Linear Elastic Tape Spring Modeling

With the use of deployable space structures growing in popularity, along with the complexity and high costs associated with experimental testing of these deployables, the demand for finite element simulations soon became apparent. Early models of deployable tape springs, even those simulating composites, were often defined as linear elastic for simplicity. One such model came from a theoretical investigation of tape springs composed of an unspecified linear elastic material (Seffen, 2001). The study considered the quasi- static moment-rotation response that occurs during an opposite-sense fold using a finite element analysis in Abaqus. An opposite-sense fold was defined as one in which the longitudinal curvature formed by the fold is in a sense opposite of the natural transverse curvature of the tape spring. Conversely, an equal-sense fold is one in which the longitudinal curvature formed by the fold is in the same sense as the natural transverse curvature of the tape spring. The fold was achieved by applied end couples at each free end of the tape spring. Then a force was applied to push the two ends toward each other. Findings showed that stretching effects in the tape spring were minor compared to bending effects, the transverse curvature throughout the fold region was zero, and if unbalanced loads were applied to the ends of the tape spring, the fold region would travel along the length of the tape spring (Seffen, 2001).

Finite element analysis of CFRP tape springs using Abaqus software included foldable composite structures consisting of a hollow tube with tape spring hinges at its midsection (Yee and Pellegrino, 2003). The hinges were created by cutting three parallel slots into the tube at the desired folding location, and a single tape spring from the tube hinge was modeled in opposite sense bending. The CFRP tube was fabricated using one or

two plies at an orientation of ±45°. The material was assumed to be linear elastic. Principal strains and shear strains were investigated on the tape spring surface under opposite- and equal-sense bending throughout the bending process for each of the three tape springs made up of one and two plies. The findings showed that for one ply the maximum fiber strain was barely within the material limits, but for two plies it was well-exceeding the limits (Yee and Pellegrino, 2003).

The correction capacity of a deployable tape spring hexapod composed of six rolled steel tape springs was studied using linear elastic finite element modeling and experimental testing (Aridon et al., 2008). The experimental setup of the hexapod prototype was used to measure the tape springs’ natural frequencies. Accurate deployment positioning was achieved by eliminating a degree of freedom at the upper junction and by using thicker blades (Aridon et al., 2008).

A finite element analysis of CFRP tape springs was developed to include deployment in addition to folding of two-ply ±45° plain weave slot-tube tape spring hinges with two slots (Mallikarachchi and Pellegrino, 2008). The quasi-static finite element model depicted the folding and deployment behavior of the slot-tube hinges. The model assumed a linear elastic material. Moment versus deployment angle were compared between experiment and model to validate the model (Mallikarachchi and Pellegrino, 2008).

A two-ply plain weave CFRP two-slotted tube tape spring hinge was studied using an experimental setup consisting of a CFRP tape spring hinge connected to an aluminum tube (Mallikarachchi and Pellegrino, 2009). The dynamic deployment finite element simulation was verified experimentally to examine deployment angle versus deployment time. The model was used to investigate the margin of safety for fiber failure by finding

the five configurations with the largest mid-plane strain and identifying two critical failure regions for each. The model results showed that although the boom latched immediately following deployment in the gravity simulation, it took four oscillations to latch in the zero- gravity simulation (Mallikarachchi and Pellegrino, 2009).

The design of a one-meter-long boom intended to be folded to encircle a spacecraft was made of two plies of plain weave CFRP (Mallikarachchi and Pellegrino, 2011b). Finite element simulations examined the stowage and deployment behavior and were experimentally validated. Concern was expressed over the harmful dynamic effects upon deployment completion that could potentially damage the tape spring, while on the other hand, slow, significantly damped deployment could stall the tape spring before achieving a completely deployed configuration. Thermal and viscoelastic effects were not taken into account in the simulation (Mallikarachchi and Pellegrino, 2011b).

An experimental and numerical study of a two-ply ±45° plain weave CFRP tape spring hinge in folding and deployment was performed using a quasi-static finite element model, which did not include viscoelastic effects (Mallikarachchi and Pellegrino, 2011c). The simulation began with a micromechanical model of the woven laminate, and it resulted in an overestimated snapback, overestimated rotation angle, and underestimated deployment-moment average, possibly due to the lack of viscoelasticity included in the model, as well as experimental tow misalignment and deadband effects in the machine (Mallikarachchi and Pellegrino, 2011c).

Two bistable CFRP tape springs were simulated (one twill and one plain weave) as simplified unit cells (Prigent et al., 2011). In plain weave fabric, odd bundles of fibers pass over one and under one of the perpendicular bundles, while in twill, odd bundles of fibers

pass over two and under one perpendicular bundle. The finite element simulation was based on a unit cell model to more accurately simulate bending, but it did not simulate creep, sensitivity to low temperatures, or deployment friction (Prigent et al., 2011).

Ultrathin two-slot booms incorporating tape spring hinges composed of two plies of plain weave CFRP were also studied (Mallikarachchi and Pellegrino, 2014a). Deployment experiments indicated that the initial deployment and vibration behaviors were repeatable, but the latching behavior contained noticeable scatter. Quasi-static finite element simulations of folding and deployment were produced to compare deployment, latching attempts, and vibration to that of the experiment. Viscoelasticity, air drag, and acoustic emissions were not investigated (Mallikarachchi and Pellegrino, 2014a).