SECTION B:

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, $\backslash ($ v$=0\mathrm{.}3\backslash )$

Thickness, $\backslash (\backslash$mathrm$\{$t$\}=100\mathrm{.}0\backslash$mathrm$\{$~mm$\}\backslash )$

Young's modulus, $\backslash (\backslash$mathrm$\{$E$\}=150\backslash$mathrm$\{$GPa$\}\backslash )$

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 $(\backslash (\backslash$boldsymbol$\{\backslash$varepsilon$\}\backslash ))$ and stress $(\backslash (\backslash$sigma $\backslash ))$ 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