Localized elastic buckling: non-linearities versus inhomogeneities

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Abstract

Buckling of an elastic beam-column resting on an inhomogeneous Winkler foundation is revisited from the standpoint of multiscale asymptotic analysis. Despite the complexity posed by the presence of non-linearity and variable coefficients in the governing eigenproblems, our analytical strategy is shown to capture successfully both the linear and the incipient post-buckling regimes. In particular, the present investigation produces a non-linear amplitude equation with variable coefficients that accounts for the spatial inhomogeneity in the normal restoring force of the foundation. Localization is here due to the spectral properties of the corresponding linearized buckling operator, whereas the role of the non-linearities remains confined to that of amplifying such behaviour.

LanguageEnglish
Pages461-474
Number of pages14
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume75
Issue number3
Early online date24 Feb 2010
DOIs
Publication statusPublished - Jun 2010
Externally publishedYes

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Variable Coefficients
Buckling
Inhomogeneity
Nonlinearity
Postbuckling
Multiscale Analysis
Amplitude Equations
Eigenproblem
Spectral Properties
Asymptotic Analysis
Nonlinear Equations
Asymptotic analysis
Operator
Strategy

Cite this

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title = "Localized elastic buckling: non-linearities versus inhomogeneities",
abstract = "Buckling of an elastic beam-column resting on an inhomogeneous Winkler foundation is revisited from the standpoint of multiscale asymptotic analysis. Despite the complexity posed by the presence of non-linearity and variable coefficients in the governing eigenproblems, our analytical strategy is shown to capture successfully both the linear and the incipient post-buckling regimes. In particular, the present investigation produces a non-linear amplitude equation with variable coefficients that accounts for the spatial inhomogeneity in the normal restoring force of the foundation. Localization is here due to the spectral properties of the corresponding linearized buckling operator, whereas the role of the non-linearities remains confined to that of amplifying such behaviour.",
keywords = "Amplitude equations, Bifurcations, Elastic stability, Multiscale asymptotics, Winkler foundation",
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T2 - IMA Journal of Applied Mathematics

AU - Coman, Ciprian D.

PY - 2010/6

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N2 - Buckling of an elastic beam-column resting on an inhomogeneous Winkler foundation is revisited from the standpoint of multiscale asymptotic analysis. Despite the complexity posed by the presence of non-linearity and variable coefficients in the governing eigenproblems, our analytical strategy is shown to capture successfully both the linear and the incipient post-buckling regimes. In particular, the present investigation produces a non-linear amplitude equation with variable coefficients that accounts for the spatial inhomogeneity in the normal restoring force of the foundation. Localization is here due to the spectral properties of the corresponding linearized buckling operator, whereas the role of the non-linearities remains confined to that of amplifying such behaviour.

AB - Buckling of an elastic beam-column resting on an inhomogeneous Winkler foundation is revisited from the standpoint of multiscale asymptotic analysis. Despite the complexity posed by the presence of non-linearity and variable coefficients in the governing eigenproblems, our analytical strategy is shown to capture successfully both the linear and the incipient post-buckling regimes. In particular, the present investigation produces a non-linear amplitude equation with variable coefficients that accounts for the spatial inhomogeneity in the normal restoring force of the foundation. Localization is here due to the spectral properties of the corresponding linearized buckling operator, whereas the role of the non-linearities remains confined to that of amplifying such behaviour.

KW - Amplitude equations

KW - Bifurcations

KW - Elastic stability

KW - Multiscale asymptotics

KW - Winkler foundation

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JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

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