1. Kinematically incompatible F\'oppl-von K\'arm\'an plates: analysis and numerics
- Author
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Fabbrini, Edoardo, Baldelli, Andrés Alessandro León, and Cesana, Pierluigi
- Subjects
Mathematics - Analysis of PDEs ,Mathematics - Numerical Analysis ,35B65, 65K10, 37L65, 74K20 ,G.1.8 - Abstract
We investigate thin plates where out-of-plane deformations arise due to membrane kinematic incompatibility of rotational type, specifically Volterra wedge disclinations, which are commonly observed in metal plates and graphene. We present theorems that guarantee the existence and regularity of equilibrium solutions in the presence of a finite number of disclinations and a dead load, for clamped plates. To solve the equilibrium equations, we implement a numerical code in the FEniCS environment and apply it to a series of parametric test studies. Our Finite Element method follows the Discontinuous Galerkin approach with C0 elements., Comment: 24 pages, 18 Figures
- Published
- 2025