Kinematically incompatible Föppl-von Kármán plates: Analysis and numerics

Abstract

This work investigates isotropic 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. Theoretical results are presented to guarantee the existence and regularity of equilibrium solutions in the presence of a finite number of disclinations and a dead load, under clamped boundary conditions. To solve the equilibrium equations, a numerical implementation is developed and applied to a series of parametric test studies. The finite element method adopted follows the Discontinuous Galerkin approach using continuous elements.