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

Monique Dauge, Manil Suri

We consider the buckling problem for a family of thin plates with thickness parameter epsilon. This involves finding the least positive multiple Lmin(epsilon) 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

Lmin(epsilon) = O(epsilon2)

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. This paper completes the analysis dome in the Previous Paper.

Rennes, Baltimore, July 2004.

Preprint Rennes 04-39

Math. Meth. Appl. Sc. Vol. 29, 2006, pp 789-817.

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