Pipe subject to temperature and pressure

QuickField simulation example

A very long thick-walled cylinder pipe is subjected to an internal pressure and a steady state temperature distribution with T_i and T_o 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 T_i = 100 °C;
Outer surface temperature T_o = 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.

Task
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 and stress distribution in a cylinder pipe:

Radial and circumferential stress at R=1.2875 cm:

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

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