1.1. How Mechanical APDL Handles Magnetic Analysis

The program uses Maxwell's equations as the basis for electromagnetic field analysis. The primary unknowns (degrees of freedom) that the finite element solution calculates are magnetic and electric potentials. Other magnetic field quantities such as magnetic field flux density, current density, energy, forces, loss, inductance, and capacitance are derived from these degrees of freedom. Depending on the element type and element option you choose, the degrees of freedom may be scalar magnetic potentials, vector magnetic potentials, or edge flux, as well as non-time integrated and time integrated electric potential.

The program offers several formulations, depending on the type of analysis, the material properties in your analysis, and the overall physics of your analysis. Electromagnetic analyses may be coupled to circuit, heat transfer, mechanical, or fluid dynamics analyses.

Options available for low frequency electromagnetic analyses are summarized in the following figures and tables.

To understand which formulation may be suitable for your analysis, you need to consider how current is introduced into the model. The following graphics show the basic current loading configurations for 3D models. These configurations are referenced in the tables that follow.

Figure 1.1: Current-Fed Stranded Source - Current Density Known

Where:

J = current density

n = number of turns

i = current in a filament

A = coil cross section area

In this case, the current density is specified on each element via body-force loading (BFE,,JS).

Figure 1.2: SOURC36 Current-fed Stranded Conductor

In this case, the current loading is fed in via SOURC36 coil primitives. The coil primitives are simple predefined geometric shapes that you use to locate and prescribe current, without the need to physically create a finite element model and mesh of the coil domain.

Figure 1.3: Current-Fed Solid Conductor - Current Known

Figure 1.4: Voltage-Fed Solid Conductor - Voltage Known

Figure 1.5: Circuit-Fed Solid Conductor

The following tables summarize the physics regions, elements, and loading options available for each of the various formulations.

Table 1.1: Formulation Comparison

Formulation	Conductor Model	Dim.	Applications	Element Types	Analysis Type
MSP	SOURC36 current-fed stranded conductor - coil not meshed, underlying region meshed	3D	Magnetostatic without eddy current.	SOLID5, SOLID96, SOLID98	Static
Nodal MVP	Current, voltage, or circuit-fed solid conductor - Coil meshed as part of model	2D	Magnetostatic, eddy current.	PLANE13, PLANE233	Static, harmonic, transient
Edge-Based	Both stranded and solid conductors permitted. Supports current, circuit, voltage fed, and direct current specification	3D	Magnetostatic, eddy current, magnetic allowed.	SOLID236, SOLID237	Static, harmonic, transient

Table 1.2: 3D Edge Formulation

The 3D Edge Formulation uses SOLID236and SOLID237 elements, with KEYOPT(1) = 0 unless otherwise noted.
Physical Region	Current	Magnetic Material Props	Electric Material Props	DOFs	Current Loading	Notes
Non-magnetic (air, copper, aluminum)	None	MURX (Y,Z) = 1		AZ	N/A
Soft Magnetic (typically iron or steel)	None	MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		AZ	N/A
Hard Magnetic (such as Alnico or samarium cobalt)	None	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		AZ	N/A
Stranded Conductor (typically copper)	Current (neglecting eddy current)	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX, RSVY, RSVZ	AZ	BFE,,JS
Solid Conductor (typically copper, aluminum, etc.)	Current (neglecting eddy current)	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX, RSVY, RSVZ	AZ, VOLT	F,,AMPS, D,,VOLT, or circuit loading	Uses SOLID236 or SOLID237 with KEYOPT(1) = 1 in a static analysis and with KEYOPT(1) = 1 and KEYOPT(5) = 1 in a harmonic or transient analysis.
Solid Conductor (typically copper, aluminum, etc.)	Eddy current	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX, RSVY, RSVZ	AZ, VOLT	F,,AMPS, D,,VOLT	Uses SOLID236 or SOLID237 with KEYOPT(1) = 1
Stranded Coil	Current (neglecting eddy current)	MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX	AZ, VOLT, EMF	F,,AMPS, D,,VOLT, or circuit loading	Uses SOLID236 or SOLID237 with KEYOPT(1) = 1

Table 1.3: 2D MVP Formulation

The 2D MVP Formulation uses PLANE13, and PLANE233 elements with KEYOPT(1) = 0 unless otherwise noted.
Physical Region	Current	Magnetic Material Props	Electric Material Props	DOFs	Current Loading	Notes
Non-magnetic (air, copper, aluminum)	None	MURX (Y,Z) = 1		AZ	N/A
Soft Magnetic (typically iron or steel)	None	MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		AZ	N/A
Hard Magnetic (such as Alnico or samarium cobalt)	None	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		AZ	N/A
Stranded Conductor (typically copper)	Current (neglecting eddy current)	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		AZ	BFE,,JS
Solid Conductor (typically copper, aluminum, etc.)	Eddy current	MGXX(YY,ZZ)[1], MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX, RSVY, RSVZ	AZ, VOLT	F,,AMPS or circuit loading	Uses PLANE13 with KEYOPT(1) = 6 or PLANE233 with KEYOPT(1) = 1
Stranded Coil	Current (neglecting eddy current)	MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)	RSVX	AZ, VOLT, EMF	F,,AMPS, D,,VOLT, or circuit loading	Uses PLANE233 with KEYOPT(1) = 2

Table 1.4: 3D Nodal MSP Formulation

The 3D Nodal MSP Formulation uses SOLID5 with KEYOPT(1) = 10, SOLID96, and SOLID98 with KEYOPT(1) = 10 elements, unless otherwise noted.
Physical Region	Current	Magnetic Material Props	Electric Material Props	DOFs	Current Loading	Notes
Non-magnetic (air, copper, aluminum)	None	MURX (Y,Z) = 1		MAG	N/A
Soft Magnetic (typically iron or steel)	None	MURX (Y,Z) > 1 (linear) or B-H curve (nonlinear)		MAG	N/A
Hard Magnetic (such as Alnico or samarium cobalt)	None	MGXX(YY,ZZ)[1], MURX (Y, Z) > 1 (linear) or B-H curve (nonlinear)		MAG	N/A
Stranded Conductor (typically copper)	Current (neglecting eddy current)	Any of above	N/A	MAG	SOURC36
Solid Conductor (typically copper, aluminum, etc.)	Current (neglecting eddy current)	Any of above	N/A	MAG	SOURC36	Uses KEYOPT(1) = 1 or 9 on SOLID5 or SOLID98 only

Coercive force in terms of vector components, MGXX, MGYY, MGZZ. Polarization direction is determined by coercion force (magnetization) terms MGXX, MGYY and MGZZ in conjunction with the element coordinate system.