Solve the following $2$ bar structures using FEM methodology.

During the solution, perform the following steps:

a$)$ Number the element and nodes.

b$)$ Find the projection matrix $[$T$]$ for each element.

c$)$ Find the element stiffness matrices $[$k$\text{'}]$ and $[$k$]$ for each element.

d$)$ Set up the overall $($global$)$ stiffness matrix $[$K$]$

e$)$ Show how you implement boundary conditions and load forces.

f$)$ Solve the system equations $[$K$]\{$U$\}=\{$F$\}$

g$)$ Find the forces and stresses in the elements from displacements in the nodes.

h$)$ Find basic forces by inserting nodal displacements into system simulations.

i$)$ Show deformations and stresses graphically

Show and explain all solution steps to the solution

Task $1$:

Material is aluminum $(68$GPa$)$ in rods $1$ and $2$ and steel $(207$ GPa$)$ in rods $3.$

The area of $$bars $1$ is $10$ cm$2$ and $6$ cm$2$ of bars $2$ and $3$

Project $2$

Material in all bars is steel $(207$ GPa$)$ and cross section $600$mm$2.$

Please provide a hand written solution and a matlab code for this problem