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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Rigorous bounds for the Föppl-von Kármán theory of isotropically compressed plates
Hafedh Ben Belgacem, Sergio Conti, Antonio DeSimone and Stefan MüllerAbstract
We study the Föppl-von Kármán theory for isotropically compressed thin plates in a geometrically linear setting, which is commonly used to model weak buckling of thin films. We consider generic smooth domains with clamped boundary conditions, and obtain rigorous upper and lower bounds on the minimum energy linear in the plate thickness sigma. This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead to energies of order
- Received:
- 04.08.00
- Published:
- 04.08.00