Folding Angle Research Articles

Quantitative validation of the analytical mode shapes of a beam-like structure with a Z-shaped configuration

Beam-like structures are widely used in engineering. The accuracy of the analytical mode shapes of these structures is important for studying their dynamic characteristics. A method is presented in this study to theoretically obtain and quantitatively validate the analytical mode shapes of a beam-like structure with a Z-shaped configuration. The governing equations and boundary conditions of the structure’s planar motion are derived using Hamilton’s principle. Frequencies and analytical mode shapes of the structure are theoretically obtained and compared with the numerical results from finite element method. The comparison of frequencies and modal assurance criterion is used to quantitatively validate the analytical mode shapes. Examples are presented to show the analytical mode shapes of Z-shaped beams with different fold angles. The proposed method is useful for improving the accuracy of analytical mode shapes’ which is beneficial to the design and control of beam-like structures in engineering fields.

Autonomous origami: pre-programmed folding of inkjet printed structures

Self-folding, whereby a 2D net autonomously folds into a pre-ordained 3D shape when exposed to a stimulus, shows potential, in a manner similar to 3D printing, as a means of easily customisable digital manufacture. It also presents some inherent advantages over conventional additive manufacturing techniques, such as the low cost associated with mass-production of polymer sheets and coatings, the compatibility with most planar manufacturing techniques, and the ease of storage and transportation. A self-folding mechanism was developed by inkjet printing silver nanoparticle suspensions onto polyethylene terephthalate (PET) sheets. By providing sufficient electrical power to the printed tracks, resistive heating causes folding to occur along the printed silver lines. A bilayer strip model was adapted to analyse the steady-state fold angle of the PET substrate, which shows good qualitative agreement, and reasonable quantitative agreement, with the experimental data. Furthermore, inkjet-printed silver tracks are known for a significant reduction in resistivity as the sintering temperature increases. Therefore, a power control system that utilises a real-time resistance sensor was developed to enable power reference tracking. The developed mechanism was able to achieve folds up to 90° and a fast actuation time of 35 s when 2.25 W was provided to a 3 mm by 40 mm silver track.

Origami fold states: concept and design tool

Abstract. The ability of origami to alter its properties and behaviors with its shape makes it an elegant source of inspiration for many engineering designs challenges. Fold states specify the shape of the origami – its facets, creases, and fold angles. Origami research recognizes several acknowledged fold states: the unfolded, fully folded, and flat-folded states. However, these fold states are not comprehensive, excluding some of the most predominant fold states in origami-based devices. In this paper we propose a comprehensive list of fold states based on fold angles. We support the method of categorizing fold states by evaluating the functions and fold states of a large sample of origami-based devices. These correlations provide insight for selecting fold states for origami-based design. We discuss properties and behaviors of the fold states individually and provide a process for fold-state selection.

Deformation Pattern and Energy Absorption Analysis on Initial Fold Crash Box by Oblique Crash Test

In the previous study, many researchers have done to improve the energy absorption of crash box due to axial impact. In the crash test, crash box is commonly subjected to both axial and oblique. In this study, crash box design with initial fold is modelled by using application software based on Finite Element Analysis. The effect of placement ratio and initial fold angle on crash box subjected to oblique loading is investigated. The placement ratio is set as 1:2, 1:1, and 2:1 measured from the total height of crash box. The initial fold angle is varied with 90°, 60° and 45°. Crash box material is Mild Steel ASTM E-04. Crash box material is assumed as bilinear isotropic hardening material. The crash test is modelled as oblique loading crash test. The oblique loading angle used on impactor is 60°. Based on computer simulation results, it can be showed that the deformation pattern of initial fold crash box occurred as buckling and axial mode. The crash box design with placement ratio 1:2 and initial fold angle 90° produce the highest value of energy absorption.

