Shape-sizing nested optimization of deployable structures using SQP

The potential role of formal structural optimization was investigated for designing foldable and deployable structures in this work.Shape-sizing nested optimization is a challenging design problem.Shape,represented by the lengths and relative angles of elements,is critical to achieving smooth deployment to a desired span,while the section profiles of each element must satisfy structural dynamic performances in each deploying state.Dynamic characteristics of deployable structures in the initial state,the final state and also the middle deploying states are all crucial to the structural dynamic performances.The shape was represented by the nodal coordinates and the profiles of cross sections were represented by the diameters and thicknesses.SQP(sequential quadratic programming) method was used to explore the design space and identify the minimum mass solutions that satisfy kinematic and structural dynamic constraints.The optimization model and methodology were tested on the case-study of a deployable pantograph.This strategy can be easily extended to design a wide range of deployable structures,including deployable antenna structures,foldable solar sails,expandable bridges and retractable gymnasium roofs.

Recent Advances in Space-Deployable Structures in China

Deployable space structure technology is an approach used in building spacecraft,especially when realizing deployment and folding functions.Once in orbit,the structures are released from the fairing,deployed,and positioned.With the development of communication,remote-sensing,and navigation satellites,space-deployable structures have become cutting-edge research topics in space science and technology.This paper summarizes the current research status and development trend of spacedeployable structures in China,including large space mesh antennas,space solar arrays,and deployable structures and mechanisms for deep-space exploration.Critical technologies of space-deployable structures are addressed from the perspectives of deployable mechanisms,cable-membrane form-finding,dynamic analysis,reliable environmental adaptability analysis,and validation.Finally,future technology developments and trends are elucidated in the fields of mesh antennas,solar arrays,deployable mechanisms,and on-orbit adjustment,assembly,and construction.

A flat-foldable equiangular spiral folding pattern inspired by sunflowers for deployable structures

Flasher origami pattern has been widely utilized to improve the stowage efficiency of deployable structures.Nevertheless,flasher origami cannot be folded fully flat,and they still have great potential for optimization in terms of storage volume and folding creases.In this paper,a flat foldable equiangular spiral folding pattern inspired by the sunflower disk is introduced.Then,a parametric design method for this equiangular spiral crease diagram is introduced in detail.Subsequently,a kinematic model of the equiangular spiral folding pattern is established based on the kinematic equivalence between rigid origami and spherical linkages.A simulation of the developed model demonstrates that the equiangular spiral folding pattern can be folded flat.Using the folded ratio as an evaluation index,the calculated results and experiments show that the equiangular spiral crease pattern can yield fewer creases and improve stowage efficiency in comparison to flasher origami pattern.Equiangular spiral folding pattern can save a considerable amount of space and provide a new approach to spatially deployable structures.

An origami shield with supporting frame structures optimized by a feature-driven topology optimization method

In this paper,the design,manufacture and testing of an origami protective shield with a supporting frame structure are presented.It consists of an origami shield surface and a deployable supporting frame structure that needs to be portable and sufficiently stiff.First,for the design of the shield surface,a threestage origami crease pattern is developed to reduce the shield size in the folded state.The shield surface consists of several stiff modular panels and layered with flexible fabric.The modular panels are made of a multi-layer composite where a ceramic layer is made of small pieces to improve durability as those small pieces enable restriction of crack propagation.Then,the supporting frame structure is designed as a chain-of-bars structure in order to fold into a highly compact state as a bundle of bars and deploy in sequence.Thus,a feature-driven topology structural optimization method preserving component sequence is developed where the inter-dependence of sub-structures is taken into account.A bar with semi-circular ends is used as a basic design feature.The positions of the bar’s end points are treated as design variables and the width of the bars is kept constant.Then,a constraint on the total length of the chain of bars is introduced.Finally,the modular panels made of multi-layer composite and the full-scale prototype of the origami shield are fabricated and tested to verify the bullet-proof performance.

