Edoardo Fabbrini (Université de Kyushu, Fukuoka, Japon)

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 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 demonstrated under additional assumptions on the boundary of the plate and on the external load. 

In the second part of the talk, I introduce a novel Interior Penalty C⁰-Discontinuous Galerkin (IPC⁰-DG) formulation for the von Kármán plate problem and validate it using known analytical solutions and other IPC⁰-DG formulations present in the literature. 

A direct application of this study is in the continuum modeling of graphene sheets with wedge disclinations in the crystal lattice.