Stability of the Von Kármán regime for thin plates under Neumann boundary conditions

Dipartimento di Matematica F. Casorati, Università di Pavia, Italy

^* Corresponding author: edoardogiovann.tolotti01@universitadipavia.it

Received: 19 September 2024
Accepted: 3 June 2025

Abstract

We analyse 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.