# Design and Manufacture of Composite Landing Gear for a Light Unmanned Aerial Vehicle
## 3 Static Structure Analysis of Landing Gear  
The strength and weight are the major considerations for the UAV landing gear. In this study, simulations of the layered CFRP were performed using static structure analysis of Ansys Composite Pre-Post (ACP). The material properties are as follows: [PERSON]'s modulus, E1 = 160.8 GPa and E2 = 11.9 GPa; [PERSON]'s ratio, \(\
u\) = 0.326; shear modulus, G = 6.8 GPa; density, \(\rho\) = 1530 kg/m3; and yield stress, E3 = 650 MPa. The formula used in ACP comes from the stress-strain relations for a lamina of arbitrary orientation, as shown in Figure 5. The transformation equations for stresses in an x-y coordinate system in terms of stresses in a 1-2 coordinates system are:  
\[\left\{ \begin{array}{c}\sigma_{xx}\\ \sigma_{yy}\\ \tau_{xy}\end{array} \right\}=\left[ \begin{array}{ccc}cos^{2}\theta&sin^{2} \theta&-2 sin\theta cos\theta\\ sin^{2}\theta&cos^{2}\theta&2 sin\theta cos\theta\\ sin\theta cos\theta&-sin\theta cos\theta&cos^{2}\theta-sin^{2}\theta\end{array}  \right]\left\{ \begin{array}{c}\sigma_{11}\\ \sigma_{22}\\ \tau_{12}\end{array} \right\}=\left[T\right]^{-1}\left\{ \begin{array}{c} \sigma_{11}\\ \sigma_{22}\\ \tau_{12}\end{array} \right\} \tag{1}\]  
where \(\theta\) is the rotational angle from the \(x\)-axis to the 1-axis. The strain transformation equations are:  
\[\left\{ \begin{array}{c}\epsilon_{xx}\\ \epsilon_{yy}\\ \frac{\gamma_{yy}}{2}\end{array} \right\}=\left[T\right]^{-1}\left\{ \begin{array} []{c}\epsilon_{11}\\ \epsilon_{22}\\ \frac{\gamma_{12}}{2}\end{array} \right\} \tag{2}\]  
The stress-strain relationships of composite materials in principal orientation are:  
\[\left\{ \begin{array}{c}\sigma_{11}\\ \sigma_{22}\\ \tau_{12}\end{array} \right\}=\left[ \begin{array}{ccc}Q_{11}&Q_{12}&Q_{16}\\ Q_{12}&Q_{22}&Q_{26}\\ Q_{16}&Q_{26}&Q_{66}\end{array} \right]\left\{ \begin{array}{c}\epsilon_{1 1}\\ \epsilon_{22}\\ \tau_{12}\end{array} \right\}=\left[Q\right]\left\{ \begin{array}{c}\epsilon_ {11}\\ \epsilon_{22}\\ \tau_{12}\end{array} \right\} \tag{3}\]  
where \(Q_{ij}\) is the reduced stiffness in terms of the material properties, \(E_{i}\) is the [PERSON]'s modulus, and \(\
u_{ij}\) is [PERSON]'s ratio. The stress-strain relationships of composite materials in an x-y coordinate system are obtained by using Equations (1)-(3), as follows. \[\left\{ \begin{array}{c}\sigma_{xx}\\ \sigma_{yy}\\ \tau_{xy}\end{array} \right\}=\left[T\right]^{-1}\left[Q\right]\left[T\right]^ {-T}\left\{ \begin{array}{c}\epsilon_{xx}\\ \epsilon_{yy}\\ \gamma_{xy}\end{array} \right\}=\left[ \begin{array}{ccc}\overline{Q}_{11}& \overline{Q}_{12}&\overline{Q}_{16}\\ \overline{Q}_{12}&\overline{Q}_{22}&\overline{Q}_{26}\\ \overline{Q}_{16}&\overline{Q}_{26}&\overline{Q}_{66}\end{array} \right]\left\{ \begin{array}{c}\epsilon_{xx}\\ \epsilon_{yy}\\ \tau_{xy}\end{array} \right\} \tag{4}\]  
where \(\overline{Q}_{ij}\) denotes the transformed reduced stiffness instead of the reduced stiffness \(Q_{ij}\). In the ACP program, the natural coordinate system of the landing gear, the material properties, and the fiber principal direction of CFRP in each layer are defined and given. To simulate landing, a load is applied vertically using the MTS and the ends of the landing gear are fixed by jigs supported by the MTS in the experiments. The boundary conditions are as follows: (1) fixed support at the two ends and (2) 150-N vertical load at the upper center surface of the landing gear. Figure 5: Positive rotation of principal material axes (1–2 axes) from arbitrary x–y axes. In general, the yield stress of a composite material depends on its constituent fiber and matrix base. Additives and/or processing methods influence the yield stress. For example, the yield stresses of composites with steel, aluminum alloy, and magnesium alloy are 300-1100, 250-550, and 160-210 MPa, respectively. Table 2 shows the principal stresses for the CFRP landing gear designs with 8, 10, and 12 layers.