# Continuous/Discontinuous Finite Element Modelling of Kirchhoff Plate Structures in $\mathbb{R}^3$ Using Tangential Differential Calculus

## TL;DR

This paper develops a finite element modeling approach for Kirchhoff plates in three-dimensional space using surface differential calculus, incorporating both membrane and bending deformations with a mixed continuity scheme.

## Contribution

It introduces a novel finite element formulation employing tangential differential calculus for Kirchhoff plates, including in-plane membrane effects and a mixed continuous/discontinuous element approach.

## Key findings

- Effective modeling of Kirchhoff plates with membrane effects
- Finite element method with continuous displacements and discontinuous rotations
- Use of $C^0$-elements for plate and membrane discretization

## Abstract

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.