Problem $N^{0}1.$:$(6pts)$

Consider the composite bar constituting of a tapered steel bar fastened to an aluminum rod of uniform cross section and subjected to loads as shown here. We are asked to determine primary and secondary variables at each node using a$)$ linear and b$)$ quadratic elements. Follow the usual FEM procedure ; c$)$ give your in a tabular form only for common nodes to linear and quadratic formulations, and what is your conclusions?

$A_1=0\mathrm{.}64A_0=84c{m}^2$;$h_1=120cm$;$h_2=144cm$;$P_0=140kN$;$E_S=2\mathrm{.}1{10}^{11}Pa$;$E_a=0\mathrm{.}69{10}^{11}Pa$;