2-D 8-Node Electromagnetic Solid

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PLANE233 Element Description

PLANE233 is a 2-D element capable of modeling planar or axisymmetric magnetic or electromagnetic fields. In an electromagnetic analysis, it can also model a planar or axisymmetric stranded coil. The element is defined by 8 or 6 nodes, and has up to 3 degrees of freedom per node: the Z component of the magnetic vector potential (AZ) in magnetic, electromagnetic, and stranded coil analyses, electric scalar potential (VOLT) in electromagnetic and stranded coil analyses, and electromotive force (EMF) in stranded coil analyses. The VOLT and EMF degrees of freedom may be time-integrated.

In electromagnetic analyses, all VOLT degrees of freedom must be coupled in a 2-D electromagnetic region (CP) such that the voltage drop across the thickness has a single value. In a stranded coil, all the VOLT and EMF degrees of freedom must be coupled (CP).

PLANE233 is applicable to static, time-harmonic, and time-transient magnetic analyses, electromagnetic analyses, or stranded coil analyses. The magnetic analysis option, typically used to model air, iron, nonferrous materials and permanent magnets, is driven by the current density applied as an element body load. The electromagnetic analysis option, suitable for modeling solid (massive) conductors, may be voltage-driven, current-driven, or circuit-fed. In time-varying electromagnetic analyses, the eddy current effects may be suppressed to model stranded conductors. In static and time-varying electromagnetic analyses, velocity effects (moving conductors) can be taken into account. The stranded coil analysis option is suitable for modeling a stranded winding with a prescribed current flow direction vector. The stranded coil can be voltage-driven, current-driven, or circuit-fed.

The following command macros can be used with PLANE233 for solution postprocessing: CURR2D, EMAGERR, EMFT, FLUXV, MMF, PLF2D, POWERH. See Electric and Magnetic Macros in the Low-Frequency Electromagnetic Analysis Guide for more details.

See PLANE233 theory in the Mechanical APDL Theory Reference for more details about this element. The element has nonlinear magnetic capability for modeling B-H curves or permanent magnet demagnetization curves for static and time-transient analyses.

Figure 233.1:  PLANE233 Geometry

PLANE233 Geometry

PLANE233 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 233.1: PLANE233 Geometry. A triangular-shaped element may be formed by specifying the same node number for nodes K, L and O.

The type of units (MKS or user defined) is specified via the EMUNIT command. EMUNIT also determines the value of MUZRO and EPZRO. The EMUNIT defaults are MKS units and MUZRO = 4π10-7 Henry/meter and EPZRO = 8.854 x 10-12 Farad/meter. In addition to MUZRO and EPZRO, orthotropic relative permeability is specified through the MURX and MURY material property labels. The Z-depth resistivity and permittivity are specified using the RSVZ and PERZ material property labels respectively. MGXX and MGYY represent vector components of the coercive force for permanent magnet materials. The magnitude of the coercive force is the square root of the sum of the squares of the components. The direction of polarization is determined by the components MGXX and MGYY. Permanent magnet polarization directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Nonlinear magnetic B-H properties are entered via the TB command. Nonlinear orthotropic magnetic properties can be specified with a combination of a B-H curve and linear relative permeability. The B-H curve is used in each element coordinate direction where a zero value of relative permeability is specified. Only one B-H curve may be specified per material.

For the plane option (KEYOPT(3) = 0), you can also explicitly specify the element thickness (Z depth) using the real constant THK. For the axisymmetric option (KEYOPT(3) = 1), you can specify the fraction of the 360° basis using the same real constant.

Nodal loads are defined via the D and F commands. The nodal forces, if any, should be input per unit of depth for a plane analysis and on a full 360° basis for an axisymmetric analysis unless the THK real constant is specified. For edge-based analysis, the D command with Lab = AZ applies the edge-flux constraint to the node. Flux-parallel boundary conditions are prescribed by setting AZ to zero. To set flux-normal boundary conditions, leave the AZ constraint unspecified.

For massive conductors (KEYOPT(1) = 1), Lab = VOLT is valid with the D command and VALUE defines the electric potential. Note that electric potential is time-integrated if KEYOPT(2) = 2. With the F command, Lab = AMPS and VALUE corresponds to the total current.

For stranded coils (KEYOPT(1) = 2), Lab = VOLT is valid with the D command and VALUE defines the voltage drop across the coil. The D command with Lab = EMF can be used to apply constraints on the electromotive force. Note that voltage drop and the electromotive force are time-integrated if KEYOPT(2) = 2. The total current through the coil can be applied with the F command using Lab = AMPS.

The temperature (used for material property evaluation only) body loads may be input based on their value at the element's nodes or as a single element value [BF, BFE]. In general, unspecified nodal values of temperatures default to the uniform value specified with the BFUNIF or TUNIF commands. For modeling stranded conductors with KEYOPT(1) = 0, source current density may be applied to an area [BFA] or input as an element value [BFE].

