Bifurcation instabilities in finite bending of circular cylindrical shells

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This work re-visits the finite pure bending problem for circular cylindrical shells within the elastic range. The interest here is primarily directed towards the bifurcation instabilities of such configurations when the progressive flattening of the cylindrical cross-section is explicitly taken into account (the so-called Brazier effect). By coupling Reissner's axisymmetric solution to the buckling equations for a quasi-shallow toroidal shell we formulate a novel boundary-value problem able to capture such bifurcations. Numerical simulations of this problem confirm that buckling occurs before the usual limit-point instability is reached, while singular perturbation methods allow us to obtain simple asymptotic approximations for the critical curvature and bending moment associated with the bifurcations.

LanguageEnglish
Pages249-264
Number of pages16
JournalInternational Journal of Engineering Science
Volume119
Early online date23 Jun 2017
DOIs
Publication statusPublished - Oct 2017
Externally publishedYes

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Buckling
Bifurcation (mathematics)
Bending moments
Boundary value problems
Computer simulation

Cite this

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title = "Bifurcation instabilities in finite bending of circular cylindrical shells",
abstract = "This work re-visits the finite pure bending problem for circular cylindrical shells within the elastic range. The interest here is primarily directed towards the bifurcation instabilities of such configurations when the progressive flattening of the cylindrical cross-section is explicitly taken into account (the so-called Brazier effect). By coupling Reissner's axisymmetric solution to the buckling equations for a quasi-shallow toroidal shell we formulate a novel boundary-value problem able to capture such bifurcations. Numerical simulations of this problem confirm that buckling occurs before the usual limit-point instability is reached, while singular perturbation methods allow us to obtain simple asymptotic approximations for the critical curvature and bending moment associated with the bifurcations.",
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Bifurcation instabilities in finite bending of circular cylindrical shells. / Coman, Ciprian D.

In: International Journal of Engineering Science, Vol. 119, 10.2017, p. 249-264.

Research output: Contribution to journalArticle

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T1 - Bifurcation instabilities in finite bending of circular cylindrical shells

AU - Coman, Ciprian D.

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AB - This work re-visits the finite pure bending problem for circular cylindrical shells within the elastic range. The interest here is primarily directed towards the bifurcation instabilities of such configurations when the progressive flattening of the cylindrical cross-section is explicitly taken into account (the so-called Brazier effect). By coupling Reissner's axisymmetric solution to the buckling equations for a quasi-shallow toroidal shell we formulate a novel boundary-value problem able to capture such bifurcations. Numerical simulations of this problem confirm that buckling occurs before the usual limit-point instability is reached, while singular perturbation methods allow us to obtain simple asymptotic approximations for the critical curvature and bending moment associated with the bifurcations.

KW - Boundary layers

KW - Brazier effect

KW - Cylindrical shells

KW - Shallow shell equations

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