Study of simplified elements for static and dynamic analysis of origami structures

Resumo

Research works involving structural origami have grown in recent years, especially applied to science
and engineering problems. Early applications took advantage of the idea that a system can be folded compactly
and subsequently deployed, and that self-assembly can be used to construct a three dimensional structure by
starting from a thin sheet. The present work, as part of an M.Sc. thesis carried out by the first author, compares bar
and hinge models with the simplest hybrid finite element models for plate and shell in order to represent origami

structure panels. The bar and hinge model approach, as given in the literature, is based on folded patterns as pin-
jointed truss frameworks: each vertex in the folded sheet is represented by a pin-joint, and every fold line by a bar

element. The hybrid finite element formulation is based on the Hellinger-Reissner potential for an approximation
of the stress field, thus satisfying the equilibrium equation of the elasticity problem in the domain and leading to
a consistent structural model obtained at almost no additional cost when compared with the latter, too simplified,
formulation. We assess the mechanical behavior of these structures and the folding energy measured in terms of
the eigenvalues associated to the relevant eigenmodes of a cell for both the traditional bar and hinge scheme and
the proposed equilibrium-based finite elements. The displacement response in time for a four-cell assemblage is
also investigated for the implemented models.