A very long, thickwalled cylinder is subjected to an internal pressure and a steady state temperature distribution with T_{i} and T_{0} temperatures at inner and outer surfaces respectively. Calculate the stress distribution in the cylinder.
Problem Type:
An axisymmetric problem of thermalstructural coupling.
Geometry:
Given:
Dimensions R_{i} = 1 cm, R_{o} = 2 cm;
Inner surface temperature T_{i} = 100°C;
Outer surface temperature T_{o} = 0°C;
Coefficient of thermal expansion α = 1·10^{6} 1/K;
Internal pressure P = 1·10^{6} N/m^{2};
Young's modulus E = 3·10^{11} N/m^{2};
Poisson's ratio ν = 0.3.
Problem:
Calculate the stress distribution.
Solution:
Since none of physical quantities varies along zaxis, a thin slice of the cylinder can be modeled. The axial length of the model is arbitrarily chosen to be 0.2 cm. Axial displacement is set equal to zero at the side edges of the model to reflect the infinite length of the cylinder.
Comparison of Results:
Radial and circumferential stress at r = 1.2875 cm:
σ_{r} (N/m^{2}) 
σ_{θ} (N/m^{2}) 

Theory 
–3.9834·10^{6} 
–5.9247·10^{6} 
QuickField 
–3.959·10^{6} 
–5.924·10^{6} 
Reference:
S. P. Timoshenko and Goodier, "Theory of Elasticity", McGrawHill Book Co.,
N.Y., 1961, pp. 448449.
See the Coupl2HT.pbm and Coupl2SA.pbm problems in the Examples folder for the corresponding heat transfer and structural parts of this problem.