For the thick-walled open-ended cylindrical pipe subjected to internal pressure shown in Figure P9-19, use five layers of elements to obtain the circumferential stress, σ_θ, and the principal stresses and maximum radial displacement. Compare these results to the exact circumferential stress and radial displacement equations given by

Where
Pi = inner pressure, P0 = outer pressure (set to zero in this problem)
α = inner radius of vessel, b = outer radius of vessel, r = any radial location
Let E = 205 GPa and v = 0.3?
Figure P9-19

Pa? + Pb? a?b? r2(b a), (P Po) b2 a? Ar = . E(b a)|" (1 v)XP,a Pb) + (1 + v)ab -(P; P) r2