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# Pipe subject to temperature and pressure

A very long thick-walled cylinder pipe is subjected to an internal pressure and a steady state temperature distribution with Ti and To temperatures at inner and outer surfaces respectively. Calculate the stress distribution in the cylinder.

Problem Type:
Axisymmetric multiphysics problem of Heat Transfer coupled to Stress analysis.

Geometry:

Given:
Dimensions R1 = 1 cm, R2 = 2 cm;
Inner surface temperature Ti = 100 °C;
Outer surface temperature To = 0 °C;
Coefficient of thermal expansion α = 10 -6 1/K;
Internal pressure P = 106 N/m²;
Young's modulus E = 3·1011 N/m²;
Poisson's ratio ν = 0.3.

Calculate the stress distribution in the pipe.

Solution:
Since none of physical quantities varies along z-axis, 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.

Results:
 Temperature distribution in a cylinder pipe: Stress distribution in a cylinder pipe:  Radial and circumferential stress at r=1.2875 cm:

 σr (N/m²) σq (N/m²) Theory -3.9834·106 -5.9247·106 QuickField -3.959·106 -5.924·106

See the Coupl2HT.pbm and Coupl2SA.pbm problems are for the corresponding heat transfer and structural analysis.

* Reference: S. P. Timoshenko and Goodier, Theory of Elasticity, McGraw-Hill Book Co., N.Y., 1961, pp. 448-449.

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