abstract: Origami is an art transforming a flat sheet of paper into a sculpture. Among various types of origami, the focus is on a particular class called the `Rigid Origami' ("RO"). A Rigid Origami, unlike other forms, is not intended to be folded into fancy shapes. On the contrary, an RO has a simple and a geometrically well-defined crease pattern and does not have curved/smudged faces. The folds can be carried out by a continuous motion in which, at each step, each face of the origami is completely flat. As a result, these planar faces experience very minimal strain due to loading. This property allows it to be used to fold surfaces made of rigid materials. Tapping into the geometrical properties of RO will open a new field of research with great practical utility. Analyzing each new RO pattern will require generating numerous prototypes; this is practically impossible to do, as it consumes a lot of time and material. The advantages of Finite Element Analysis/numerical modeling become very clear in this scenario. A new design concept may be modeled to determine its real world behavior under various load environments and may, therefore, be refined prior to the creation of drawings, when changes are inexpensive. Since an RO undergoes a non-local deformation when subjected to a disturbance, the usage of conventional FEA will not produce accurate results. A non-local element model was developed which can be used in conjunction with the finite element package ABAQUS, via its user-defined element (UEL). This model was tested on two RO patterns, namely Miura-Ori and Ron Resch, by carrying out basic simulations. There are many other interesting origami patterns, exhibiting different meta-material properties, yet to be explored. This Finite Element Approach equips researchers with necessary tools to study those options in great detail. / Dissertation/Thesis / M.S. Mechanical Engineering 2014

Elastic absorption of kinetic energy and distribution of impact forces are required in many applications. This may be achieved through the use of compliant corrugations. An innovative padding concept is investigated for such applications. Also, recent attention given to the potential for using origami in engineering applications may provide new corrugation configurations that are advantageous for energy absorption and force distribution. This work explores three areas related to these concepts.First, the parameters of a compliant, corrugated padding concept are investigated using Finite Element Analyses (FEA) and physical testing. The shape of the corrugation cross section is explored as well as the wavelength and amplitude by employing a full factorial design of experiments. FEA results are used to choose designs for prototyping and physical testing. The results of the physical testing were consistent with the FEA predictions although the FEA tended to underestimate the peak pressure compared to the physical tests. A performance metric is proposed to compare different padding configurations. The concept shows promise for sports padding applications. It may allow for designs which are smaller, more lightweight, and move better with an athlete than current technologies yet still provide the necessary protective functions.Second, the elastic energy absorbing properties of a particular origami folding pattern, the Miura-ori, is investigated. Analytical models for the kinematics and force-deflection of a unit cell based on two different modes of elastic energy absorption are derived. The models are used to explore the effects of the key geometrical parameters of the tessellation. Physical prototypes are compared to the analytical models.Third, a three-stage strategy is presented for selecting materials for origami-inspired corrugations that can deform to achieve a desired motion without yielding, absorb elastic strain energy, and be light weight or cost effective. Two material indices are derived to meet these requirements based on compliant mechanism theory. Using Finite element analysis, it is shown that the properties of Miura-ori pattern has advantages for energy absorption and force distribution when compared to a triangular wave corrugation. While the focus of these studies is the Miura-ori tessellation, the methods developed can be applied to other tessellated patterns used in energy absorbing or force distribution applications.

This thesis addresses the design difficulties encountered when designing deployable origami-based arrays. Specific considerations regarding thickness accommodation, deployment, and parameter modifications are discussed. Patterns such as the Miura-ori, flasher, and hexagon are investigated, with emphasis placed on pattern modification from zero-thickness to finite-thickness. Applying origami principles to form engineering solutions is a complicated task. Competing requirements may create confusion around which pattern is most favorable for the space array application. Implementing origami into a finite-thickness, engineered system poses challenges that are not manifest in a zero-thickness model. As such, it is important to understand and address the limitations of the pattern before implementing it into an engineered system. A preliminary set of approaches to address and mitigate design difficulties is provided. This thesis seeks to improve understanding of design parameters, objectives, and trade offs of origami pattern configurations. Emphasis is placed on finite-thickness models suitable for engineering applications. As a result, engineers and designers should be better prepared to integrate origami principles into space system design.

Trends in the aerospace industry are driving payloads to be smaller and less expensive while yet delivering comparatively large antennas. Deployable reflectarray antennas (RA) are the object of much research to meet these demands because they operate in a flat plane and are easier to stow than parabolic reflector antennas. Because they operate in flat plane, deployable RAs are well-suited to thickness-accommodated origami-inspired mechanisms. This work addresses pattern selection and modification, thickness accommodation, actuation, and stabilization of origami-inspired mechanisms intended to be used as RAs. First, a modified Miura-ori pattern termed volume-efficient Miura-ori (VEMO) is introduced, selected for its ability to fold into a rectangular profile and easily adapt to different aspect ratios. An optimization algorithm seeking to maximize surface area subject to the constraints of an allotted cuboid volume and a deployed aspect ratio of one is introduced. Second, a set of five genres of magnetic hinge concepts are presented to serve as actuation and stabilization mechanisms. Particular focus is given to hinges composed of a single pair of cuboid magnets. Two such self-actuating and self-stabilizing hinges are presented and characterized. Third, the behavior of such hinges is explored. We demonstrate the existence of bistability in select configurations and characterize their equilibrium positions. Potential energy, axial force data, angular position of unstable equilibria, and transition values from bistability to monostability are also modeled. Results are verified through experimental torque and stability data for selected configurations. Fourth, the union of magnetic hinges and surrogate folds is explored. The lamina-emergent torsion (LET) array is selected with justification. Novel stress considerations are presented for LET arrays with thin torsion elements and various magnetic hinges demonstrate viability for actuation and stabilization. Finally, current methods for accommodating thickness in flashers are presented and issues associated with those methods are discussed. Two methods for accommodating thickness in flashers such that panels are constant thickness are proposed.