Problem $4\mathrm{.}2$

Consider a five$-$node element in one dimension. The element length is $4,$ with node $1$ at $x=2,$ and the

remaining nodes are equally spaced along the $x-$axis.

a$.$ Construct the shape functions for the element.

b$.$ The temperatures at the nodes are given by $T_1=3C,T_2=1C,T_3=0C,T_4=-1C,T_5=2C.$

Find the temperature field at $x=3\mathrm{.}5$ using shape functions constructed in $($a$).$