Measurement of incomplete fusion cross sections in Li6,7+U238 reactions

Background: Incomplete fusion (ICF) in reactions involving weakly bound projectiles is understood to play an important role in enhancing the ratio of asymmetric to symmetric fission at $E\ensuremath{\le}{V}_{b}$, widening the fission fragment folding angle distribution at $E\ensuremath{\le}{V}_{b}$ and suppressing the complete fusion (CF) cross section at $Eg{V}_{b}$. Experimental cross sections for individual ICF channels are necessary to obtain quantitative estimates of the above effects.Purpose: Measurement of the cross sections for individual transfer-induced or ICF-fission channels in $^{6,7}\mathrm{Li}+^{238}\mathrm{U}$ reactions to explain quantitatively the difference in the ratio of asymmetric to symmetric fission for total fission and CF fission.Methods: Triple coincidence measurement of two fission fragments and one light charged projectilelike fragment (PLF) is carried out using two multiwire proportional counter (MWPC) detectors and an array of CSI(Tl) scintillation detectors at energies near the Coulomb barrier. By calculating the efficiency of the detectors by Monte Carlo simulation and fission probability by GEF code, the angle-integrated ICF cross sections corresponding to p, d, t, and $\ensuremath{\alpha}$ emission are obtained. Mass distributions for total fission are calculated by adding the distributions for CF fission and all ICF fissions with weight factors proportional to the measured cross sections.Results: ICF cross sections corresponding to $\ensuremath{\alpha}$ emission are found to be the highest in both the reactions. The relative contribution of ICF to total fusion at the lowest measured energy is found to be $\ensuremath{\approx}70%$ and it decreases with increasing projectile energy, consistent with the systematics of several reactions involving the same weakly bound projectiles. The simulated mass distributions for total fission are found to reproduce the experimental mass distributions.Conclusions: Deuteron (triton) capture is observed to be the major ICF channel in the reaction involving $^{6}\mathrm{Li}\phantom{\rule{0.28em}{0ex}}(^{7}\mathrm{Li})$ projectile. The ratio of the sum of ICF to total fusion cross section for the present systems are consistent with the systematics. The difference in the ratio of asymmetric to symmetric fission between total fission and CF fission is explained quantitatively.

Performance of a straight-bladed vertical axis wind turbine with inclined pitch axes by wind tunnel experiments

Abstract This paper investigated the performance of an innovative straight-bladed vertical axis wind turbine (VAWT) with inclined pitch axes (not coincident with the aerodynamic center line of blades). A straight blade with an inclined pitch axis used in VAWTs was described and the corresponding VAWT prototype was built and tested in a low speed wind tunnel to validate the feasibility of power output control using the novel design. Effect of blade folding movements on the VAWT performance was illustrated. It is found that the maximum power coefficient is reduced by 62.5% when blades are folded to the fold angle of 2°from the optimal fold angle of 8°. The decrease of the maximum power coefficient is also observed to be 59.0% when blades are folded to the fold angle of 13°. In addition, the control rule of the blade fold angle to maintain constant power output and the folding sensitivity at the rated rotation rate were investigated.

Quasi-static large deformation compressive behaviour of origami-based metamaterials

An analytical model of the quasi-static response of Miura-ori based metamaterial to in-plane compression was first developed to describe the major mechanical characteristics related to the strength and energy absorption capacity of this material in the analysed loading direction. It is assumed that the base material is ductile and can be approximated as a perfectly plastic material. The results revealed that the initial strength and densification strain of the Miura-ori based metamaterial cannot be uniquely defined by its relative density, in contrast to most conventional cellular materials used for energy absorption applications. A particular value of the initial folding angle γ0 corresponds to the minimum relative density for each static sector angle α. This value determines the transition point separating the region where the initial material strength increases with the increase of the relative density from the one where this strength decreases with the increase of the relative density. Miura-ori based metamaterials with large initial dihedral angle γ0 have larger energy absorption capacity per unit mass, however exhibiting significant variations of Poisson's ratios during compression. The energy absorption efficiency of the Miura-ori based metamaterials was compared with that of single-walled regular honeycombs under in-plane compression. It is demonstrated that, for certain combination of the geometric parameters a, b, α and γ0, the origami-based materials can outperform the honeycombs with the same relative density. The analytical model was verified by the numerical simulations of the response of single cells with various geometries and multi-sheet origami configurations. The model predictions were also validated by a quasi-static compression test of a four-sheet origami specimen.

