Quasi-static Folding Research Articles

Folding mechanics of a bistable composite tape-spring for flexible mechanical hinge

A bistable composite tape-spring (CTS) structure is stable in both extended and coiled configurations, which can be fully coiled or folded. Its bistable coiling feature has been employed in a Roll-Out Solar Array and successfully deployed in space; its foldable characteristics is analogous to a flexible mechanical hinge, showing great potential to be applied in an aircraft landing gear. Both the structural coiling and folding mechanics are dependent on tape geometry; whilst the correlated scale effect has not been investigated, which significantly constrains its foldable mechanical hinge designs and smart driving analysis in order to further reduce weight and complexity for conventional mechanical hinges. Here, we studied the folding stability mechanics of the CTS structure towards its full tape-length range, where novel stress and shape transitional mechanisms are revealed. This is achieved by investigating the quasi-static folding process of the CTS, where new stable shape features in terms of critical transitional length and stable folded angle are observed and identified through experimental observations, finite element model, as well as theoretical analysis. Theoretical criteria were then determined from the strain energy analysis in comparison to the predefined folded tape shape features. The folding stability mechanisms towards its full tape-length range were proposed in order to facilitate customized flexible hinge design and in-situ smart driving analysis in order to replace conventional mechanical hinges.

Folding of sealed origami-inspired capsule with rigid panels and hyperelastic hinges

Origami structures have great potential for space applications owing to the advantages of high packaging ratio, diversified design and predetermined deployment. Inspired from a rigid origami pattern, a novel architecture for large-scale expandable capsules that incorporates a hybrid origami combining rigid panels and flexible hinges is proposed in this paper. The rigid panels ensure the structure with good loading capacity and reliable performance. The flexible hinges with hyperelastic behavior address the geometric mismatch and incompatibility when folding a 3D sealed structure. This paper focuses on the mechanical behavior of the expandable space capsule inspired from origami. Based on our previous work about kinematic analysis, two deformation modes of hyperelastic hinges are determined. Theoretical models to characterize the hyperelastic hinges are described using the hyperelastic constitutive model. Specific experimental devices are designed for the hinges with different deformation modes individually. The accuracies of theorical models are compared to finite element simulations and experiments, and the applicable ranges are evaluated respectively. Furthermore, the mechanical properties of a representative capsule unit are studied with the energy method. Using the theoretical model, a self-energizing deployment of the structure is discovered and then validated through simulation analysis and quasi-static folding tests. The results demonstrate that this proposed concept provides a novel approach to designing origami-inspired deployable structures for on-orbit construction in future space missions.

Quasi-static folding and deployment of rigidizable inflatable beams

This paper is concerned with a theoretical and experimental study of the deployment of inflated curved slender beams. A theoretical model for a beam with effects from restoring force and moment on deployment angle is proposed. Assuming slow deployment, a quasi-static viewpoint is utilized to simplify the model which the buckling cross-section is considered. The relation between deployment angle and contact area at the instability bending point is studied for the membrane chamber of a thermally rigidizable inflatable beam. While an inflated beam was constrained as simply-supported and fixed-free at its ends, the relations between the restoring force and moment and the internal pressure and its angle were tested by adding to the mechanical experimental method an infrared thermal imager. Results show that the restoring force and moment are increasing with the pressure at a given angle. Moreover, the restoring moment is nonlinearly related to the deployment angle. The correctness of the theoretical model was verified through experiments.

Generalized modeling of origami folding joints

Origami robots self-reconfigure from a quasi two-dimensional manufactured state to three-dimensional mobile robots. By folding, they excel in transforming their initial spatial configuration to expand their functionalities. However, unlike paper-based origamis, where the materials can remain homogeneous, origami robots require varying payloads and controllability of their reconfigurations. Therefore, the mechanisms to achieve automated folding adapt flat thin panels and folding hinges that are often of different materials to achieve the folding. While the fundamental working principle of an origami hinge remains simple, these multi-component, multi-material origami joints can no longer be modeled by beam theory without considering the semi-rigid connections at the material interfaces. Currently, there is no comprehensive model to analyze physical behavior of an actuated folding hinge accurately. In this work, we propose a model based on the plate theory to predict the origami folding joint: we adapt a torsional spring to capture this semi-rigid connection, predict the folding stiffness and bending of origami joints. Herein, the semi-rigid connection is calibrated by quasi-static folding tests on a series of physical origami folding joints, and the accuracy of our model is compared to finite element simulations. With this analytical model, we can accurately simulate the mechanics of physical origami folding joints.