Novel Surface Design of Deployable Reflector Antenna Based on Polar Scissor Structures

Space-deployable mechanisms can be used as supporting structures for large-diameter antennas in space engineering.This study proposes a novel method for constructing the surface design of space reflector antennas based on polar scissor units.The concurrency and deployability equations of the space scissor unit with definite surface constraints are derived using the rod and vector methods.Constraint equations of the spatial transformation for space n-edge polar scissor units are summarized.A new closed-loop deployable structure,called the polar scissor deployable antenna(PSDA),is designed by combining planar polar scissor units with spatial polar scissor units.The overconstrained problem is solved by releasing the curve constraint that locates at the end-point of the planar scissor mechanism.Kinematics simulation and error analysis are performed.The results show that the PSDA can effectively fit the paraboloid of revolution.Finally,deployment experiments verify the validity and feasibility of the proposed design method,which provides a new idea for the construction of large space-reflector antennas.

Topology Structure Synthesis and Analysis of Spatial Pyramid Deployable Truss Structures for Satellite SAR Antenna

Many attentions for structural synthesis are paid to planar linkages and parallel mechanisms, while design novel pyramid deployable truss structure（PDTS） of satellite SAR mainly depends on experience of designer. To design novel configuration of PDTS, a two-step topology structure synthesis and analysis approach is proposed. Firstly, a conceptual configuration of PDTS is synthesized. Weighted graph and weighted adjacency matrix are established to realize topological description for PDTS. Graph properties are then summarized to distinguish differentia between PDTS and other type structures. According to graph properties, a procedure for synthesis conceptual configuration of PDTS is presented. Secondly, join relationship of components in a PDTS is analyzed. Kinematic chain and corresponding incidence/adjacency matrix are employed to analyze join relationship of PDTS. Properties and simplified rules of kinematic chain are extracted to construct kinematic chain. A procedure for construction kinematic chain of PDTS is then established. Finally, with this two-step approach all 11 rectangular pyramid deployable structures whose folded state is planar are discovered and their kinematic chains are constructed. Based on synthesis results, a novel deployable support structure for satellite SAR is designed. The proposed research can be applied to obtain some novel PDTSs, which is of great importance to design some novel deployable support structures for satellite SAR antenna.

Buckling analysis of planar linear uniform deployable structures consisting of scissor-like element in space under compression

This paper comprehensively investigates the buckling load and the stability of a planar linear array deployable structure composed of scissor-like element(SLE)under compression.At present,the researches on deployable structure are mainly focused on configuration design and dynamics characteristics of the mechanisms,but less on structural instability.In fact,when the external load exceeds the structural critical load value,the deployable structure will be permanently deformed or even collapse directly and no longer have any bearing capacity.To address this issue,a new stability model is derived using linear elastic analysis method and substructure method to evaluate the buckling characteristics of the deployable structure with n SLEs when it is carried out in space,which can accurately obtain the structural instability load and can be used quantitatively to optimize the structure for making it have the most stable configuration.In addition,the effects of the number of elements,the length,material properties and flexibility of the bar,and the deployment degree on the buckling of the scissor deployable structure are investigated,and the results of the theoretical analysis are compared with simulation and analytical results,respectively,confirming that the proposed stability model not only is able to effectively predict the structural instability load but also determine which part of the deployable structure is unstable.It can be concluded that the stability of the deployable structure gradually decreases with the increase of the number of elements or the bar flexibility.In the calculation process,the critical load of each sub-element should be considered,and the minimum value of the critical loads of all subunits can be regarded as the instability load of the whole structure.

Nonlinear Dynamics Analysis of Joint Dominated Space Deployable Truss Structures

Joints are necessary components in the larger space deployable truss structures which have significant effect on the dynamics behavior of these deployable joint-dominated structures. Four kinds of joints' nonlinear force-displacement relationship are analyzed based on describing function method. The dynamic responses of one-DOF jointed system under different exciting force levels are investigated to understand the influence of joint nonlinearity on dynamic responses. The influences of joint characterizing parameters on joint nonlinearities are analyzed. Dynamic responses of the modular beam-like deployable joint-dominated truss structure are tested under different sinusoidal exciting force levels. The experimental results show obvious nonlinear behaviors contributed by joints that dynamic response shifts to lower resonance frequency and higher amplitude with the increase of exciting force. The nonlinearity of the joints in the tested structure is compared with the theoretical results and identified to meet with the hysteresis nonlinearity.

