Q$3)(20$ points$)$ The wedge and semi$-$infinite domain are shown in Figure $1.$ The two boundaries are defined by the lines $=$ and $=.$ The Airy stress function is chosen as:

$=r^2(a_2+a_6+a_{21}cos2+b_{21}sin2)$

where $a_2,a_6,a_{21},b_{21}$ are constants.

$($a$)$ Determine the stresses ${}_{rr},{}_{}$ and ${}_r(12$ points$)$

$($b$)$ A specific case of a quarter plane in which $(=0$ and $=\frac{}{2})$ with a uniform shear stress $S$ along one boundary $($y$-$axis$)$ and no loading on the other boundary is shown in Figure $2.$ Write the boundary conditions for this quarter plane in and compute the constants $a_2,a_6,a_{21},b_{21}(18$ points$).$