Edge-buckling in stretched thin films under in-plane bending

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.

LanguageEnglish
Pages510-525
Number of pages16
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume58
Issue number3
Early online date5 Oct 2006
DOIs
Publication statusPublished - May 2007
Externally publishedYes

Fingerprint

Wrinkling
wrinkling
buckling
Buckling
Thin Films
eigenvalues
Stiffness
Thin films
stiffness
Bifurcation
thin films
Compound Matrices
Eigenvalue
Differential equations
thin plates
Thin Plate
Singularly Perturbed
Variable Coefficients
Wavelength
Numerical Computation

Cite this

@article{677b70dd789b4cd38966e50037d6a3dd,
title = "Edge-buckling in stretched thin films under in-plane bending",
abstract = "The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von K{\'a}rm{\'a}n bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.",
keywords = "Bending, Thin films, WKB analysis, Wrinkling",
author = "Coman, {Ciprian D.}",
year = "2007",
month = "5",
doi = "10.1007/s00033-006-6036-0",
language = "English",
volume = "58",
pages = "510--525",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

Edge-buckling in stretched thin films under in-plane bending. / Coman, Ciprian D.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 58, No. 3, 05.2007, p. 510-525.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Edge-buckling in stretched thin films under in-plane bending

AU - Coman, Ciprian D.

PY - 2007/5

Y1 - 2007/5

N2 - The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.

AB - The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.

KW - Bending

KW - Thin films

KW - WKB analysis

KW - Wrinkling

UR - http://www.scopus.com/inward/record.url?scp=34247551776&partnerID=8YFLogxK

U2 - 10.1007/s00033-006-6036-0

DO - 10.1007/s00033-006-6036-0

M3 - Article

VL - 58

SP - 510

EP - 525

JO - Zeitschrift fur Angewandte Mathematik und Physik

T2 - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 3

ER -