A truss is illustrated as below, use two linear elements in total to obtain the displacement of node $2$ and stresses of element $1$ and $2.$

$(25$ points$)$

Note: the global stiffness matrix is calculated as

$k=\frac{E_e{A}_e}{l_e}\left[\begin{array}{cccc}{l}^2& m& -t^2& -lm\\ lm& m{m}^2& -lm& -m^2\\ -t^2& -im& l^2& m\\ -tm& -m^2& lm& m^2\end{array}\right]$

The relationship between stress and displacement is

$=\frac{E_r}{f_r}-l-m,lmq$

where $l_e$ is the element length.

$q={\left[\begin{array}{cccc}{q}_1& q_2& q_3& q_4\end{array}\right]}^T$ is the nodal displacement corresponding to each element.