PROBLEM $3.$ The cross$-$section of a long steel axle shown in the figure has a radius of $50$ mm $.$ A linearly varying pressure load is applied to right and left sides of the axle and its maximum value is $800$ MPa $.$

$($a$)$ model the cross$-$section of disc with two constant strain triangles $($use the symmetry of geometry and loads, i$.$e$.$ a quarter model$)$

$($b$)$ determine the nodal displacements and draw the deformed and undeformed shapes

$($c$)$ calculate the element stresses.

$($d$)$ compare the Constant Strain Triangle $($with three nodes$)$ and the Lineer Strain Triangle elements $($with six nodes$)$ according to the modelling of the geometry and accuracy of the results.