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

Monique Dauge (1) , Manil Suri (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics and Statistics, University of Maryland Baltimore County

We consider the buckling problem for a family of thin plates with thickness parameter \epsilon. This involves finding the least positive multiple \lambda_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 \lambda_\min(\epsilon) = O(\epsilon^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.

Domaines: Analyse numérique [math.NA]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Monique Dauge, Manil Suri. On the asymptotic behavior of the discrete spectrum in buckling problems for thin plates. Mathematical Methods in the Applied Sciences, 2006, 29, pp.789-817. ⟨hal-00012083⟩