2024/09/03 by Edoardo Giovanni Tolotti, Tolotti, Edoardo Giovanni
Computer Science · Mathematics · #49J45 #74B20 #74G65 #74K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2409.01748
openalex publication_date 2024/09/03 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28
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 Kirchoff model applies.