Quasi-static Folding Mechanical Behavior Analysis and Optimization Design for Composite Tube Hinge

Quasi-static Folding Mechanical Behavior Analysis and Optimization Design for Composite Tube Hinge

Quasi-static analysis and multi-objective optimization for tape spring hinge

Mechanical attributes of interest are always mutually exclusive in the design process of tape spring hinge. Here we present a complete optimization framework consisting of computational mechanics, optimization design, engineering application, and experimental research to compromise mechanical attributes such that an optimal solution set can be obtained to provide design strategies for engineering practices. Tape spring hinge in folding and unfolding processes with large non-linearity is firstly simulated using quasi-static analysis technique. During the quasi-static process, the ratio of kinetic energy to strain energy is observed to determine mass scaling parameters that measure the precision of analysis. Based on the parameters analyzed, moment-rotation responses of tape spring hinge in quasi-static folding and unfolding processes are investigated and experimentally verified. Yield theory derived from the combination of thin shell theory and Tresca yield criterion is introduced to control the yield of the hinge during folding and deploying processes. In addition, tape spring hinge is released transiently when in spatial conditions; thus the fundamental frequency is calculated and selected herein to be a measurement of stiffness that is maximized to avoid the vibration. Then a multi-objective optimization model is established using the derived yield theory control equation and critical moment as optimization constraints, with the fundamental frequency and strain energy as objectives. The non-dominated sorting genetic algorithm is used to solve the optimization model, and then feasible solution distribution and Pareto frontier are obtained. These results are compared and discussed with two additional single-objective optimizations. Ultimately we achieve the optimal design for tape spring hinge, which is verified well with numerical simulation.

Design Optimization of Opposite Tape-Spring Flexure Hinges

An optimal design method for the qusai-static folding and deployment of opposite tape-spring flexure (OTSF) hinges is presented based on the response surface method. The full factorial method is employed to design of experiments, and the qusai-static folding and deployment nonlinear analysis is obtained by ABAQUS/Explicit slover. The surrogate models of the OTSF flexure hinge are derived by the response surface method. Considering lightweight and high stability, the peak moment of quasi-static folding and deployment, and maximum Mises stress in complete folding configuration as well as mass are set as the objectives to get the optimal performances. The modified NSGA-II is used to seek for an optimal design. The relative errors of the objectives between the optimal design and the FE analysis results are less than 3.5%.

Experiment and multiobjective optimization design of tape-spring hinges

Flexible tape-spring hinges can be folded elastically and are able to self-deploy by releasing stored strain energy with fewer component parts and slight weights. This study presents a detailed investigation of the folding and deployment of single-layer tape-spring (SLTS) hinges and double-layer tape-spring (DLTS) hinges under pure bend loading. The material properties of tape-spring hinges are measured using an INSTRON machine. A DLTS hinge construction is created, and its moment-rotation relationship during quasi-static deployment is measured. An experiment is conducted to verify the validation of the numerical models for the DLTS hinges. The quasi-static deployment behavior of SLTS hinges and DLTS hinges is then analyzed using nonlinear finite element ABAQUS/Explicit solver, starting from the complete folded configuration. The DLTS hinge has good quasi-static deployment performances with regard to maximum stress (Sm), steady moment (M*) and the peak moment (Md) during the DLTS hinge quasi-static deployment. In addition, the sampling designs of the DLTS hinges are created based on a three-level full factorial design of experiments (DOE) method. The surrogate models of Sm, M* and Md of the DLTS hinges are derived using response surface method (RSM) to reduce the computational cost of quasi-static folding and deployment of numerical simulations. The Multiobjective optimization design (MOD) of the DLTS hinge is performed using modified non-dominated sorting genetic algorithm (NSGA-II) algorithm to achieve the optimal design. The finite element models for the optimal design based on numerical method are established to validate the optimization results.

Parameter Study of Opposite Tape-Spring Flexure Hinge

Parameter study for the qusai-static folding and deployment of opposite tape-spring flexure (OTSF) hinges is presented. The full factorial method is employed to design of experiments, and the qusai-static folding and deployment nonlinear analysis is obtained by ABAQUS/Explicit solver. Parametric studies show that both the section radius and the central angle have significant effects to the peak moment of quasi-static folding and deployment of the OTSF hinges. However, the maximum Mises stress in complete folding configuration is more sensitive to the central angle than the section radius.

