The structure shown in Figure $2$ was modelled using three plane strain triangular shaped elements. The loading and corresponding boundary conditions are shown together with the relevant material

properties provided. The nodal coordinates are in mm $.$

Poisson's ratio, v$=0\mathrm{.}3$

Thickness, t$=100\mathrm{.}0$mm

Young's modulus, E$=150$GPa

Figure $2$: Structure modelled with plane strain elements

Requirements for Section B:

Using $2$D stress analysis, determine the displacement vector of node $4$ due to the loads applied on the structure and calculate the corresponding strain $($epsilon$)$ and stress $($sigma$)$ vectors in element $(3).$

In your solution, you will need to clearly show your working$/$calculations for the following components:

i$)$ The stiffness matrix $[$ k $]$ for each of the $3$ individual elements

ii$)$ Formulation of the global stiffness matrix

iii$)$ Assembly of the system equations with the appropriate boundary conditions $/$ unknown variables $($nodal displacements, reaction forces etc.$)$ in order that the displacements can be calculated.

iv$)$ The corresponding $[$B$]$ and $[$D$]$ matrices