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We employ surface differential calculus to derive models for Kirchhoff platesincluding in-plane membrane deformations. We also extend our formulation tostructures of plates. For solving the resulting set of partial differentialequations, we employ a finite element method based on elements that arecontinuous for the displacements and discontinuous for the rotations, using$C^0$-elements for the discretisation of the plate as well as for the membranedeformations. Key to the formulation of the method is a convenient definitionof jumps and averages of forms that are $d$-linear in terms of the element edgenormals.

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