Abstract
The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.
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Work supported by NSF Grant No. DCR81-14726.
Work supported by NSF Grant No. DMS87-01895.
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Day, W., Karwowski, A.J. & Papanicolaou, G.C. Buckling of randomly imperfect beams. Acta Appl Math 17, 269–286 (1989). https://doi.org/10.1007/BF00047074
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DOI: https://doi.org/10.1007/BF00047074