Oval cylindrical shells under asymmetric bending

a singular-perturbation solution

Research output: Contribution to journalArticle

Abstract

A singular asymptotic limit of the bifurcation instability experienced by short oval cylindrical shells under asymmetric pure bending is explored both analytically and numerically. Of primary interest here is the interplay between the variable geometrical stiffness of the cross section and the arbitrary orientation of the applied bending moments. By using boundary layer arguments, it is shown that the localised cross-sectional eigen-deformations are concentrated around a point determined by the solution of a simple trigonometric equation. The non-symmetric shape of the eigenmodes is also captured by a reduced fourth-order ordinary differential equation, which represents a generalisation of an earlier form found previously for the case of circular cylindrical shells under the same type of loading.

Original languageEnglish
Article number120
Pages (from-to)1-16
Number of pages16
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume69
Issue number5
Early online date10 Sep 2018
DOIs
Publication statusPublished - Oct 2018
Externally publishedYes

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Perturbation Solution
cylindrical shells
Cylindrical Shell
Singular Perturbation
Bending moments
Ordinary differential equations
Boundary layers
Trigonometric equation
Stiffness
circular shells
bending moments
perturbation
Singular Limit
Asymptotic Limit
Fourth Order
Boundary Layer
boundary layers
stiffness
Ordinary differential equation
Cross section

Cite this

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abstract = "A singular asymptotic limit of the bifurcation instability experienced by short oval cylindrical shells under asymmetric pure bending is explored both analytically and numerically. Of primary interest here is the interplay between the variable geometrical stiffness of the cross section and the arbitrary orientation of the applied bending moments. By using boundary layer arguments, it is shown that the localised cross-sectional eigen-deformations are concentrated around a point determined by the solution of a simple trigonometric equation. The non-symmetric shape of the eigenmodes is also captured by a reduced fourth-order ordinary differential equation, which represents a generalisation of an earlier form found previously for the case of circular cylindrical shells under the same type of loading.",
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Oval cylindrical shells under asymmetric bending : a singular-perturbation solution. / Coman, Ciprian D.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 69, No. 5, 120, 10.2018, p. 1-16.

Research output: Contribution to journalArticle

TY - JOUR

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T2 - a singular-perturbation solution

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PY - 2018/10

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AB - A singular asymptotic limit of the bifurcation instability experienced by short oval cylindrical shells under asymmetric pure bending is explored both analytically and numerically. Of primary interest here is the interplay between the variable geometrical stiffness of the cross section and the arbitrary orientation of the applied bending moments. By using boundary layer arguments, it is shown that the localised cross-sectional eigen-deformations are concentrated around a point determined by the solution of a simple trigonometric equation. The non-symmetric shape of the eigenmodes is also captured by a reduced fourth-order ordinary differential equation, which represents a generalisation of an earlier form found previously for the case of circular cylindrical shells under the same type of loading.

KW - Boundary layers

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