Control of Net Radiative Heat Transfer With a Variable-Emissivity Accordion Tessellation

Abstract Origami tessellations have been proposed as a mechanism for control of radiative heat transfer through the use of the cavity effect. This work explores the impact of a changing projected surface area and varying apparent radiative properties on the net radiative heat transfer of an accordion fold comprised of V-grooves. The net radiative heat transfer of an accordion tessellation is obtained by a thermal energy balance at the cavity openings with radiative properties of the cavities given as a function of various cavity parameters. Results of the analytical model are experimentally confirmed. An accordion tessellation, constructed of stainless-steel shim stock, is positioned to achieve a specified fold angle and placed in a vacuum environment while heated by Joule heating. A thermal camera records the apparent temperature of the cavity openings for various fold angles. Results are compared to apparent temperatures predicted with the analytical model. Analytically and experimentally obtained temperatures agree within 5% and all measurements fall within experimental uncertainty. For diffusely irradiated surfaces, the decrease in projected surface area dominates, causing a continuous decrease in net radiative heat transfer for a collapsing accordion fold. Highly reflective specular surfaces exposed to diffuse irradiation experience large turn-down ratios (7.5× reduction in heat transfer) in the small angle ranges. Specular surfaces exposed to collimated irradiation achieve a turn down ratio of 3.35 between V-groove angles of 120 deg and 150 deg. The approach outlined here may be extended to modeling the net radiative heat transfer for other origami tessellations.

High filtration efficiency fluffy material: nano-fiber constructing gradient structure on recycled curved PET micro-fibers web

High efficiency filtration materials focus on electreted melt-blown polypropylene nonwoven and nano-scale fibers membrane in industry. However, the charge decay and the balance of efficiency and resistance are still facing challenges on research and practical applications. In this research, combined with traditional electrospinning and carding process, a simple and new fluffy gradient filtration material was designed by constructing nano-scale poly(lactic acid) (nano-PLA) fiber membranes on recycled three-dimensional curved poly(ethylene terephthalate) (R-PET) micro-fibers webs. Influences of basis weights of nano-PLA membranes and curved types of R-PET fibers on the filtration performance and the dust-holding capacity of R-PET/nano-PLA mats were investigated. Besides, the filtration mechanism of R-PET/nano-PLA mats was systemically studied. Results show that R-PET with zigzag curve (R/Z-PET) possesses the highest filtration efficiency of 99.992% comparing with 99.517% of linear R-PET, the pressure drop fall to 201.11 Pa, and a quality factor level up from 0.024 to 0.047 Pa−1. The pressure raising rate of the R/Z-PET/nano-PLA mat is the slowest. R/Z-PET fibers with a folding angle of 90° benefit to decrease the friction between fiber and particles when the location angle of zigzag fiber is 45° along the airflow direction, which decrease the pressure drop at high filtration efficiency. Surface residual charges contribute some effect on the overall filtration performance of the R-PET/nano-PLA mat. A new way of simple curved micro-PET fiber combining with nano-scale fibers provides an industrial available path to mass production of high efficiency filtration material serving for air pollution control without electret process.

Curving to Fly: Synthetic Adaptation Unveils Optimal Flight Performance of Whirling Fruits.

