A thick walled cylinder has internal and external diameters of 120 mm and 420 mm correspondingly.  It is made from a ductile elastic material of your choice and is employed to contain hot gas at a constant pressure.
 
1. Carry out a finite element analysis to determine the stress distributions across the cylinder wall when the internal pressure reaches a value that will cause the material to start yielding according to a proper elastic failure criterion. You are not anticipated to take temperature effects into account in your analysis.  
 
2. The design is now modified to enable cooling water to pass through the cylinder wall. The water flows through six 40 mm diameter holes uniformly spaced on a 200 mm pitch circle diameter and six 40 mm diameter holes uniformly spaced on a 320 mm pitch circle diameter.  The hole-patterns are offset by 30° relative to each other. Re-model and comment on the effect that this modification has on the stress distributions.  Predict the maximum pressure for the new design and the same failure criterion as part (1).