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Given the following fiber-matrix uni-directional ply material, calculate the homogenous orthotropic compliance [S], orthotropic stiffness [C], orthotropic plan stress compliance [S'], and orthotropic plane stiffness [Q] matrices. Please show your step-by-step calculations and equations used. Do not use any software, i.e. Excel for the calculations. \[ \begin{array}{l} E_{l}=154 \mathrm{GPa} \\ E_{2}=9 \mathrm{GPa} \\ v_{12}=v_{l 3}=0.312 \\ v_{23}=0.260 \\ G_{12}=G_{12}=5 \mathrm{GPa} \\ G_{23}=3.6 \mathrm{GPa} \end{array} \]

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