190th MSL Lecture "Modeling and analysis of kinematically incompatible Von Kármán plates"
| Date/Time | 2024/11/19 14:00 - 15:00 |
|---|---|
| Place | Tokyo Institute of Technology, Suzukakedai Campus, Room 2002, 20th floor, J2-J3 Building (Map No.29） |
| Organizer | Laboratory for Materials and Structures |
| Contact | Professor Tomonari Inamura (Email: inamura.t.aa@m.titech.ac.jp) |
| Language | English |
Subject & Detail
Speaker: Professor Cesana Pierluigi (Kyushu University)
Title: "Modeling and analysis of kinematically incompatible Von Kármán plates"
Abstract:
We investigate the existence and regularity of solutions to the Von Kármán equations, which are a widely used model for nonlinear deflection in thin plates, in the presence of kinematic incompatibility for the membrane strain. Our proof utilizes the direct method in the calculus of variations, following a similar approach to Ciarlet's classical proof for kinematically compatible plates. A direct application of our analysis is in the continuum modeling of graphene sheets in the presence of disclinations in the crystal lattice. Additionally, we present numerical solutions obtained via a Finite Element formulation of the equations. As the Von Kármán equations are a set of non-linear, coupled, 4th order elliptic equations, we employ the discontinuous Galerkin finite element methods for boundary-value problems involving the biharmonic operator. This work is in collaboration with Edorado Fabbrini (Kyushu) and AAL Baldelli (CNRS-Sorbonne).
