An open thick cylinder shown below has an inner radius, a $=1$ m$,$ outer radius, b $=1\mathrm{.}5$ m$,$ length L $=6$ m$,$ and has a pressure load p $=10$ MPa applied on the inner surface. The cylinder is free to deform along the length

direction and also along its outer diameter. Compute the radial and tangential stresses in the cylinder in ANSYS Workbench by using symmetry to model only half the length of the cylinder and use a $2-$D axisymmetric analysis to model the $2$D cross$-$section of the cylinder that represents the $3$D solid of revolution. Assume Young's modulus, $\backslash ($ E$=200\backslash )$ GPa and Poisson's ratio, $\backslash ($ v$=0\mathrm{.}3\backslash ).$

a$.$ Perform the Preliminary analysis of the cylinder to determine $($using standard formulas in the literature$)$ the variation of the radial and tangential stresses in the thick cylinder for the given geometry and internal pressure loading.

b$.$ Perform the preprocessing analysis using ANSYS SpaceClaim to model the $2$D plane of the cylinder $($for axisymmetric analysis$).$ Generate a quadrilateral mesh using Face meshing and an Element size $\backslash (=0\mathrm{.}05\backslash$mathrm$\{$~m$\}\backslash ).$ Apply the appropriate pressure and displacement $($symmetry$)$ boundary conditions $($BCs$)$ to the model. Provide screenshots of the FE mesh, force$/$pressure and displacement BCs applied to the model.

c$.$ Solve the FE equations in ANSYS WB and perform post$-$processing and provide screenshots of $($i$)$ the radial deformation with undeformed wireframe, $($ii$)$ contours of the radial and tangential stresses in the model and $($iii$)$ the variation of the tangential$/$circumferential and radial stresses along a radial path $($from inner radius to outer radius$)$ of the cylinder.

d$.$ Verify the FE analysis by comparing the variation of the tangential and radial stresses along a radial path with the preliminary analysis. Provide a screenshot of the graph that compares the closed$-$form solution to your FE analysis results for the variation of the tangential and radial stresses along a radial path in the cylinder.