preprint

Inserted: 4 sep 2024
Last Updated: 9 oct 2024

Year: 2024

Abstract:

We analyze the stability of the Von Kármán model for thin plates subject to pure Neumann conditions and to dead loads, with no restriction on their direction. We prove a stability alternative, which extends previous results by Lecumberry and Müller in the Dirichlet case. Because of the rotation invariance of the problem, their notions of stability have to be modified and combined with the concept of optimal rotations due to Maor and Mora. Finally, we prove that the Von Kármán model is not compatible with some specific types of forces. Thus, for such, only the Kirchhoff model applies.