Express the isotropic moduli (tilde{E}) and (tilde{G}) of a randomly oriented fiber composite in Equations 6.43 in

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Express the isotropic moduli \(\tilde{E}\) and \(\tilde{G}\) of a randomly oriented fiber composite in Equations 6.43 in terms of the orthotropic lamina stiffnesses \(Q_{i j}\).

\(\begin{aligned}
& \tilde{E}=\frac{\left(U_1-U_4\right)\left(U_1+U_4\right)}{U_1} \\
& \tilde{G}=\frac{U_1-U_4}{2} \\
& \tilde{\mathrm{v}}=\frac{U_4}{U_1}
\end{aligned} \tag{6.43}\)

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