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Modelling, Analysis, and Finite Element simulations of kinematically incompatible von Kármán plates

Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
Date: Wednesday, 04 December 2024 10:30 - 11:30

Venue: Edoardo Fabbrini - Aula Buzano (DISMA Politecnico di Torino)

In the first part of the talk, I investigate the existence and regularity of solutions of kinematically incompatible von Kármán thin plates. The mathematical model consists of two coupled, non-linear, fourth-order elliptic partial differential equations. The kinematic incompatibility arises from a distribution of isolated wedge disclinations in the crystalline lattice and enters in the mathematical formulation as a discrete distribution of Dirac delta measures. The existence of solutions is established using the direct method in the calculus of variations, following a similar approach to Ciarlet's proof for kinematically compatible plates. The regularity of the solutions is obtained under additional assumptions regarding the smoothness of the boundary and the external load. In the second part of the talk, I introduce a novel C0 -Discontinuous Galerkin formulation for the numerical solution of the von Kármán plate problem. After validating it with known analytical solutions, I identify the relevant dimensionless parameters and perform some experiments by varying them in appropriate ranges. A direct application of this study is in the continuum modeling of graphene sheets with wedge disclinations in the crystal lattice.

 

Speaker
Edoardo Fabbrini
Affiliation
Kyushu University, Japan
Room
Aula Buzano
Proposed by
Marco Morandotti

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