Question $1$

For the element shown in figure $1$ assuming plane stress conditions:

a$.$ Evaluate the stiffness matrix

b$.$ For the nodal displacements given, determine the element stresses ${}_x,{}_y,{}_{xy},{}_1,{}_2$

c$.$ Determine the principal angle ${}_p$

d$.$ Determine the von Mises stress

$u_1=0\mathrm{.}0mm,v_1=0\mathrm{.}0625mm$

$u_2=0\mathrm{.}03mm,v_2=0\mathrm{.}0mm$

$u_3=0\mathrm{.}0mm,v_3=0\mathrm{.}0625mm$

Figure $1$