Finite element modeling of non-rigid origami

Abstract

Origami has become a source of inspiration in engineering for structural design and the creation of mechanical metamaterials. In the often used analytic geometric and energy methods, it is difficult to incorporate deformation of the faces in non-rigid origami. However, deformation of the faces can play a significant role in their mechanical behaviour. This thesis aims to investigate and improve the design of non-rigid origami structures by using the Finite Element Method (FEM), which is well suited to model all deformations of these structures.
In collaboration with the Bertoldi Group at Harvard University, FEM is applied on the new bistable non-
rigid origami structure called the Star bellow. The suitable building blocks of the FEM approach, are
finite rotation shell elements to model the faces of the structure, torsional spring elements to model the crease lines, and a Newton-Raphson arc-length control solution procedure. In addition to the numerical analysis, experimental work is performed. A parametric study, FEM simulations, and physical load tests of prototypes, are performed to understand the mechanical properties of the Star bellow structure and to improve its bistable behaviour. In addition, the Star bellow structure was considered as a unit cell and tessellated into a 1D-array to create a Star bellow metamaterial. Simulations and physical load tests were performed to investigate the influence of the tessellation on the bistable properties of the metamaterial.
A design improvement was successfully proposed with a decrease of the minimum force value of 0.11
[N]. The tessellated Star bellow metamaterial into a 1D-array is feasible and keeps its bistable proper-
ties, although the bistability is reduced compared to a non-tessellated, single Star bellow structure.
The application of FEM to study the Star bellow structure enhances the design process of the Star
bellow. It has been shown that a parametric study using FEM is a way to gain understanding of the
structure’s mechanical properties. Furthermore, a design change of the Star bellow was proposed
which improved its bistable properties. It is also found that the results of the FEM simulations, for the
force values, did not match the results of the physical load tests for various reasons. To improve this,
another load testing setup and a more advanced implementation of the torsional spring elements to
model the crease lines is advised.