Continuous/Discontinuous Finite Element Modelling of Kirchhoff Plate Structures in $\mathbb{R}^3$ Using Tangential Differential Calculus
This work provides a novel finite element formulation for Kirchhoff plates with membrane coupling, relevant for computational mechanics researchers.
The authors derive Kirchhoff plate models including membrane deformations using surface differential calculus and extend the formulation to plate structures. They solve the PDEs with a finite element method using C0-elements for both plate and membrane deformations, defining jumps and averages of d-linear forms in edge normals.
We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using $C^0$-elements for the discretisation of the plate as well as for the membrane deformations. Key to the formulation of the method is a convenient definition of jumps and averages of forms that are $d$-linear in terms of the element edge normals.