Appendages of seeds, fruits, and other diaspores (dispersal units) are essential for their wind dispersal, as they act as wings and enable them to fly. Whirling fruits generate an autogyrating motion from their sepals, a leaflike structure, which curve upwards and outwards, creating a lift force that counteracts gravitational force. The link of the fruit's sepal shape to flight performance, however, is as yet unknown. We develop a theoretical model and perform experiments for double-winged biomimetic 3D-printed fruits, where we assume that the plant has a limited amount of energy that it can convert into a mass to build sepals and, additionally, allow them to curve. Both hydrodynamic theory and experiments involving synthetic, double-winged fruits show that to produce a maximal flight time there is an optimal fold angle for the desiccated sepals. A similar sepal fold angle is found for a wide range of whirling fruits collected in the wild, highlighting that wing curvature can aid as an efficient mechanism for wind dispersal of seeds and may improve the fitness of their producers in the context of an ecological strategy.

A highly adhesive PIL/IL gel polymer electrolyte for use in flexible solid state supercapacitors

In this work we have demonstrated how to prepare a novel gel polymer electrolyte (GPE) with remarkable adhesive characteristics by combining a synthesized poly(ionic liquid) consisting of poly(1-vinyl-3-propylimidazolium bis(fluorosulfonyl)imide) (poly(VPIFSI)) and a commercial ionic liquid: 1-ethyl-3-methyl imidazolium bis(fluorosulfonyl)imide (EMIFSI). For this purpose several PIL/IL-GPEs systems (considering the amount of IL) were subjected to electrochemical characterization. The influence of the PIL/IL-GPE (50 wt% of IL) on the properties of a flexible solid state supercapacitor was evaluated using electrochemical impedance spectroscopy, cyclic voltammetry and the galvanostatic charge/discharge technique that allows synchronous measurements of the cell voltage and the potential of the positive and negative electrodes. The influence of the ions on the formation of the electric double layer in the device during cycling employing different conditions and folding angles is discussed. The properties of the adhesive PIL/IL-GPE, such as high conductivity, good interaction between the PIL matrix and the IL liquid phase that prevents any leakage (thereby contributing to greater safety) together with the good adherability and wettability of the gel electrolyte on the electrode surface have produced a device with an improved rate capability and cyclability that undergoes hardly any changes in Csp,cell, Ereal, and Preal of the cell when folded.

Spin-Selective Transmission in Chiral Folded Metasurfaces.

Controlling the spin angular momentum of light (or circular polarization state) plays a crucial role in the modern photonic applications such as optical communication, circular dichroism spectroscopy, and quantum information processing. However, the conventional approaches to manipulate the spin of light require naturally occurring chiral or birefringent materials of bulky sizes due to the weak light-matter interactions. Here we experimentally demonstrate an approach to implement spin-selective transmission in the infrared region based on chiral folded metasurfaces that are capable of transmitting one spin state of light while largely prohibiting the other. Due to the intrinsic chirality of the folded metasurface, a remarkable circular dichroism as large as 0.7 with the maximum transmittance exceeding 92% is experimentally demonstrated. The giant circular dichroism is interpreted within the framework of charge-current multipole expansion. Moreover, the intrinsic chirality can be readily controlled by manipulating the folding angle of the metasurface with respect to the cardinal plane. Benefiting from its strong chirality and spin-dependent transmission characteristics, the proposed folded metasurface may be applied to a range of novel photon-spin selective devices for optical communication technologies and biophotonics.

Effects of rotational velocity and hold time at folding posture on time-dependent release behavior of creased white-coated paperboard

In this work, a folding experiment was performed to investigate the time-dependent creasing characteristics of white-coated paperboard of 0.3mm thickness. After folding up to the tracking angle of 90° under a specified rotational velocity, the creased part was hold for a chosen short time (0~20s) and the time-dependent release behavior of folding angle was experimentally investigated for the elapsed release time of 10s. When using the paperboard scored with a specified indentation depth, both the hold time of folded posture of creased part and the rotational velocity of fixture were varied. The folding angle of the paperboard was measured by a CCD camera of digital microscope and the bending moment resistance was measured by a load cell of bending test apparatus in the folding experiment. Through the experiment, it was found that the time-dependent release angle consisted of the hold time based intercept part and the creep-recovery based gradient part as a logarithmic function of the elapsed release time. When varying the folding velocity against a fixed unfolding velocity, the unfolded released behavior was isolated by the hold time from the first half folding velocity. Seeing the drop rate of bending moment at the tracking position and the dependency of initial release angle on the rotational velocity, a transient state and quasi-stationary state of bending moment relaxation were revealed.

