Consider a rectangular composite panel with fibers at angle $.$

$($a$)$ For the panel subjected to stresses ${}_{}$ and ${}_{yy},$ find what shear stress ${}_{xy}$ should be applied in order to keep the deformed panel shape rectangular $($i$.$e$.,{}_{xy}=0).$ Give results symbolically in terms of $\frac{?}{\text{b}\text{a}\text{r}}(S{)}_{ij}.$

$($b$)$ Numerical calc: for $=45$ and properties $E_1=140$GPa,$E_2=10$GPa,$G_{12}=7$GPa,$v_{12}=0\mathrm{.}3,$ and for stresses ${}_{}=20$MPa and ${}_{yy}=-5$MPa, calculate a value for ${}_{xy}.$ Answ. $6\mathrm{.}25$ MPa

$($c$)$ For this global stress state, report the global strain state. Does it satisfy the problem constraints $($i$.$e$.,$ remains rectangular$)?$

Find ${}_{yy}=-7\mathrm{.}97e-4$