A Shape-Memory Deployable Subsystem with a Large Folding Ratio in China’s Tianwen-1 Mars Exploration Mission

Once China’s Tianwen-1 Mars probe arrived in a Mars orbit after a seven-month flight in the deep cold space environment,it would be urgently necessary to monitor its state and the surrounding environment.To address this issue,we developed a flexible deployable subsystem based on shape memory polymer composites(SMPC-FDS)with a large folding ratio,which incorporates a camera and two temperature telemetry points for monitoring the local state of the Mars orbiter and the deep space environment.Here,we report on the development,testing,and successful application of the SMPC-FDS.Before reaching its Mars remote-sensing orbit,the SMPC-FDS is designed to be in a folded state with high stiffness;after reaching orbit,it is in a deployed state with a large envelope.The transition from the folded state to the deployed state is achieved by electrically heating the shape memory polymer composites(SMPCs);during this process,the camera on the SMPC-FDS can capture the local state of the orbiter from multiple angles.Moreover,temperature telemetry points on the SMPC-FDS provide feedback on the environment temperature and the temperature change of the SMPCs during the energization process.By simulating a Mars on-orbit space environment,the engineering reliability of the SMPC-FDS was comprehensively verified in terms of the material properties,structural dynamic performance,and thermal vacuum deployment feasibility.Since the launch of Tianwen-1 on 23 July 2020,scientific data on the temperature environment around Tianwen-1 has been successfully acquired from the telemetry points on the SMPCFDS,and the local state of the orbiter has been photographed in orbit,showing the national flag of China fixed on the orbiter.

Static analysis of synchronism deployable antenna

A 3D synchronism deployable antenna was designed, analyzed, and manufactured by our research group. This an-tenna consists of tetrahedral elements from central element. Because there are springs at the ends of some of the rods, spider joints are applied. For analysis purpose, the structure is simplified and modelled by using 2D beam elements that have no bending stiffness. Displacement vectors are defined to include two translational displacements and one torsional displacement. The stiff-ness matrix derived by this method is relatively simple and well defined. The analysis results generated by using software de-veloped by our research group agreed very well with available test data.

Effects of Joint on Dynamics of Space Deployable Structure

Joints are necessary components in large space deployable truss structures which have significant effects on dynamic behavior of these joint dominated structures.Previous researches usually analyzed effects of one or fewer joint characters on dynamics of jointed structures.Effects of joint stiffness,damping,location,number,clearance and contact stiffness on dynamics of jointed structures are systematically analyzed.Cantilever beam model containing linear joints is developed based on finite element method,influence of joint on natural frequencies and mode shapes of the jointed system are analyzed.Analytical results show that frequencies of jointed system decrease dramatically when peak mode shapes occur at joint locations,and there are cusp shapes present in mode shapes.System frequencies increase with joint damping increasing,there are different joint damping to achieve maximum system damping for different joint stiffness.Joint nonlinear force-displacement is described by describing function method,one-DOF model containing nonlinear joints is established to analyze joints freeplay and hysteresis nonlinearities.Analysis results show that nonlinear effects of freeplay and hysteresis make dynamic responses switch from one resonance frequency to another frequency when amplitude exceed demarcation values.Joint contact stiffness determine degree of system nonlinearity,while exciting force level,clearance and slipping force affect amplitude of dynamic response.Dynamic responses of joint dominated deployable truss structure under different sinusoidal exciting force levels are tested.The test results show obvious nonlinear behaviors contributed by joints,dynamic response shifts to lower frequency and higher amplitude as exciting force increasing.The test results are further compared with analytical results,and joint nonlinearity tested is coincident with hysteresis nonlinearity.Analysis method of joint effects on dynamic characteristics of jointed system is proposed,which can be used in optimal design of joint parameters to achieve optimum dynamic performance of jointed system.