Influence of angular damping coupling on the vibrations of a triaxial two-section non-suspension wheeled vehicle

This article is devoted to the study of the influence of angular damping coupling (АDС) on the vibrations of a triaxial two-section non-suspension wheeled vehicle. To assess the effect of the damper in the articulation unit on the vibrations of such a vehicle, three options for combining the parameters of the suspension system and the ADC are considered: wheeled articulated vehicle with suspension and without ADC; wheeled articulated vehicle without suspension and without ADC; wheeled articulated vehicle without suspension and with ADC. Based on the generally accepted assumptions of the linear theory of suspension, a calculation scheme and a mathematical model of the angular oscillations of a triaxial two-section non-suspension wheeled vehicle with ADC in the articulation unit are presented. During finding analytical solution, expressions for the gain of oscillations for the folding angle of identical sections were found and their maximum values in resonance were determined. For the considered options, the ratios of the amplification coefficients of the angular oscillations in resonance and the expressions for the relative damping coefficient of the oscillations along the folding angle of the sections are determined. The calculated amplitude-frequency characteristics (AFC) of the folding angle of the sections for various combinations of ADC parameters in the presence and absence of suspension of the vehicle sections are presented. It is established that the introduction of ADC for a wheeled non-suspension vehicle allows one to reduce the amplitude of angular oscillations in resonance by 10 times. And, when using wheels, the rigidity of which is equal to the stiffness of the suspension, for non-suspension articulated vehicles, an even greater decrease in angular oscillations to a dynamic coefficient of 1,7 is possible. At the same time, the angular damper for the non-suspension vehicle, the inelastic resistance of which is equal to the total power of all 8 shock absorbers of the sprung vehicle, provides smaller angular oscillations in the entire frequency range of the kinematic disturbance on the side of the road. It is advisable to use the proposed articulated layout arrangement of non-suspension vehicle with UDS for developing promising wheeled vehicles, for example, tractors and heavy vehicles with large-diameter wheels.

Topological zero-line modes in folded bilayer graphene

A folded bilayer graphene device as an experimentally realizable platform to produce one-dimensional topological zero-line modes is proposed. The new scheme has the advantage that it completely obviates the conventional approach, which relies on the precise alignment of split gates, and is supported by the experimental fabrication of folded bilayer graphene with a well-controlled folding angle. These findings open up a new field for the application of folded graphene, and pave the way to realize low-power-consuming topological quantum devices.

High‐Energy‐Density Foldable Battery Enabled by Zigzag‐Like Design

AbstractFlexible batteries, seamlessly compatible with flexible and wearable electronics, attract a great deal of research attention. Current designs of flexible batteries struggle to meet one of the most extreme yet common deformation scenarios in practice, folding, while retaining high energy density. Inspired by origami folding, a novel strategy to fabricate zigzag‐like lithium ion batteries with superior foldability is proposed. The battery structure could approach zero‐gap between two adjacent energy storage segments, achieving an energy density that is 96.4% of that in a conventional stacking cell. A foldable battery thus fabricated demonstrates an energy density of 275 Wh L−1 and is resilient to fatigue over 45 000 dynamic cycles with a folding angle of 130°, while retaining stable electrochemical performance. Additionally, the power stability and resilience to nail shorting of the foldable battery are also examined.

