$2\mathrm{.}31$ For a particular plane strain problem the strain$-$displacement equations in cylindrical co$-$ordinates

$(r,,z)$ are ${}_r=d\frac{w}{d}r,{}_{}=\frac{u}{r},{}_z={}_r={}_{}={}_{zr}=0.$ Show that the appropriate compatibility equation

in terms of stress is $rvd\frac{{}_r}{d}$rcdotsr$(1-v)d\frac{{}_{}}{d}r+{}_r$cdots${}_{}=0.$ State the nature of a problem represented

by the above equations. $($CEI$)$