QuickField

A new approach to field modelling

Main >> Applications >> Sample problems

Stress distribution in a long solenoid

solenoid stress distribution, magnetic forces in solenoid, mechanical stress in electric coil, multiphysics analysis

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
Stress distribution in a long solenoid Calculate the magnetic flux density and stress distribution in a solenoid R1 R2 Winding Air

Given
Dimensions R1 = 1 cm, R2 = 2 cm;
Relative permeability of air and coil μ = 1;
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
in a long solenoid:
Mechanical stress distribution
in a long solenoid:
solenoid simulation solenoid stress simulation

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

  Bz (T) σq (N/m)
Reference* 8.796·10-3 97.407
QuickField 8.798·10-3 96.71

See the Coupl1MS.pbm and Coupl1SA.pbm problems for magnetic and structural analysis respectively.

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

  • Video: Stress distribution in a long solenoid
  • Watch on YouTube.
  • View simulation report in PDF
  • Download simulation files (files may be viewed using any QuickField Edition).
  • Eddy currents simulation with QuickField

    Product
    Order
    Evaluation request
    Editions
    Version history
    Packages
    Components
    Programming
    Consulting

    Applications
    Industrial
    Educational
    Scientific
    Sample problems
    Success stories
    Customers

    Support
    Webinars
    Virtual Classroom
    Online courses
    Customer login
    Glossary
    QuickField help
    FAQ

    Downloads
    QuickField Student Edition
    User manual
    Data Libraries
    Video
    Free tools

    News
    Product News
    Events
    Publications
    Subscription

    Contacts
    Tera Analysis info
    Resellers
    Contact us
    Online chat
    About us