Joseph M. Gattas

Miura-Base Rigid Origami: Parameterizations of First-Level Derivative and Piecewise Geometries

Miura and Miura-derivative rigid origami patterns are increasingly used for engineering and architectural applications. However, geometric modelling approaches used in existing studies are generally haphazard, with pattern identifications and parameterizations varying widely. Consequently, relationships between Miura-derivative patterns are poorly understood, and widespread application of rigid patterns to the design of folded plate structures is hindered. This paper explores the relationship between the Miura pattern, selected because it is a commonly used rigid origami pattern, and first-level derivative patterns, generated by altering a single characteristic of the Miura pattern. Five alterable characteristics are identified in this paper: crease orientation, crease alignment, developability, flat-foldability, and rectilinearity. A consistent parameterization is presented for five derivative patterns created by modifying each characteristic, with physical prototypes constructed for geometry validation. It is also shown how the consistent parameterization allows first-level derivative geometries to be combined into complex piecewise geometries. All parameterizations presented in this paper have been compiled into a matlab Toolbox freely available for research purposes.

Miura-Base Rigid Origami: Parametrizations of Curved-Crease Geometries

Curved-crease (CC) origami differs from prismatic, or straight-crease origami, in that the folded surface of the pattern is bent during the folding process. Limited studies on the mechanical performance of such geometries have been conducted, in part because of the difficulty in parametrizing and modeling the pattern geometry. This paper presents a new method for generating and parametrizing rigid-foldable, CC geometries from Miura-derivative prismatic base patterns. The two stages of the method, the ellipse creation stage and rigid subdivision stage, are first demonstrated on a Miura-base pattern to generate a CC Miura pattern. It is shown that a single additional parameter to that required for the straight-crease pattern is sufficient to completely define the CC variant. The process is then applied to tapered Miura, Arc, Arc-Miura, and piecewise patterns to generate CC variants of each. All parametrizations are validated by comparison with physical prototypes and compiled into a matlab Toolbox for subsequent work.

One-DOF Superimposed Rigid Origami with Multiple States

Origami-inspired engineering design is increasingly used in the development of self-folding structures. The majority of existing self-folding structures either use a bespoke crease pattern to form a single structure, or a universal crease pattern capable of forming numerous structures with multiple folding steps. This paper presents a new approach whereby multiple distinct, rigid-foldable crease patterns are superimposed in the same sheet such that kinematic independence and 1-DOF mobility of each individual pattern is preserved. This is enabled by the cross-crease vertex, a special configuration consisting of two pairs of collinear crease lines, which is proven here by means of a kinematic analysis to contain two independent 1-DOF rigid-foldable states. This enables many new origami-inspired engineering design possibilities, with two explored in depth: the compact folding of non-flat-foldable structures and sequent folding origami that can transform between multiple states without unfolding.

Geometric Design and Construction of Structurally Stabilized Accordion Shelters

Accordion patterns are widely used for deployable shelters, due to their simple construction, elegant deployment mechanism, and folded plate form with an inherent structural efficiency. This paper proposes two new accordion-type shelters that use modified geometries to improve on the structural stability and stiffness of the typical accordion form. The first shelter is termed a distributed frame accordion shelter and is generated by separating fully folded accordion frames between spacer plates aligned with the transverse direction. A transverse stiffness and increased flexural rigidity can therefore be achieved while maintaining a nonzero floor area. The second shelter is termed a diamond wall accordion shelter and is generated by inserting secondary wall elements that increase wall sectional depth and counteract the coupled rotational-transverse displacements at accordion roof–wall junctions. For both shelter types, a geometric parameterization and a full-scale prototype are presented. Good correlation is seen between the designed and constructed surfaces. A numerical investigation also shows that the new forms have substantially increased flexural rigidities compared to the typical accordion form

Parametrisation and application of cube and eggbox-type folded geometries

There exist several kirigami, or non-developable folded plate patterns that share the most useful properties of the widely-used Miura-ori pattern, namely rigid-foldability, a tessellated unit geometry, and constituent elements composed of a single parallelogram plate. This paper first presents parametrisations of five such patterns, two cube-type and three eggbox-type, consistent with that previously developed for Miura-type patterns. For each pattern, the parametrisation establishes relationships between crease pattern, volumetric, and kinematic parameters. Along with the Miura-type patterns, these geometries form a set termed parallelogram-plate folded geometries and together they suggest a range of interesting structural engineering applications. This paper discusses two applications specifically enabled by the new parametrisations: space frame synthesis and hierarchical sandwich panels.

