DESIGN AND FOLDED FABRICATION OF NOVEL SELF-BRACED TRIANGULAR STRUCTURAL SECTIONS AND FRAMES

XiaoQiang Shi 1 , Joseph M. Gattas2,* 1 Master’s student, School of Civil Engineering, University of Queensland, Australia

2 Lecturer, School of Civil Engineering, University of Queensland, Australia * Corresponding author email: j.gattas@uq.edu.au

ABSTRACT Origami-inspired foldable structures have seen much recent interest for applications in which transportability or rapid construction are primary design drivers, for example emergency shelters and temporary staging structures. This paper proposes a new type of a structural module that can be manually folded from flat steel sheet into a novel self-braced triangular structural section. Simple geometric relations are presented for the unit module, which can then be tessellated for the design of larger elements and frame assemblies. It thus avoids many of the geometric complexities typically encountered in origami-inspired folded structure designs. A set of integral connection details are then developed for computer-numerically controlled (CNC) manufacture of a foldable proof-of-concept prototype to validate geometric and folded fabrication processes. Finally, preliminary numerical analyses are conducted comparing typical hollow and folded self-braced triangular sections.

KEYWORDS Folded frame structures; origami-inspired structures; folded fabrication; thin-walled structures.

INTRODUCTION Origami Inspired Structures

Origami-inspired design techniques have been utilized in many industry applications such as appliance manufacturing, packaging design, and space exploration. Such designs utilise origami folding to deliver a compact package that contains a relatively large structure, which is favourable when transportation capacity is a driving design concern. Famous examples include the Miura Origami based solar power array deployed in a research vessel launched by Japan in 1995 (Miura, 2009), the foldable space telescope ‘Eyeglass’ designed in 2002 (Lang, 2004), and the ‘Origami Stent’ developed in 2003, which can be implanted into a patient’s vein in a collapsed state and then manoeuvred to and expanded in a blocked artery to enable a better blood flow (Kuribayashi et al., 2006).

Other applications use origami folding to achieve a significant increase of stiffness at minimal expense of weight. One example is foldable military shelters, in which the folds can provide structural stiffness when deployed and can easily pack into a smaller volume for transportation or storage (Thrall and Quaglia, 2014). An optimised design for this been proposed in Martinez-Martin and Thrall (2014). Another example is folded sandwich structures, or foldcores, which consist of two outer faces and an origami geometry core. The proposed applications for foldcores include impact-resistant or isotropic sandwich panels (Heimbs, 2013; Miura, 1972) and lightweight or morphing building components (Schenk and Guest, 2011; Gattas and You, 2014). The above structural applications mainly utilise shell forms developed from a known origami pattern. This requires advanced geometric design methods (Tachi, 2010; Gattas et al., 2013) and thus widespread application had been hindered. Folded Sheet Metal Fabrication Folded sheet metal is widely used in manufacturing. The most common method is using a bending brake and press bend to form the bend line along the sheet metal (Gupta et al., 1998). Two problems are commonly encountered in folded sheet material fabrication. First, the metal sheet needs considerable force for bending and so heavy machinery is required for the manufacture of most items. Second, precise location of the bends can be difficult to control because of bending tolerance and the accumulation of tolerance errors. For origami-inspired designs, the crease lines often must be precisely controlled as kinematic or mechanical behaviours can be highly sensitive to imperfections and eccentricities (Cash et al., 2015).

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Industrial Origami has proposed a method of precisely bending sheet metal by placing a series of curved slits along the notional bending line on sheet metal, see Figure 1. The area between slits, termed ‘straps’, connects adjacent edges and is twisted during fabrication, greatly reducing the required bending force (Durney and Pendley, 2005). Slit locations and thus bends can be precisely controlled with the use of CNC machines such as a waterjet or laser cutters. Additional benefits of the specific proposed slit geometry include a reduction in stress concentrations at the curved slit ends, and the ‘edge to face’ engagement whereby during the bending process, the strap will be twisted and pull the face toward the edge (Durney and Rangarajan, 2008). As a result, under vertical loading the face will be able to transfer shear forces directly across folded edges.

This paper presents a design method, folded proof-of-concept prototype, and preliminary numerical analyses of novel self-braced folded structural sections and frames. Section 2 describes a new foldable modular geometry and two basic uniaxial triangular elements generated from the module. Section 3 describes extended assemblies including floor slab and frame assemblies. Section 4 describes the manufacture of a proof-of-concept steel prototype manufactured with integral hinge and self-lock connections. Section 5 presents preliminary numerical investigations comparing typical hollow and the new folded self-braced triangular sections.

Figure 1 Precision sheet-metal bending with slits and straps connection crease line detail.

MODULAR UNIT AND UNIAXIAL SECTIONS Figure 2a shows a portion of a typical triangular hollow section with axial length L, side length W, and wall thickness tp. It can be unfolded to a configuration with area L × 3W . An equivalent triangular module is shown in Figure 2b with hexagonal plates embedded into two sides of the section such that they can be folded internally to brace all section walls at two points each. For the hexagon to contact all three walls, it must have side length WH = W/3. An expansion ratio λ can be calculated as unfolded volume over folded volume VU / V . Given V = LW 2√3/4 and VU = 3LWtp , expansion ratio λ can be shown to vary linearly with slenderness ratio λ = (12tP )/( √3W ). The flat-packed compacted state and the resultant slenderness relationship are substantially different to deployable bar structures (Chen and You, 2005). These typically have a minimum packaged size dictated by the structural section dimensions, for example CHS diameter.

