# Parametric Study of a Composite Skin for a Twist-Morphing Wing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Description

## 3. Torsional Compliance Study

^{2}, ${N}_{L}$ = 2, and α = 0°. The mesh convergence plot can be seen in Figure 5b. The mesh with 22,000 elements was utilized. This corresponds to an element size of 1.346 mm, which was used for all configurations.

#### 3.1. Effects of ${N}_{es}$, β and ${K}_{el}$

#### 3.2. Effect of α

^{2}. Figure 8a shows α-β sweep for ${N}_{es}$ = 10, whereas Figure 8b shows α-${N}_{es}$ sweep for β = 70%. The trends at different constant values of ${N}_{es}$ or β are almost identical to the plots in Figure 8a,b, respectively. It is very interesting to see that in the α axis, there is a dip in the structural compliance that occurs when the fiber-orientation angle of the Twistkins’ plies is 30°. This indicates that the fibers are aligned with the maximum applied stresses in this orientation and the skin is at its stiffest. On the other hand, the skin is most compliant at an α of 90°. As was shown before, when β increases, C also increases linearly, and as ${N}_{es}$ increases, C decreases exponentially. This holds true for all values of α.

#### 3.3. Effect of ${N}_{L}$

^{2}, respectively, while ${N}_{L}$ is swept, along with β in Figure 9a and ${N}_{es}$ in Figure 9b. The trends of the ${N}_{L}$-β and ${N}_{L}$-${N}_{es}$ sweeps are the same at different values of ${N}_{es}$ and β, respectively. Increasing the number of plies exponentially decreases C. The figures continue to show the linear increase and exponential decrease of C with an increase in β and ${N}_{es}$, respectively. One additional ply in the Twistkin laminate can dramatically increase the torsional stiffness of the whole skin.

## 4. Out-of-Plane Stiffness Study

#### 4.1. CFD Model

^{3}, dynamic viscosity of ${\mu}_{\infty}$ = 1.7894 × 10

^{−5}kg/m-s, ambient pressure of 101.3 kPa, and ambient temperature of 15 °C. This gives a Reynolds number of approximately Re = 215,600. These are typical flying conditions for UAVs [6]. A standard k-ε turbulence model within ANSYS Fluent was used in CFD simulations on a 2D airfoil at different angles of attack (AOAs). This is a Reynolds-Average Navier-Stokes (RANS) based model which solves the ensemble-average Navier-Stokes equations. The standard k-ε model is a commonly used turbulence model, as it is reasonably accurate and requires less computational power when compared to other models such as the realizable k-ε, standard k-ω, or SST k-ω models. The maximum lift for the NACA 0012 airfoil occurs at 12°, which was confirmed by Airfoil Tools at a similar Re of 200,000 [29]. The largest pressure load occurs at an AOA of 12°, hence the corresponding load was considered in the structural analysis. In order to use the pressure data points from the CFD study into the FEA study, rational function models were used to obtain curve fits. Figure 10 shows the pressure data on the top and bottom sides of the airfoil at an AOA of 12° along with the curve fits. The top curve fit (${P}_{12T}$) and the bottom curve fit (${P}_{12B}$) are expressed as:

#### 4.2. FEA Models

^{2}, α = 0°, and ${N}_{L}$ = 2. The reference and total displacements recorded from the simulation can be seen in Figure 13a. Subtracting the reference displacement from the total displacement gives the “load displacement” plot, shown in Figure 13b. The maximum load displacement ratio occurs near the leading edge, which is where the greatest pressure loads are applied at a 12° angle of twist.

#### 4.3. Effects of ${N}_{es}$, β, and ${K}_{el}$ on the Elastomeric Section’s Displacement Ratio

#### 4.4. Effects of α and ${N}_{L}$ on the Twistkin’s Displacement Ratio

_{L}= 2 to N

_{L}= 3. The same out-of-plane stiffness obtained with 5 plies of 90° fiber-orientation angle, can be obtained with only two 0° plies. The effect of α is enhanced at lower values of ${N}_{L}$, and the effect of ${N}_{L}$ is enhanced at higher fiber-orientation angles.

