Foldable FEM

Abstract

Origami structures have become of increasing importance in the field of engineering, due to their lightweight, compact and stiff properties. To design these structures, progress is being made into incorporating origami modeling in the Finite Element Method. To implement an arbitrarily located fold on an existing mesh, either re-meshing or enriched finite elements are required. In fold pattern optimisation of origami structures, re-meshing each intermediate design would not be time efficient, whereas enriched elements may be very time efficient. In this thesis foldable Kirchhoff-Love plate elements are derived using a mixed/hybrid element formulation in combination with an enriched Finite Element formulation. The use of a mixed/hybrid element formulation enables great simplification of the enrichment functions, since the discontinuous rotation field is evaluated at the boundaries of the enriched plate elements, instead of the element domain. Six foldable plate elements are derived and tested for accuracy and stability. The stability is improved by either local condensation of the enriched elements or by applying a precondition matrix.