Quasi-static impact response of alternative origami-core sandwich panels

Foldcore sandwich panels have been the focus of much recent study in the aerospace industry. Existing foldcores are composed of a partially folded Miura origami pattern sandwiched between two stiff facings, and have been shown to possess numerous useful properties for impact-resistant applications. Non- Miura origami pattern with similar geometric properties, specifically rigid-foldability and tessellation, may be used as potential alternative origami-cores for sandwich panels, however the mechanical performance of such cores remains an unexplored area. This paper conducts a preliminary investigation into the impact resistance of five non-Miura sandwich panels. The selected patterns are numerically analysed under quasi-static lateral impact loads, and comparisons are drawn with existing foldcore designs. Two particular patterns are found to have failure modes suited for energy-absorbing applications. Prototypes of these two cores are constructed from polypropylene sheet material and experimentally tested to validate numerical results. Reasonable correlation is seen in the force-displacement response of numerical and experimental models. Copyright

Analysis of Miura-Type Folded and Morphing Sandwich Beams

Folded-core sandwich structures have previously been proposed as lightweight, thin-plate building elements. Such structures typically use a Miura-type core pattern and have an efficient load transfer behaviour, however cannot be used for deployable structures as the attachment of face sheets suppresses any core kinematic behaviours. This limitation can be overcome with patterned face sheets that preserve rigid-foldability and form a layered meta-material, here termed a morphing sandwich structure. The relative performance of folded and morphing sandwich structures is unknown, with few studies on the structural behaviour of either configuration. The following paper uses a new digital fabrication methodology to manufacture folded and morphing beam prototypes from 0.9mm thick steel plate. These are subjected to experimental three point bending tests to assess force-displacement behaviour and failure modes. A numerical finite element analysis is conducted to simulate the failure behaviour of the experimental beams. It is seen that the morphing beam has a 44% reduction in strength compared with the folded beam, thought to be attributable to face plate eccentricity and flexibility introduced by the morphing beam hinge connection detail.

Synthesis of Folded Frame Structures From Cube-Type and Eggbox-Type Kirigami Geometry

Rigid-foldable cube-type and eggbox-type kirigami geometries have been of interest for applications including folded-core sandwich panels and deployable structures. Recent studies of these geometry families noticed that their convex pattern vertices enabled several further potential applications that were not otherwise possible with the concave vertices of more common pattern families such as Miura-type patterns. The following paper investigates one such application: the synthesis of folded frame structures from kirigami pattern geometric parametrisations. A new synthesis method is proposed for two geometries: a twoway orthogonal lattice frame generated from a kirigami cube pattern; and a multi-layer octahedral frame generated from a non-developable eggbox pattern. Both frames are developed with initial translation of folded geometries to frame element centrelines and subsequent generation of integral frame elements with pattern sub-folds. Simple prototypes are manufactured to validate the synthesis method and it is found that the cube-generated frame compares favourable with typical frames with respect to packaging efficiency. Keywords: folded frame, kirigami, folded structure.

Quasi-Static Impact Response of Single-Curved Foldcore Sandwich Shells

Honeycomb core sandwich shells are used for many applications, but available unit architectures and global curvatures are limited. Numerous origami-core sandwich shells, known as foldcores, have been proposed as alternatives, but studies into their mechanical performance are few. This paper conducts a preliminary investigation into the impact resistance and energy absorption of single-curved foldcore sandwich shells that utilise Miura-derivative patterns as their core geometry. A numerical analysis on three Miura-derivative core patterns, the Arc-Miura (AM), Non-Developable Miura (ND), and Non-Flat Foldable Miura (NF) patterns, shows that ND and AM-type shells have similar impact resistance to each other, and superior impact resistance to NF-type shells. Prototypes of aluminium ND and AM-type foldcores are constructed and used to validate numerical models. Numerical models were then used to draw comparisons with an over-expanded honeycomb (OX-core) sandwich shell. It was seen that the OX-core had a better energy absorption capacity than either of the foldcores. However the AM-type foldcore possessed superior initial strength, and the ND-type possessed superior response uniformity, attributes that might be exploitable with future research. A brief parametric study on ND-type shells suggested that in general, for a given design radius and density, a foldcore shell configuration with a lower unit cell area-to-height ratio will have a higher energy absorption capability.Copyright

Hybrid fibre-reinforced polymer–timber thin-walled structural members

The increasing interest in timber as a sustainable construction material has led to the development of a new type of structures referred to as ‘hybrid fibre-reinforced polymer–timber thin-walled structures’. In these structures, thin layers of fibre-reinforced polymer are combined with timber veneers to create high-performance, lightweight and easy-to-construct structural members. This new type of structural members harnesses the orthotropic properties of both timber and fibre-reinforced polymer by appropriately orientating material fibre directions for optimal composite properties as well as efficient thin-walled cross-sectional shapes. Hybrid fibre-reinforced polymer–timber thin-walled members can be used in many applications such as load-bearing walls, roofs, floor panels and bridge decks. This article describes several novel hybrid fibre-reinforced polymer–timber structural member forms and presents results from a preliminary experimental investigation into the compressive behaviour of hybrid fibre-reinforced polymer–timber wall panels. A comparison of behaviour between a hybrid fibre-reinforced polymer–timber wall panel and a pure timber wall panel is presented to show that the hybrid fibre-reinforced polymer–timber system significantly outperforms the pure timber system in terms of both load resistance and axial strain at failure.