Dynamic analysis and nonlinear identification of space deployable structure

The dynamic equivalent continuum modeling method of the mast which is based on energy equivalency principle was investigated. And three kinds of mast dynamic model were established, which were equivalent continuum model, finite element model and simulation model, respectively. The mast frequencies and mode shapes were calculated by these models and compared with each other. The error between the equivalent continuum model and the finite element model is less than 5% when the mast length is longer. Dynamic responses of the mast with different lengths are tested, the mode frequencies and mode shapes are compared with finite element model. The mode shapes match well with each other, while the frequencies tested by experiments are lower than the results of the finite element model, which reflects the joints lower the mast stiffness. The nonlinear dynamic characteristics are presented in the dynamic responses of the mast under different excitation force levels. The joint nonlinearities in the deployable mast are identified as nonlinear hysteresis contributed by the coulomb friction which soften the mast stiffness and lower the mast frequencies.

Deployment Dynamic Modeling and Driving Schemes for a Ring-Truss Deployable Antenna

Mesh reflector antennas are widely used in space tasks owing to their light weight,high surface accuracy,and large folding ratio.They are stowed during launch and then fully deployed in orbit to form a mesh reflector that transmits signals.Smooth deployment is essential for duty services;therefore,accurate and efficient dynamic modeling and analysis of the deployment process are essential.One major challenge is depicting time-varying resistance of the cable network and capturing the cable-truss coupling behavior during the deployment process.This paper proposes a general dynamic analysis methodology for cable-truss coupling.Considering the topological diversity and geometric nonlinearity,the cable network's equilibrium equation is derived,and an explicit expression of the time-varying tension of the boundary cables,which provides the main resistance in truss deployment,is obtained.The deployment dynamic model is established,which considers the coupling effect between the soft cables and deployable truss.The effects of the antenna's driving modes and parameters on the dynamic deployment performance were investigated.A scaled prototype was manufactured,and the deployment experiment was conducted to verify the accuracy of the proposed modeling method.The proposed methodology is suitable for general cable antennas with arbitrary topologies and parameters,providing theoretical guidance for the dynamic performance evaluation of antenna driving schemes.

A generalization of Kempe’s linkages

A new, general type of planar linkages is presented, which extends the classical linkages developed by Kempe consisting of two single-looped kinematic chains of linkages, interconnected by revolute hinges. Together with a locking device, these new linkages have only one degree of freedom (DOF), which makes them ideal for serving as deployable structures for different purposes. Here, we start with a fresh matrix method of analysis for double-loop planar linkages, using 2D transformation matrices and a new symbolic notation. Further inspection for one case of Kempe’s linkages is provided. Basing on the inspection, by means of some novel algebraic and geometric techniques, one particularly fascinating solution was found. Physical models were built to show that the derivation in this paper is valid and the new mechanisms are correct.

Computational dynamics of soft machines

Soft machine refers to a kind of mechanical system made of soft materials to complete sophisticated missions, such as handling a fragile object and crawling along a narrow tunnel corner, under low cost control and actuation. Hence, soft machines have raised great challenges to computational dynamics. In this review article, recent studies of the authors on the dynamic modeling, numerical simulation, and experimental validation of soft machines are summarized in the framework of multibody system dynamics. The dynamic modeling approaches are presented first for the geometric nonlinearities of coupled overall motions and large deformations of a soft component, the physical nonlinearities of a soft component made of hyperelastic or elastoplastic materials, and the frictional contacts/impacts of soft components, respectively. Then the computation approach is outlined for the dynamic simulation of soft machines governed by a set of differential-algebraic equations of very high dimensions, with an emphasis on the efficient computations of the nonlinear elastic force vector of finite elements. The validations of the proposed approaches are given via three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of a spacecraft, and the deployment of a mesh reflector of a satellite antenna, as well as the corresponding experimental studies. Finally, some remarks are made for future studies.

THEORETICAL STUDIES ON MICROBUCKLING MODE OF ELASTIC MEMORY COMPOSITES

Elastic memory composites （EMCs） have great potential applications in future deployable space structures due to their high packaging strain and shape memory characteristics. Microbuckling of compressed fibers is the primary deformation mechanism of such structures to receive a higher packaging strain than that of traditional fiber-reinforced composites. In order to have a better understanding of such deformation mechanism, the microbuckling model of EMC laminates under bending is analyzed firstly. Then the theoretical critical microbuckling parameters are predicted, which are compared with experimental observations and other models.