A summary of the element input is given in "PLANE233 Input Summary". A general description of element input is given in Element Input.

PLANE233 Input Summary


I, J, K, L, M, N, O, P

Degrees of Freedom

Set by KEYOPT(1).

Real Constants

Thickness (THK) is the only real constant for KEYOPT(1) = 0 or 1.

The following are the real constants for KEYOPT(1) = 2:


See Table 233.1: PLANE233 Real Constants for more information.

Material Properties

TB command: Magnetic

MP command: MURX, MURY, MGXX, MGYY, RSVZ, PERZ (See ""PLANE233 Assumptions and Restrictions"")


Surface Loads


Body Loads

Temperature --

T(I), T(J), ..., T(O), T(P)

Source Current Density (valid for KEYOPT(1) = 0 only) --

spare, spare, JSZ(I), PHASE(I),

spare, spare, JSZ(J), PHASE(J),


spare, spare, JSZ(O), PHASE(O),

spare, spare, JSZ(P), PHASE(P)

Velocity (valid for KEYOPT(1) = 1 only) --

VELOX(I), VELOY(I), spare, spare, spare, OMEGAZ(I)

VELOX(J), VELOY(J), spare, spare, spare, OMEGAZ(J)


VELOX(P), VELOY(P), spare, spare, spare, OMEGAZ(P)

Special Features

Linear perturbation


Element capability and degrees of freedom:

0 -- 

Magnetic: AZ

1 -- 

Electromagnetic: AZ, VOLT

2 -- 

Stranded coil: AZ, VOLT, EMF


Coupling method between magnetic and electric degrees of freedom (KEYOPT(1) = 1 or 2); also defines the meaning of the VOLT and EMF degrees of freedom:

0 -- 

Strong coupling (through matrix terms). Applicable to static, harmonic, and transient analyses. Produces an unsymmetric matrix and, in a linear analysis, requires only one iteration to achieve a coupled response.

1 -- 

Weak coupling (through the load vector). Applicable to static and transient analyses only. Produces a symmetric matrix and requires at least two iterations to achieve a coupled response. (See "PLANE233 Assumptions and Restrictions")

2 -- 

Strong coupling (through matrix terms). VOLT is time-integrated voltage drop and EMF is time-integrated electromotive force. Applicable to harmonic and transient analyses only.

For electromagnetics (KEYOPT(1) = 1), produces a symmetric matrix. For a stranded coil (KEYOPT(1) = 2), produces a symmetric matrix if the coil symmetry factor is 1; produces an unsymmetric matrix if the coil symmetry factor is greater than 1. In a linear analysis, requires only one iteration to achieve a coupled response.


Element behavior:

0 -- 


1 -- 



Eddy current or velocity effects in harmonic or transient electromagnetic (KEYOPT(1) =1) analyses:

0 -- 

Eddy current and velocity effects are active

1 -- 

Eddy current effects are suppressed, velocity effects are active

2 -- 

Velocity effects are suppressed, eddy current effects are active

3 -- 

Eddy current and velocity effects are suppressed


Electromagnetic force output:

0 -- 

At each element node (corner and midside)

1 -- 

At element corner nodes only (midside node forces are condensed to the corner nodes)


Electromagnetic force calculation:

0 -- 


1 -- 


Table 233.1:  PLANE233 Real Constants

1THKThickness (plane) or fraction of the 360° basis (axisymmetric)1Applicable to all KEYOPT(1) = 0, 1, or 2.
2SCCoil cross-sectional areanoneTrue physical cross-section of the coil regardless of symmetry modeling considerations. It includes the cross-sectional area of the wire and the non-conducting material filling the space between the winding.
3NCNumber of coil turns1Total number of winding turns in a coil regardless of any symmetry modeling considerations.
4RADMean radius of the coil (axisymmetric)noneMean radius of the axisymmetric coil model. If the mean radius is not known, input VC/((2π)(SC)(THK)) , where VC is the full symmetry true physical volume of the coil. VC includes the volume occupied by the wire and the non-conducting material filling the space between the winding.
5TZCurrent polarity

1 (plane)

-1 (axisymmetric)

The current flow direction (1 or -1) with respect to Z-axis
6RCoil resistancenoneTotal coil DC resistance regardless of any symmetry modeling considerations.
7SYMCoil symmetry factor 1Ratio of the full symmetry coil cross-sectional area (SC) to the modeled coil area. The input should be equal to or greater than 1.

PLANE233 Output Data

The solution output associated with the element is in two forms:

The element output directions are parallel to the element coordinate system. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates the item can be accessed by the Component Name method [ETABLE, ESOL]. The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.

In either the O or R columns, Y indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and a - indicates that the item is not available.

