Consider the five$-$node plane strain isoparametric element shown.

$($a$)$ Evaluate appropriate interpolation functions $h_i,i=1$ to $5.$

$($b$)$ Evaluate the column in the strain$-$displacement matrix corresponding to the displacement $u_1$ at the point $x=2\mathrm{.}5,y=2\mathrm{.}5.$