Chapter 6: 3D Magnetostatics and Fundamentals of Edge-Based Analysis

The edge method is a version of the magnetic vector potential method where the magnetic degrees of freedom are located on element edge nodes, rather than corner nodes.

You can use the edge method to solve a static analysis when the scalar method is not convenient or efficient. You also can use the edge method for harmonic and transient analyses when the scalar method cannot be used.

Typical uses for edge-based analysis are as follows:

  • Electric machines

  • Transformers

  • Induction heating

  • Solenoid actuators

  • High-field magnets

  • Nondestructive testing

  • Magnetic stirring

  • Electrolyzing cells

  • Particle accelerators

  • Medical and geophysical instruments.

See the Mechanical APDL Theory Reference for more information on the magnetic edge-based formulation.

In an edge element, the magnetic degree of freedom is edge-flux (AZ). In the MKS system, it has the units of magnetic flux - weber (Volt-sec). The edge-flux DOF represents the integral of the tangential component of the vector potential A, along the element edge. The sum the values of the edge-flux DOF around a closed loop formed by the edges is the flux passing through the closed loop. A positive flux value along an element edge indicates that the edge vector is oriented from the lower corner node number to the high corner node number (shared by the element edge). The closed loop orientation and the flux direction is related by the right hand rule.

Support is available for 3D static, harmonic, and transient edge-based analyses. 3D Harmonic Magnetic Analysis (Edge-Based) discusses and presents examples of 3D harmonic edge-based analysis, as well as linear perturbation static and harmonic analyses. 3D Transient Magnetic Analysis (Edge-Based) describes and demonstrates 3D transient edge-based analysis.