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On the asymptotic behaviour of the discrete spectrum in buckling problems for thin plates

✍ Scribed by Monique Dauge; Manil Suri

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 446 KB
Volume: 29
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.710

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✦ Synopsis

Abstract

We consider the buckling problem for a family of thin plates with thickness parameter ε. This involves finding the least positive multiple λ of the load that makes the plate buckle, a value that can be expressed in terms of an eigenvalue problem involving a non‐compact operator. We show that under certain assumptions on the load, we have λ = 𝒪(ε^2^). This guarantees that provided the plate is thin enough, this minimum value can be numerically approximated without the spectral pollution that is possible due to the presence of the non‐compact operator. We provide numerical computations illustrating some of our theoretical results. Copyright © 2005 John Wiley & Sons, Ltd.

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