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Model of a UAV with a twist-morphing wing, (

**b**) Dimensions of the twisting section featuring CFRP “Twistkins” (grey) and elastomeric sections (blue).

**Figure 3.**Twisting section without the flexible sections at (

**a**) φ = 0° and (

**b**) φ = 12°. First Twistkin (blue) is attached to the fixed section while the last Twistkin (red) is attached to the rotating spar (red).

**Figure 4.**Different model configurations with (

**a**) ${N}_{es}$ = 5 and β = 40%, (

**b**) ${N}_{es}$ = 5 and β = 100%, (

**c**) ${N}_{es}$ = 15 and β = 40%, and (

**d**) ${N}_{es}$= 15 and β = 100%.

**Figure 5.**(

**a**) Torsional compliance study model with two CFRP Twistkins and one elastomeric section, (

**b**) Mesh convergence plot.

**Figure 6.**Torsional compliance sweeping ${N}_{es}$ and β for (

**a**) ${K}_{el}$ = 16 N-m

^{2}, (

**b**) ${K}_{el}$ = 73 N-m

^{2}, (

**c**) ${K}_{el}$ = 134 N-m

^{2}.

**Figure 7.**Torsional compliance sweeping (

**a**) ${K}_{el}$ and β for ${N}_{es}$ = 5, (

**b**) ${K}_{el}$ and ${N}_{es}$ for β = 100%.

**Figure 8.**Torsional compliance sweeping (

**a**) α and β for ${N}_{es}$ = 10, (

**b**) α and ${N}_{es}$ for β = 70°.

**Figure 9.**Torsional compliance sweeping (

**a**) ${N}_{L}$ and β for ${N}_{es}$ = 10, (

**b**) ${N}_{L}$ and ${N}_{es}$ for β = 70%.

**Figure 11.**Out-of-plane stiffness model with (

**a**) two Twistkins (grey) and one elastomeric section (blue) at loads corresponding to φ = 12°. (

**b**) one Twistkin.

**Figure 12.**Example of total displacement ( ${N}_{es}$ = 5, β = 100%, ${K}_{el}$ = 16 N-m

^{2}, α = 0°, and ${N}_{L}$ = 2).

**Figure 14.**(

**a**) Total displacement of CFRP Twistkin, (

**b**) Displacement ratio at both edges of the CFRP Twistkin.

**Figure 15.**Maximum displacement ratio for the elastomeric section sweeping ${N}_{es}$ and β for (

**a**) ${K}_{el}$ = 16 N-m

^{2}, (

**b**) ${K}_{el}$ = 73 N-m

^{2}, (

**c**) ${K}_{el}$ = 134 N-m

^{2}.

**Figure 16.**Maximum displacement ratio for the elastomeric section sweeping (

**a**) ${K}_{el}$ and β for ${N}_{es}$ = 5, (

**b**) ${K}_{el}$ and ${N}_{es}$ for β = 100%.

**Figure 17.**Displacement ratios sweeping (

**a**) ${w}_{s}$ and α, (

**b**) ${N}_{L}$ and α, for the left edge.

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**MDPI and ACS Style**

Bishay, P.L.; Aguilar, C.
Parametric Study of a Composite Skin for a Twist-Morphing Wing. *Aerospace* **2021**, *8*, 259.
https://doi.org/10.3390/aerospace8090259

**AMA Style**

Bishay PL, Aguilar C.
Parametric Study of a Composite Skin for a Twist-Morphing Wing. *Aerospace*. 2021; 8(9):259.
https://doi.org/10.3390/aerospace8090259

**Chicago/Turabian Style**

Bishay, Peter L., and Christian Aguilar.
2021. "Parametric Study of a Composite Skin for a Twist-Morphing Wing" *Aerospace* 8, no. 9: 259.
https://doi.org/10.3390/aerospace8090259