$2.$ A displacement field in a titanium structure is given by: u $=($x $^2+10)(10^4),$ v $=2$yz$(10^-4),$ w $=(-$ x $*$ y $+$ z $^3)(10^4)$

$($SI units$)$

$($a$)$ Check if the above displacement fields are compatible. Knowing that for titanium, G $=48$ GPa and v $=0\mathrm{.}33$ determine the $($b$)$ state of strain and $($c$)$ state of stress at the point P $(2,2,0).$