Folding and Deployment of a New Thin-Walled Tube Flexible Hinge

A new thin-walled tube flexible hinge with six slots is proposed. The slot geometry is parameterized in terms of slot width, length and distance between two adjacent slots. The experiment for tension test of the thin-walled tube hinge with six-slots is conducted by INSTRON and the tensile stress-strain curve is measured. Finite element analysis to investigate the quasi-static folding and deployment of the new hinges by ABAQUS/Explicit solver are employed to perform a series of parameter studies for the slots longitude lengthl0, the slot widthwand the distancedbetween two adjacent slots.

Optimizing the qusai-static folding and deploying of thin-walled tube flexure hinges with double slots

The thin-walled tube flexure(TWTF) hinges have important potential application value in the deployment mechanisms of satellite and solar array, but the optimal design of the TWTF hinges haven’t been completely solved, which restricts their applications. An optimal design method for the qusai-static folding and deploying of TWTF hinges with double slots is presented based on the response surface theory. Firstly, the full factorial method is employed to design of the experiments. Then, the finite element models of the TWTF hinges with double slots are constructed to simulate the qusai-static folding and deploying non-linear analysis. What’s more, the mathematical model of the TWTF flexure hinge quasi-static folding and deploying properties are derived by the response surface method. Considering of small mass and high stability, the peak moment of quasi-static folding and deploying as well as the lightless are set as the objectives to get the optimal performances. The relative errors of the objectives between the optimal design results and the FE analysis results are less than 7%, which demonstrates the precision of the surrogate models. Lastly, the parameter study shows that both the slots length and the slots width both have significant effects to the peak moment of quasi-static folding and deploying of TWTF hinges with double slots. However, the maximum Mises stress of quasi-static folding is more sensitive to the slots length than the slots width. The proposed research can be applied to optimize other thin-walled flexure hinges under quasi-static folding and deploying, which is of great importance to design of flexure hinges with high stability and low stress.

Analysis and testing of ultrathin shell 2 m diameter reflector demonstrator

Ultra-thin shell foldable and self-deploying composite reflectors are being developed for space antennas to meet low cost, low mass and high surface accuracy. For Ku-band missions, a full-scale offset parabolic reflector antenna is designed by considering different concepts of monolithic and nonmonolithic structures, different stiffening schemes, manufacturing ease, and lower cost. The resulting reflector is based on stiffened spring back reflector concept but it provides much simpler design, significantly lower mass and lower cost. It is a simple monolithic structure and consists of a reflector surface and a flat skirt. The skirt is an integral part of the reflector and is used to stiffen the reflector. The full-size version is an offset parabolic reflector with a diameter of 6 m, a focal length of 4.8 m, and an offset of 0.3 m. In order to demonstrate the concept, 1/3-scaled version is designed, manufactured, and tested. Experiments of the demonstrator are conducted for quasi-static folding, dynamic deployment behavior, stiffness measurements, modal analysis, and surface accuracy in deployed configuration; the experimental results are compared with the results of finite elements solutions where applicable.

Quasi-Static Folding and Deployment of Ultrathin Composite Tape-Spring Hinges

Deployable structures made from ultrathin composite materials can be folded elastically and are able to selfdeploy by releasing the stored strain energy. This paper presents a detailed study of the folding and deployment of a tape-spring hinge made from a two-ply plain-weave laminate of carbon-fiber reinforced plastic. Aparticular version of this hinge was constructed, and its moment-rotation profile during quasi-static deployment was measured. The present study is the first to incorporate in the simulation an experimentally validated elastic micromechanical model and to provide quantitative comparisons between the simulations and the measured behavior of an actual hinge. Folding and deployment simulations of the tape-spring hinge were carried out with the commercial finite element package Abaqus/Explicit, starting from the as-built unstrained structure. The folding simulation includes the effects of pinching the hinge in the middle to reduce the peak moment required to fold it. The deployment simulation fully captures both the steady-state moment part of the deployment and the final snap back to the deployed configuration. An alternative simulation without pinching the hinge provides an estimate of the maximum moment that could be carried by the hinge during operation. This is about double the snapback moment.