Design of a Light, Foldable and Flexibility Lunar Base

In this paper, to meet the environmental requirements for the lunar surface, we outline the design of an intelligent shape memory polymer(SMP) capsule structure of lightweight using a flexible composite skin. Key breakthrough technology for manufacturing the high-performance multilayer composite is utilized to realize the requirements for folding and compressing during launching, and unfolding on the lunar surface, taking into account the current opposing requirements for launching and the space transportation mission of large equipment. Based upon the reduced constraints, better expansibility and easy assembly, this lunar base is suited to the initial and interim phases of a moon construction, and provides a national solution in the construction of lunar base on moon.

Deployment analysis of composite thin-walled lenticular tubes with effect of storage time and temperature

Composite Thin-walled Lenticular Tube(CTLT)is increasingly utilized in small satellites missions as a lightweight,foldable,and rollable structural material that facilitates the construction of large deployable systems.The CTLT is initially flattened and coiled around a central hub for storage before launch,during which elastic energy is stored as deformation energy,allowing it to be self-deployed on demand for use in orbit.This work presents a comprehensive investigation into the coiling,storage and deployment behaviors of CTLT that wraps around a central hub.A nonlinear explicit dynamic finite element model was developed with both deformable CTLT and rigidbodies mechanisms including the central hub and guide rollers,as well as the complex interactions among them.The coiling mechanics characteristics such as stored strain energy and rotational moment were presented and validated against experimental data in the literature.Then,the dynamic deployment behaviors were analyzed in terms of two different deployment methods,namely,controlled deployment and free deployment.The effect of material property change during storage was also discussed through numerical experiments.

Preliminary design and analysis of a cubic deployable support structure based on shape memory polymer composite

The deployable structures based on shape memory polymer com-posites(SMPCs)have been developed for its unique properties,such as high reliability,low-cost,lightweight,and self-deployment without complex mechanical devices compared with traditional deployable structures.In order to increase the inflatable structure system’s robustness and light the weight of it,a cubic deployable support structure based on SMPC is designed and analyzed pre-liminarily.The cubic deployable support structure based on SMPC consists of four dependent spatial cages,each spatial cage is composed of 12 three-longeron SMPC truss booms and end con-nections.The shape recovery of arc-shaped deployable laminates drive the three-longeron SMPC truss booms to unfold,thus realize the expansion of the deployable support structure.The concept and operation of the cubic deployable support structure are described in detail.A series of experiments are performed on the three-longeron deployable laminates unit and the simplified cubic deployable support structure to investigate the shape recovery behavior in the deployment process.Results indicate that the cubic deployable support structure has a high deployment-tgo-stowage volume ratio and can achieve self-deployment,package,and deploy without complex mechanical devices.

Techniques for Determining the Geographic Location of IP Addresses in ISP Topology Measurement

A brief survey on the state-of-the-art research of determining geographic location of IP addresses is presented. The problem of determining the geographic location of routers in Internet Service Provider （ISP） topology measurement is discussed when there is inadequate information such as domain names that could be used. Nine empirical inference rules are provided, and they are respectively （1） rule of mutual inference, （2） rule of locality, （3） rule of ping-pong assignment, （4） rule of bounding from both sides, （5） rule of preferential exit deny, （6） rule of uureachable/timeout, （7） rule of relay hop assignment, （8） rule of following majority, and （9） rule of validity checking based on interface-finding. In totally 2,563 discovered router interfaces of a national ISP topology, only 6.4% of them can be located by their corresponding domain names. In contrast, after exercising these nine empirical inference rules, 38% of them have been located. Two methods have mainly been employed to evaluate the effectiveness of these inference rules. One is to compare the measured topology graph with the graph published by the corresponding ISP. The other is to contact the administrator of the corresponding ISP for the verification of IP address locations of some key routers. The conformity between the locations inferred by the rules and those determined by domain names as well as those determined by whois information is also examined. Experimental results show that these empirical inference rules play an important role in determining the geographic location of routers in ISP topology measurement.