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

ABSTRACT The deployable structures based on shape memory polymer composites (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 preliminarily. 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 connections. 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.

In the early of the twenty-first century, the space inflatable structure is one of the emerging enabling technologies for space applications because inflatable structures are lightweight and have a small packing volume [28][29][30][31]. It can potentially revolutionize the designs and applications of large space structural systems. Currently existing deployment approaches of large space structures typically rely upon electromechanical mechanisms, which ensure them to unfold and maintain the fully deployed, operational configuration [32]. For traditional inflatable structures, these support structures and their associated deployment mechanisms, launch restraints and controls, comprise more than 90% of the total mass budget for a deployed assembly [33,34]. In order to light the weight and reduce the mechanical complexity of the inflatable structure system, we have designed and analyzed a cubic deployable support structure based on SMPC preliminarily. The cubic deployable support structure performs high packaging efficiency for launch, self-deployment without complex mechanical devices and can improve the robustness of the inflatable structure system.

Dynamic mechanical analysis test
In this study, a type of carbon fiber-reinforced epoxy-based SMPC is chosen as the primary material. The matrix used in this work is epoxy-SMP proceed by Leng's research group [11]. The SMPC is fabricated by the hand molding technique for fiber-reinforced composite materials and the reinforcement is four plies carbon plain fabric. Dynamic mechanical analysis tests are carried out to investigate the basic thermo-mechanical performances of the SMP and SMPC. The test mode is tension. The scanning range of temperature is 20~180 o C at a heating rate of 2 o C= min and a frequency of 1 Hz. The dimensions of specimens are 18 mm × 2 mm × 3 mm. The results of the DMA tests are presented in Figure 1.
The peak value of tangent delta is defined as the glass transition temperature (T g ). The glass transition temperature of epoxy-SMP is about 96.2°C as indicated in Figure 1 (a). The storage modulus of epoxy-SMP is 2.03 GPa at 20°C. With the increasing of temperature, storage modulus decreases from 2 GPa to 15 MPa (100°C) due to the phase transition. Figure 1(b) shows that the T g of SMPC fabricated in this study is 100.2 o C. The storage modulus of SMPC is about 7 GPa at 20 o C; and it decreases from 6 GPa to 1 GPa precipitously within the region of 60~100 o C, when the temperature above 100 o C, the SMPC's matrix turns to viscoelastic state, the storage modulus is about 0.5 GPa.

Design of the cubic deployable support structure
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 connections, as shown in Figure 2. The three-longeron SMPC truss boom is the main component of the structure; it consists of one extendable central bracket, arc-shaped deployable laminates, and connectors. The extendable central bracket is made up of sleeves. Three arc-shaped deployable laminates with an angle of 120 o to each other can be treated as one cell (as shown in Figure 2(b)) and every cell is connected by connectors. A resistor heater is stuck to the surface of every arc-shaped deployable laminate. The arc-shaped deployable laminates are the longerons of the SMPC truss boom, which are packaged into an 'V-shape' first; when the resistor heaters are electrified, the laminates gradually deploy with increasing time. The laminates provide the deployable driving force and undergo the tip payloads at the end of deployment. Once the deployment is done, the three-longeron SMPC truss booms will form a tubular-shaped boom. Here are the two ways of deploying, one is the SMPC truss booms in all three orthotropic directions deploy simultaneously, which can save time (as shown in Figure 3); the other is the SMPC truss booms in the same direction deploy simultaneously, when the deployment in one direction finishes, the next deployment of different direction starts. The time of second way would be longer, but it can reduce the incoordination possibility in deployment process.
For the requirements of different deployment-to-stowage volume ratio of the cubic deployable support structure, it can be realized by changing the size of three-longeron  SMPC truss boom. Also, the changes of sleeves, arc-shaped deployable laminates' geometry parameters, and the angle between the two adjacent arc-shaped deployable laminates can meet the specific requirements of the three-longeron SMPC truss boom.

Manufacture of the deployable structure
For verifying the feasibility of the cubic deployable support structure, we manufactured a simplified one. The simplified structure has one cage, which comprises 12 threelongeron deployable laminates units. The deployed three-longeron deployable laminates unit (as shown in Figure 2(b)) consists of three arc-shaped deployable laminates, two connectors, and two sleeves. Figure 4 shows the components of the structure, the arc-shaped deployable laminate is made of carbon fiber-reinforced SMPC, the extendable central bracket is made of aluminum alloy sleeve, the connector, and end connection are made of acrylic board. Figure 5 presents the simplified structure.

Experiment
In the cubic deployable support structure based on SMPC, the basic effective unit is three-longeron deployable laminates unit whose properties reflect the characteristics of the whole structure. Two experiments of the three-longeron deployable laminates are carried out to test its recovery properties. One experiment of the simplified cubic deployable support structure is done to test its recovery feasibility. The parameters of the arc-shaped deployable laminate used in the experiment are: length 300 mm, outer radius 25 mm, inner radius 23 mm, thickness 2 mm, arc angle 120°, carbon fiberreinforced epoxy-based SMPC, the four ply carbon fiber orientation is 0°/90°/0°/90°.

