Remarks on elastic buckling for sectorial plates

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.

Original languageEnglish
Pages (from-to)1002-1013
Number of pages12
JournalInternational Journal of Engineering Science
Volume47
Issue number10
Early online date19 May 2009
DOIs
Publication statusPublished - Oct 2009
Externally publishedYes

Fingerprint

Buckling
Direct numerical simulation
Eigenvalues and eigenfunctions
Boundary layers
Differential equations

Cite this

@article{788dec292fa1484696c1c82adc94b3ce,
title = "Remarks on elastic buckling for sectorial plates",
abstract = "This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.",
keywords = "Boundary layers, Edge-buckling, Elastic stability, Sectorial plates, WKB methods",
author = "Coman, {Ciprian D.}",
year = "2009",
month = "10",
doi = "10.1016/j.ijengsci.2009.04.004",
language = "English",
volume = "47",
pages = "1002--1013",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier Limited",
number = "10",

}

Remarks on elastic buckling for sectorial plates. / Coman, Ciprian D.

In: International Journal of Engineering Science, Vol. 47, No. 10, 10.2009, p. 1002-1013.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Remarks on elastic buckling for sectorial plates

AU - Coman, Ciprian D.

PY - 2009/10

Y1 - 2009/10

N2 - This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.

AB - This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.

KW - Boundary layers

KW - Edge-buckling

KW - Elastic stability

KW - Sectorial plates

KW - WKB methods

UR - http://www.scopus.com/inward/record.url?scp=67651004870&partnerID=8YFLogxK

U2 - 10.1016/j.ijengsci.2009.04.004

DO - 10.1016/j.ijengsci.2009.04.004

M3 - Article

VL - 47

SP - 1002

EP - 1013

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

IS - 10

ER -