Figure 2 Foldable modules of a) triangular hollow and b) self-braced triangular sections. The module can be directly tessellated to create uniaxial structural elements. If the module is tessellated longitudinally, a configuration shown in Figure 3a is created. Deployment from unfolded to folded occurs in two stages as for the module, with internal hexagonal plates folded upwards and then adjacent sectional walls folded inwards to form the self-braced triangular element. A concept preliminary packaging stage is also shown whereby the unfolded section is rolled to reduce shipping volume. If the module is tessellated laterally, a truss-like configuration shown in Figure 3b is created. Every two additional side panels generate a single additional triangular module and sufficient hexagonal plates to provide the required internal self-bracing. Deployment is able to occur sequentially, i.e. module-by-module. Either tessellation is easily designed based on the initial module definition and so a folded section can be designed with conventional methods. This design method avoids geometric complexities typically encountered in origami-inspired folded structure designs.

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Figure 3 Deployment sequence of a) longitudinally and b) laterally tessellated uniaxial configurations. EXTENDED ASSEMBLIES There are several ways by which to adapt or assemble the above sections to form a wider range of folded sections and frames. Rectangular or nested self-braced sections as shown in Figure 4a can be formed with simple geometric adjustments to the basic module. Simultaneous tessellation in both longitudinal and lateral directions generates a space-filling structure, shown in Figure 4b and 4c, that could be used for example as a floor slab. Selective assembly as shown for example in Figure 4d enables the creation of a complete frame structure. The structural feasibility of such assemblies is not known at this early stage of development, but these examples serve to show that the simple geometry of the folded component module enables simple and rapid design of conventional and unconventional sections and frames.

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Figure 4 Extended and assembled forms of self-braced folded sections. a) Non-triangular sections. b), c) Floor slab assembly. d) Frame assembly.

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STEEL PROTOTYPE FABRICATION For practical use of the self-braced triangular structures, on-site deployment must be achievable either manually or with low-force machinery, depending on the thickness of the plate. Construction must require a minimum number of additional connection components, i.e. all items necessary for assembly should be contained within the transported package or the sheet material itself. From inspection of the foldable module in Figure 2b it can be seen that there are two functions employed during deployment: folding about hinge lines and connection of free edges. The former occurs at two panel junctions and a single hexagon edge. The latter occurs at a single panel edge and two hexagon edges.

Integral connection details were designed to achieve these two functions. A hinge connection was designed based on Industrial Origami connections (Durney and Pendley, 2005). A self-lock connection that joins two free edges was designed based on slot-and-tab joints typically seen in packaging design (Cash et al., 2015). Connection details are shown in Figure 5a. Connection locations on a double-module with dimensions L = W = 0.3m are shown in Figure 5b. Hinge locations are designated ‘H‘, and male and female self-lock locations designated ‘Tm’ and ‘Tf’, respectively. The superposition of connection details at appropriate locations generates the part drawing shown in Figure 5c.

A full scale prototype was cut from a sheet of 0.9mm thick Galvanneal Steel with a CNC waterjet cutter. The manufactured sheet and the folded structure are shown in Figure 5d. Waterjet cutting took approximately two hours and subsequent manual folding took approximately 10 minutes for one person. Manual folding was found to be extremely easy, with hinge and self-lock alignment both working to produce an accurate folded form. The hexagonal bracing plate was also seen to provide good bracing to wall panels, although this will be quantified properly in future experimental investigations. For thick plate (tp >10mm) applications, both hinge and edge connections could be subsequently welded to secure the connection. A second larger prototype was constructed with eight modules and took approximately eight hours to waterjet cut and approximately one hour for four people to fold.

Figure 5 Steel prototype fabrication. a) Integral connection types. b) Connection locations. c) Part drawing. d) Waterjet cut and folded part. 796

PRELIMINARY NUMERICAL ANALYSIS

A preliminary numerical investigation was conducted using Abaqus finite element software. A linear buckling analysis was conducted on a self-braced folded section and an equivalent hollow section subjected to uniaxial compression. Part geometry had dimensions corresponding to the prototype described above and was meshed with S3R and S4R shell elements with an approximate mesh size of 10mm, shown in Figure 6a. Material elastic properties were taken as typical steel values of E =210 GPa and v =0.3. Pinned boundary supports were applied to the column base edge and a uniform compressive load to the top edge. The first buckled mode of the self-braced section occurred at an eigenvalue of 10.7MPa and had an eigenmode shown in Figure 6b. The first buckled mode of the hollow section occurred at an eigenvalue of 7.8MPa and an eigenmode shown in Figure 6c. These values are preliminary only, as the numerical model did not consider geometric imperfections or folded edge stiffness reductions generated from the folded fabrication method. These will have a significant effect on buckling capacities, however these early results are promising. Ongoing work is being conducted towards experimental studies to improve and validate numerical models, a full nonlinear buckling analysis with consideration of geometric imperfections and stiffness reduction will be carried out.

Figure 6 Section and isometric views of numerical models. a) Meshed part. b) Buckled mode of self-braced section. c) Buckled mode of triangular hollow section. CONCLUSION The above paper introduces geometric design and folded fabrication procedures for a new type of self-braced triangular structural section. Preliminary numerical results are also presented and indicated the structural form may have significant improvement in buckling capacity compared to a typical extruded hollow section. Future work will develop extended geometric procedures for non-triangular and assembled forms of the self-braced section. The fabrication procedures will also be used for experimental procedures and validated extended numerical investigations.

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ACKNOWLEDGEMENTS The corresponding author is grateful for the financial support provided by UQ NSRSF Grant 1403.

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