Continuous/discontinuous finite element modelling of Kirchhoff plate structures in R3 using tangential differential calculus

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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 C0-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.

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Hansbo, P., & Larson, M. G. (2017). Continuous/discontinuous finite element modelling of Kirchhoff plate structures in R3 using tangential differential calculus. Computational Mechanics, 60(4), 693–702. https://doi.org/10.1007/s00466-017-1431-2

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