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

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

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.

PDF file (2 MB)