Experiment of three-longeron deployable laminates unit bending recovery
In this experiment, laser rangefinder equipment is used to measure the displacement of the three-longeron deployable laminates unit in deployment process (as shown in Figure 6). The experimental method is as follows: First, stick one resistor heater to the inside surface of the arc-shaped deployable laminate, use a high temperature furnace (the temperature is above the T g ) to heat the arc-shaped deployable laminate until it soften, bend the arc-shaped deployable laminate to 180°along the shortest center line. Second, assemble the three-longeron deployable laminates with three bent arc-shaped deployable laminates and two connectors, then fix one end of it, the other end fixed a level paper baffle (light) for laser ranging (as shown in Figure 6(a)). Third, put the laser rangefinder above the three-longeron deployable laminates unit, measure the initial distance between level paper baffle and laser rangefinder, clear the instrument reading to zero. Finally, electrify the resistor heaters simultaneously; the actual output voltage is 40 V. The resistor heaters heat the arc-shaped deployable laminates and the three-  longeron deployable laminates unit begins to shape recovery automatically. The laser rangefinder records the displacement data and sends it to the computer to obtain experimental data. The deployment time-displacement curve ( Figure 7) and the deployment timevelocity curve (Figure 8) are obtained. Figures 7 and 8 indicate that the displacement and velocity are almost zero before 30 s, because there is a preheating process at the beginning; then after the temperature above T g , the arc-shaped deployable laminates begin recovering, the displacement curve increases linearly, and the velocity reaches the maximum 4.66 mm=s at about 80 s; with the deployment towards to the end, the displacement curve upward trend becomes slower, the velocity curve has a small peak before the end which means there is a sudden speed, the reason is the bended arcshaped deployable laminate has buckling deformation and the geometry shape recover  after deployment. Although there is a small impact, the whole process of deployment is stable.
According to the existing three-longeron deployable laminates unit's deployment time-displacement data, we obtain the relationship of the arc-shaped deployable laminate's deployment time and deployment angle (Figure 9), deployment time and angular velocity ( Figure 10). From Figures 7 and 9, it can be seen that the tendency of deployment time-deployment angle curve is similar to the deployment time-displacement curve. At the beginning, the curves of deployment time-deployment angle and deployment time-angular velocity increase slowly; after 60 s, the deployment angle increases linearly, the angular velocity reaches the maximum about 2.08 o =s; in the end, there is sudden angular velocity, the reason is the same as in the deployment time-velocity curve.

Experiment of three-longeron deployable laminates unit bending recovery force
Since it is difficult to measure a single arc-shaped deployable laminate's recovery force and the basic effective unit is three-longeron deployable laminates unit whose main consideration is the axial thrust, we propose the method: measure the maximum vertical load of the three-longeron deployable laminates unit, with the load the three-longeron deployable laminates unit can deploy fully, to get the bending recovery force (as shown in Figure 11). The detailed experiment method is as follows: assemble a three-longeron deployable laminates unit, place it vertically and fix one end of it, load weights on the other end, get the maximum vertical load with which the three-longeron deployable laminates unit can deploy successfully. The experiment result is that the three-longeron deployable laminates unit's maximum vertical load is about 8.5 N. Considering the rough experiment design, the result of the experiment is just a reference value.

Experiment of the simplified cubic deployable support structure's recovery feasibility
In order to verify the feasibility of the cubic deployable support structure and the synchronization of parallel three-longeron deployable laminates units, a test of the simplified cubic deployable support structure's recovery feasibility is carried out. Considering the support structure is symmetric and the deployment process of every direction is same, we select the maximum load direction (vertical), three-longeron deployable laminates units of three different directions deployed one after another. The average weight of every three-longeron deployable laminates unit is about 8.37 N.
Stick the resistor heaters to the inside surfaces of the arc-shaped deployable laminates, bend them to 180°along the shortest center line; assemble the simplified cubic deployable support structure with three-longeron deployable laminates units and end connections; electrify the resistor heaters of the same direction three-longeron deployable laminates units simultaneously; shoot the video of the whole deployment process. Figure 12 shows the deployment process of every direction. Figure 11. Experiment of three-longeron deployable laminates unit bending recovery force.
The result of the experiment (as shown in Table 1) is that the spatial parallel three-longeron deployable laminates units deploy simultaneously. The process is similar to the single threelongeron deployable laminates unit's. The average time of deploying is 465 s, because the average load-bearing of every three-longeron deployable laminates unit is 8.37 N.

Conclusion
In this article, a cubic deployable support structure, which can realize self-deployment without complex mechanical devices, is introduced. The primary component of the  structure is arc-shaped deployable laminate based on SMPC, the deformed arc-shaped laminate recovers to its original shape when heated, thus it can drive the folded structure to expand. The three-longeron deployable laminates unit's bending recovery regularity is slow-fast-slow, because there is a preheating process of resistor heater and the bending recovery force is small when the shape recovery is almost done. The maximum of three-longeron deployable laminates unit recovery force is about 8.5 N. The simplified cubic deployable support structure can self-deploy successfully and the average deployment time in every direction is 465 s. This study is one of the explorations of SMPs and SMPCs in large-scale deployable structures and can provide some preliminary reference for SMPCs-based deployable structures in future aerospace applications.