Finite-Discrete Element Method. Wiley, London (2004)

    Book  Google Scholar 

  16. Munjiza, A., Knight, E.E., Rouiger, E.: Computational Mechanics of Discontinua. Wiley, London (2012)

    Google Scholar 

  17. Munjiza, A., Owen, D.R.J., Bicanic, N.: A combined finite-discrete element method in transient dynamics of fracturing solids. Eng. Comput. 12(2), 145–174 (1995)

    Article  Google Scholar 

  18. Munjiza, A., Bangash, T., John, N.W.M.: The combined finite-discrete element method for structural failure and collapse. Eng. Fract. Mech. 71(4–6), 469–483 (2004)

    Article  Google Scholar 

  19. Yun, X., Gardner, L.: Stress–strain curves for hot-rolled steels. J. Constr. Steel Res. 133, 36–46 (2017)

    Article  Google Scholar 

  20. Menegotto, M., Pinto, P.E.: Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behaviour of elements under combined normal force and bending. In: Proceedings of IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, Lisbon, pp. 15–22 (1973)

  21. Swope, W.C., Andersen, H.C., Berens, P.H., Wilson, K.R.: A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters. J. Chem. Phys. 76, 637–649 (1982)

    Article  Google Scholar 

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Acknowledgements

This paper is partially supported by the Croatian Government and the European Union by the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme under the Project KK.01.1.1.02.0027.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia

    Hrvoje Smoljanović, Ivan Balić, Ante Munjiza & Boris Trogrlić

  2. Faculty of Civil Engineering, University of Mostar, Mostar, Bosnia and Herzegovina

    Vlaho Akmadžić

Authors
  1. Hrvoje Smoljanović
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  2. Ivan Balić
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  3. Ante Munjiza
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  4. Vlaho Akmadžić
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  5. Boris Trogrlić
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Correspondence to Ivan Balić.

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Smoljanović, H., Balić, I., Munjiza, A. et al. Analysis of dynamic stability of beam structures. Acta Mech 231, 4701–4715 (2020). https://doi.org/10.1007/s00707-020-02793-6

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  • DOI: https://doi.org/10.1007/s00707-020-02793-6

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