This multiphysics model examines how magnetic forces give rise to
stresses in a long thick cylindrical solenoid. A current density of
106 A/m2 is running through a wound coil with
1 cm inner to 2 cm outer radii. The material of the coil is
assumed to have a modulus of elasticity of 1.075⋅1011
N/m2 and Poisson’s ratio of 0.33, and air occupies the
inner hollow core.
As this is a one-way coupled problem, the magnetostatic effects will
be solved for first, after which the calculated magnetic forces will
be used as input to the stress-strain problem. Due to symmetry it is
also sufficient to model a 2D axisymmetric cross-section. The
resulting magnetic flux density and circumferential stress at r = 1.3
cm will be compared to the theoretical values of
8.798⋅10-3 T and 96.71 N/m, respectively
This model is available as an automated tutorial by selecting Model
Examples and Tutorials… > Multiphysics > Stress Distribution
in a Solenoid from the File menu. Or alternatively, follow the
linked step-by-step instructions.
 Moon FA. Magneto-Solid Mechanics, Chapter 4,
John Wiley & Sons, NY, 1984.