Asymptotic approximations for pure bending of thin cylindrical shells

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel–Mushtari–Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.

Original languageEnglish
Article number82
Pages (from-to)1-20
Number of pages20
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume68
Issue number4
Early online date4 Jul 2017
DOIs
Publication statusPublished - Aug 2017
Externally publishedYes

Fingerprint

shallow shells
shell theory
WKB Approximation
Wrinkling
wrinkling
Shallow Shell
Method of multiple Scales
Shell Theory
Wentzel-Kramer-Brillouin method
Asymptotic analysis
Thin Shells
cylindrical shells
Cylindrical Shell
Asymptotic Approximation
Boundary Problem
Asymptotic Analysis
Eigenvalue Problem
eigenvalues
Membrane
Bifurcation

Cite this

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abstract = "A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel–Mushtari–Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.",
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Asymptotic approximations for pure bending of thin cylindrical shells. / Coman, Ciprian D.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 68, No. 4, 82, 08.2017, p. 1-20.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotic approximations for pure bending of thin cylindrical shells

AU - Coman, Ciprian D.

PY - 2017/8

Y1 - 2017/8

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AB - A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel–Mushtari–Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.

KW - Cylindrical shells

KW - Multiple-scale asymptotics

KW - Shallow shell equations

KW - WKB approximations

KW - Wrinkling

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