3D printing of Ron-Resch-like origami cores for compression and impact load damping

Core panels made of origami structures provide effective force redistribution and energy dissipation. A wide range of origami patterns is proposed to create three-dimensional panels, which can be used as sandwich cores. The origami tessellation mainly consists of unit cells made of small faces joined together through crease lines. Ron-Resch is an origami pattern composed of star pleats joined together that exhibits pronounced shape flexibility and geometry forming as well as potential mechanical performance. These advantages can be employed for load dissipation and damping due to its high deformation and strain values. This study focuses on three different Ron-Resch-like origami tessellations based on the star pleat’s number of branches and the area of internal facets of the star pleat. An additive manufacturing technique was used to fabricate the tested samples from polylactic acid filament. In addition, compression and impact tests were conducted to evaluate the effect of the folding angle for three different angles and then the results have been discussed. The ANSYS finite element package was used to numerically simulate the compression and impact events Moreover; the study includes investigation of the shape memory effect based on the shape recovery of the unit element of the Ron-Resch-like origami tessellation.

An End-to-End Approach to Self-Folding Origami Structures

This paper presents an end-to-end approach to automate the design and fabrication process for self-folding origami structures. Self-folding origami structures are robotic sheets composed of rigid tiles and joint actuators. When they are exposed to heat, each joint folds into a preprogrammed angle. Those folding motions transform themselves into a structure, which can be used as body of 3-D origami robots, including walkers, analog circuits, rotational actuators, and microcell grippers. Given a 3-D model, the design algorithm automatically generates a layout printing design of the sheet form of the structure. The geometric information, such as the fold angles and the folding sequences, is embedded in the sheet design. When the sheet is printed and baked in an oven, the sheet self-folds into the given 3-D model. We discuss, first, the design algorithm generating multiple-step self-folding sheet designs, second, verification of the algorithm running in $O(n^2)$ time, where $n$ is the number of the vertices, third, implementation of the algorithm, and finally, experimental results, several self-folded 3-D structures with up to 55 faces and two sequential folding steps.

Stress-biased laminated composites for smooth folds in origami structures

Origami folding principles are attractive for morphing structures due to their potential for realizing drastic changes in shape. Laminated composites enable adaptive lightweight solutions for the implementation of rigid origami structures. This paper presents a strategy for the creation of smooth folds in finite-thickness laminated composites; the approach is applicable to smart folding structures with reconfigurable creases. An analytical laminated-plate model, based on strain energy minimization, is presented to calculate fold angle as a function of laminate parameters. Folds, realized as localized curvature at a crease, are modeled using piecewise displacement polynomials. Folded composites, created using prestressed elastomers with zero in-plane Poisson's ratio, are fabricated for demonstration and model validation. The calculated out-of-plane deflection of the curved creases is in agreement with measurements. A parametric study is conducted to characterize the sensitivity of fold angle and sharpness to variations in laminate modulus and thickness, crease width, and prestrain orientation. Narrow creases require higher prestress for a given fold angle than wider creases. Fold sharpness can be maximized by minimizing crease width and thickness. Anisotropy in the prestressed elastomer is a tradeoff between achieving zero in-plane Poisson’s ratio for unidirectional prestress and maximizing the range of crease orientations for foldability.

Research on the Folding Patterns and Deployment Dynamics of Inflatable Capsule Structures

The folding patterns and deployment dynamic characteristics of conical inflatable capsule structures were investigated. A six-fold-line method of packing a conical shell surface was designed. The fold-line layouts and relation formulas of the fold angles were determined. The folded state of the inflatable capsule structure was parametrically modeled; then, the deployment dynamic analysis model was established using ANSYS/LS-DYNA software. The dynamic characteristics of the inflatable capsule structure in orbit were numerically simulated. Thus, the deployment configurations and the time history curves of the dynamic characteristics were obtained. The results verified the feasibility of the fold pattern and the deployment dynamic analysis model. The influences of the residual gases from the packing process on the subsequent deployment process were investigated. The results indicated that a small amount of residual gas can lead to structures that cannot deploy smoothly, and two methods were presented to avoid this challenge. These works provide technical support for the structural designs of this type of inflatable capsule structure.