Abstract
The postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed. This is established by employing an approximate analytic technique leading to very reliable results in the vicinity of the critical state. It was found that the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections. Moreover, a simple but readily analyzed mechanical model is proposed to simulate the salient features of buckling mechanism of the column on elastic foundation with those of the model. The simplicity, reliability and efficiency of the proposed analysis as well as the successful modeling of the buckling mechanism of the column by that of a single mode mechanical model are illustrated with the aid of numerical examples.
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References
Kounadis, A.N.: Efficiency and accuracy of linearized postbuckling analyses of frames based on elastica. Int J Solids Struct 24(11): 1097–1112 (1988)
Bushnell, D.: Computerized buckling analysis of shells, vol 25. Martinus Nijhoff Publishers , Pordrecht (1985)
Timoshenko, S.P., Gere, J.M.: Theory of elastic stability. Mc Graw-Hill, New York, Sec 11.1 (1961)
Bodner, S.R., Rubin, M.B.: Modeling the buckling of axially compressed elastic cylindrical shells. AIAA J 42(12), 2004
Zhang, Y., Murphy Kevin, D.: Secondary buckling and tertiary states of a beam on a non-linear elastic foundation. Int J Non Linear Mech 40, 795–805 (2005)
Hunt, G.W., Everall, P.R.: Mode jumping in the buckling of struts and plates: a comparative study. Int J Non Linear Mech 35, 1067–1079 (2000)
Sheinman, I., Adam M.: Imperfection sensitivity of a beam on a nonlinear elastic foundation Int J Mech Sci 33(9), 753–760 (1991)
Sheinman, I., Adam, M., Altus, E.: On the role of the displacement function in Nonlinear analysis of beams on an elastic foundation. Thin Walled Struct 15, 109–125 (1993)
Hunt, G.W., Wadee, M.K. Shiacolas, N.: Localized Elasticae for the strut on the linear foundation. J Appl Mech ASME 60, 1033–1038 (1993)
Kounadis, A.N.: An efficient and simple approximate technique for solving non-linear initial and boundary-value problems. Comput Mech 9, 221–231 (1992)
Thompson, J.M.T., Hunt, G.W.: A general theory of elastic stability. Wiley, London, p. 28 (1973)
Kounadis, A.N., Ioannidis, G.: Lateral postbuckling analysis of beam columns. J Eng Mech Div ASCE 120(4) 695–706 (1994)
Brush, O.D., Almroth, O.Bo.: Buckling of bars, plates and shells. Mc Graw-Hill, New york, pp. 35–37 (1975)
Chen, W.-F., Atsuta, T.: Theory of beam-columns, vol. 1. Mc Graw- Hill, New york pp. 106–110 (1976)
Budiansky, B., Hutchinson, J.W.: Dynamic buckling of imperfection sensitive structures. Proceedings of the XI international congress of applied mechanics. Springer, Berlin, Heidelberg, New york pp. 636–651 (1966)
Kounadis, A.N.: Dynamic stability criteria of nonlinear elastic damped/undamped systems under step loading. AIAA 28 (7), pp. 1217–1223 (1990)
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Kounadis, A., Mallis, J. & Sbarounis, A. Postbuckling analysis of columns resting on an elastic foundation. Arch Appl Mech 75, 395–404 (2006). https://doi.org/10.1007/s00419-005-0434-1
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DOI: https://doi.org/10.1007/s00419-005-0434-1