Table 233.2:  PLANE233 Element Output Definitions

EL Element Number -Y
NODES Nodes - I, J,…, O,P -Y
MAT Material number -Y
THICK Thickness -Y
VOLU: Volume -Y
XC, YC Location where results are reported -2
TEMP Input temperatures T(I), T(J), ..., T(O), T(P) -Y
LOC Output location (X, Y) --
B: X, Y, SUM Magnetic flux density components and vector magnitude -1
H: X, Y, SUM Magnetic field intensity components and vector magnitude -1
EF: Z, SUM Electric field intensity Z component and vector magnitude [7]-1
JC: Z, SUM Conduction current density Z component and vector magnitude [7]-1
FMAG: X, Y, SUM Electromagnetic force components and magnitude [3] -1
JT: Z, SUM Conduction current density Z component (in the global Cartesian coordinate system) and vector magnitude [6]-1
JS: Z, SUM Current density Z component (in the global Cartesian coordinate system) and vector magnitude [4] [6]-1
JHEAT: Joule heat generation rate per unit volume [3] [5] [6]-1
SENE or MENE:Magnetic energy [3]-1
COENMagnetic co-energy [3]-1
AENEApparent magnetic energy [3]-1
IENEIncremental magnetic energy [3]-1

  1. The solution value is output only if calculated (based upon input data). The element solution is at the centroid.

  2. Available only at centroid as a *GET item.

  3. For a time-harmonic analysis, electromagnetic forces (FMAG), Joule losses (JHEAT) and stored energy (SENE, MENE) represent time-average values. These values are stored in both the real and imaginary data sets. In a linear perturbation analysis, only incremental and apparent energy values are time-averaged.

  4. JS represents the sum of element conduction and displacement current densities.

  5. Calculated Joule heat generation rate per unit volume (JHEAT) may be made available for a subsequent thermal analysis with companion elements [LDREAD].

  6. For the stranded coil analysis option (KEYOPT(1) = 2), JT and JS are the effective current densities as they are calculated based on the coil cross-sectional area (SC) that includes the wire and the non-conducting material filling the space between the winding. JHEAT represents the effective Joule heat generation rate per unit volume as it is calculated based on the modeled coil volume that includes the wire and the non-conducting material filling the space between the winding.

  7. Not available with the stranded coil option (KEYOPT(1) = 2).

Table 233.3: PLANE233 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and Table 233.3: PLANE233 Item and Sequence Numbers in this reference for more information. The following notation is used in Table 233.3: PLANE233 Item and Sequence Numbers:

Name: output quantity as defined in Table 233.2: PLANE233 Element Output Definitions

Item: predetermined Item label for ETABLE command

E: sequence number for single-valued or constant element data

Table 233.3:  PLANE233 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

PLANE233 Assumptions and Restrictions

  • The area of the element must be positive.

  • The element must lie in a global X-Y plane as shown in Figure 233.1: PLANE233 Geometry and the Y-axis must be the axis of symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.

  • A face with a removed midside node implies that the potentials vary linearly, rather than parabolically, along that edge. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information on the use of midside nodes.

  • Permanent magnets are not permitted in a harmonic analysis.

  • Use of the weak coupling option (KEYOPT(2) = 1) in a transient electromagnetic analysis with eddy currents or a transient stranded coil analysis is not recommended because multiple iterations may be required to achieve convergence.

  • In a transient, strongly coupled (KEYOPT(2) = 0 or 2) electromagnetic analysis or stranded coil analysis (KEYOPT(1) = 1 or 2), the THETA integration parameter defaults to the values shown in the following table. You can use the TINTP command to modify the default setting.

    Table 233.4:  THETA Default Values

    Analysis TypeKEYOPT ValuesTHETA Default Value
    With electric potential or voltage drop (VOLT)KEYOPT(2) = 01.0
    With time-integrated electric potential or voltage drop (VOLT)KEYOPT(2) = 20.5

  • The electrical permittivity material input (MP,PERZ) is applicable to harmonic electromagnetic analyses (KEYOPT(1) = 1) only.

  • In an electromagnetic (KEYOPT(1) = 1) domain, all VOLT degrees of freedom must be coupled (CP).

  • In a stranded coil (KEYOPT(1) = 2) domain, all VOLT and EMF degrees of freedom must be coupled (CP).

  • Unlike the 2-D magnetic element PLANE13 that models the eddy current effects with the AZ option (KEYOPT(1) = 0) when BFE,,JS is not specified, PLANE233 always acts as a stranded conductor in a harmonic or transient analysis with KEYOPT(1) = 0. In this respect, the PLANE233 behavior is consistent with the 3-D electromagnetic elements (e.g. SOLID236) behavior.

  • This element may not be compatible with other elements having a VOLT degree of freedom. See Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide) for more information. The electromagnetic analysis with time-integrated electric potential (KEYOPT(2) = 2) cannot be used with current-based circuit (e.g. CIRCU124) or low-frequency electric (e.g. PLANE230) elements.

PLANE233 Product Restrictions

There are no product-specific restrictions for this element.

Release 18.2 - © ANSYS, Inc. All rights reserved.