Stress distribution in a long solenoid

QuickField simulation example

A very long, thick solenoid has a uniform distribution of circumferential current. The magnetic flux density and stress distribution in the solenoid has to be calculated.

Problem Type
Axisymmetric multiphysics problem of DC magnetics coupled to Stress analysis.

Geometry

Given
Current density j = 10⁵ A/m²,
Young's modulus E = 1.075·10¹¹ N/m²,
Poisson's ratio ν = 0.33.

Task
Calculate the magnetic flux density and stress distribution in a solenoid.

Solution
Since none of physical quantities varies along z-axis, a thin slice of the solenoid could be modeled. The axial length of the model is arbitrarily chosen to be 0.2 cm. Radial component of the flux density is set equal to zero at the outward surface of the solenoid. Axial displacement is set equal to zero at the side edges of the model to reflect the infinite length of the solenoid.

Results
Magnetic flux density distribution and mechanical stress distribution in a long solenoid:

Magnetic flux density and circumferential stress at R = 1.3 cm:

Reference:
[1] F.A. Moon, "Magneto-Solid Mechanics", John Wiley & Sons, N.Y., 1984, Chapter 4.

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