On some approximate methods for the tensile instabilities of thin annular plates

Ciprian D. Coman, David M. Haughton

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A thin annular plate is subjected to a uniform tensile field at its inner edge which leads to compressive circumferential stresses. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially, leading to a wrinkling pattern. Using a linear non-homogeneous pre-bifurcation state, the linearised eigenvalue problem describing this instability is cast as a fourth-order linear differential equation with variable coefficients. This problem is investigated numerically and it is shown that the simple application of the Galerkin technique reported in the literature leads to gross errors in the corresponding approximations. Several novel mathematical features of the eigenvalue problem are included as well.

Original languageEnglish
Pages (from-to)79-99
Number of pages21
JournalJournal of Engineering Mathematics
Volume56
Issue number1
Early online date28 Jun 2006
DOIs
Publication statusPublished - Sep 2006
Externally publishedYes

Fingerprint

Compressive stress
Eigenvalue Problem
Buckling
Differential equations
Wrinkling
Variable Coefficients
Gross
Linear differential equation
Galerkin
Fourth Order
Bifurcation
Approximation

Cite this

@article{0e456d0e6e6c4d68a4e6fcc3546093a0,
title = "On some approximate methods for the tensile instabilities of thin annular plates",
abstract = "A thin annular plate is subjected to a uniform tensile field at its inner edge which leads to compressive circumferential stresses. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially, leading to a wrinkling pattern. Using a linear non-homogeneous pre-bifurcation state, the linearised eigenvalue problem describing this instability is cast as a fourth-order linear differential equation with variable coefficients. This problem is investigated numerically and it is shown that the simple application of the Galerkin technique reported in the literature leads to gross errors in the corresponding approximations. Several novel mathematical features of the eigenvalue problem are included as well.",
keywords = "Annular plates, Buckling, Galerkin technique, Rayleigh quotient, Wrinkling",
author = "Coman, {Ciprian D.} and Haughton, {David M.}",
year = "2006",
month = "9",
doi = "10.1007/s10665-006-9041-6",
language = "English",
volume = "56",
pages = "79--99",
journal = "Journal of Engineering Mathematics",
issn = "0022-0833",
publisher = "Springer Netherlands",
number = "1",

}

On some approximate methods for the tensile instabilities of thin annular plates. / Coman, Ciprian D.; Haughton, David M.

In: Journal of Engineering Mathematics, Vol. 56, No. 1, 09.2006, p. 79-99.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On some approximate methods for the tensile instabilities of thin annular plates

AU - Coman, Ciprian D.

AU - Haughton, David M.

PY - 2006/9

Y1 - 2006/9

N2 - A thin annular plate is subjected to a uniform tensile field at its inner edge which leads to compressive circumferential stresses. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially, leading to a wrinkling pattern. Using a linear non-homogeneous pre-bifurcation state, the linearised eigenvalue problem describing this instability is cast as a fourth-order linear differential equation with variable coefficients. This problem is investigated numerically and it is shown that the simple application of the Galerkin technique reported in the literature leads to gross errors in the corresponding approximations. Several novel mathematical features of the eigenvalue problem are included as well.

AB - A thin annular plate is subjected to a uniform tensile field at its inner edge which leads to compressive circumferential stresses. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially, leading to a wrinkling pattern. Using a linear non-homogeneous pre-bifurcation state, the linearised eigenvalue problem describing this instability is cast as a fourth-order linear differential equation with variable coefficients. This problem is investigated numerically and it is shown that the simple application of the Galerkin technique reported in the literature leads to gross errors in the corresponding approximations. Several novel mathematical features of the eigenvalue problem are included as well.

KW - Annular plates

KW - Buckling

KW - Galerkin technique

KW - Rayleigh quotient

KW - Wrinkling

UR - http://www.scopus.com/inward/record.url?scp=33748626795&partnerID=8YFLogxK

U2 - 10.1007/s10665-006-9041-6

DO - 10.1007/s10665-006-9041-6

M3 - Article

VL - 56

SP - 79

EP - 99

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1

ER -