2-D Coupled-Field Solid

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PLANE13 Element Description

Although this legacy element is available for use in your analysis, ANSYS, Inc. recommends using a current-technology element such as PLANE223.

PLANE13 has a 2-D magnetic, thermal, electrical, piezoelectric, and structural field capability with limited coupling between the fields. PLANE13 is defined by four nodes with up to four degrees of freedom per node. The element has nonlinear magnetic capability for modeling B-H curves or permanent magnet demagnetization curves. PLANE13 has large deflection and stress stiffening capabilities. When used in purely structural analyses, PLANE13 also has large strain capabilities. See PLANE13 in the Mechanical APDL Theory Reference for more details about this element. Other coupled-field elements are SOLID5, and SOLID98.

Figure 13.1:  PLANE13 Geometry

PLANE13 Geometry

PLANE13 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 13.1: PLANE13 Geometry. The element input data includes four nodes and magnetic, thermal, electrical, and structural material properties. The type of units (MKS or user defined) is specified through the EMUNIT command. EMUNIT also determines the value of MUZERO. The EMUNIT defaults are MKS units and MUZRO = 4 π x 10-7 henries/meter. In addition to MUZERO, orthotropic relative permeability is specified through the MURX and MURY material property labels.

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 and orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Nonlinear magnetic B-H, piezoelectric, and anisotropic elastic 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.

Various combinations of nodal loading are available for this element (depending upon the KEYOPT(1) value). Nodal loads are defined with the D and the F commands. 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.

Element loads are described in Nodal Loading. Pressure, convection or heat flux (but not both), radiation, and Maxwell force flags may be input on the element faces indicated by the circled numbers in Figure 13.1: PLANE13 Geometry using the SF and SFE commands. Positive pressures act into the element. Surfaces at which magnetic forces are to be calculated are identified by using the MXWF label on the surface load commands (no value is required). A maxwell stress tensor calculation is performed at these surfaces to obtain the magnetic forces. These forces are applied in solution as structural loads. The surface flag should be applied to "air" elements adjacent to the body for which forces are required. Deleting the MXWF specification removes the flag.

Body loads - temperature, heat generation rate, and magnetic virtual displacement - may be input at the element's nodes or as a single element value [BF, BFE]. Source current density loads may be applied to an area [BFA] or input as an element value [BFE]. When the temperature degree of freedom is active (KEYOPT(1) = 2 or 4), applied body force temperatures [BF, BFE] are ignored. In general, unspecified nodal temperatures and heat generation rates default to the uniform value specified with the BFUNIF or TUNIF command. Heat generation from Joule heating is applied in Solution as thermal loading for static and transient analyses.

If the temperature degree of freedom is present, the calculated temperatures override any input nodal temperatures.

Air elements in which local Jacobian forces are to be calculated may be identified by using nodal values of 1 and 0 for the MVDI label [BF]. See the Low-Frequency Electromagnetic Analysis Guide for details. These forces are not applied in solution as structural loads.

A summary of the element input is given in "PLANE13 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications see Harmonic Axisymmetric Elements.

PLANE13 Input Summary


I, J, K, L

Degrees of Freedom
AZ if KEYOPT (1) = 0
TEMP if KEYOPT (1 ) = 2
UX, UY if KEYOPT (1) = 3
UX, UY, TEMP, AZ if KEYOPT (1) = 4
VOLT, AZ if KEYOPT (1) = 6
UX, UY, VOLT if KEYOPT (1) = 7
Real Constants


Material Properties
TB command: See Element Support for Material Models for this element.
Surface Loads
Pressure, Convection or Heat Flux (but not both),  Radiation (using Lab = RDSF), and Maxwell Force Flags--  

face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)

Body Loads
Temperatures -- 

T(I), T(J), T(K), T(L)

Heat Generations -- 

HG(I), HG(J), HG(K), HG(L)

Magnetic Virtual Displacements -- 

VD(I), VD(J), VD(K), VD(L)

Source Current Density -- 
spare, spare, JSZ(I), PHASE(I), spare, spare,
JSZ(J), PHASE(J), spare, spare, JSZ(K), PHASE(K),
spare, spare, JSZ(L), PHASE(L)
Special Features
Adaptive descent
Birth and death
Large deflection
Large strain
Stress stiffening

Element degrees of freedom:

0 -- 

AZ degree of freedom

2 -- 

TEMP degree of freedom

3 -- 

UX, UY degrees of freedom

4 -- 

UX, UY, TEMP, AZ degrees of freedom

6 -- 

VOLT, AZ degrees of freedom

7 -- 

UX, UY, VOLT degrees of freedom


Extra shapes:

0 -- 

Include extra shapes

1 -- 

Do not include extra shapes


Element behavior:

0 -- 

Plane strain (with structural degrees of freedom)

1 -- 


2 -- 

Plane stress (with structural degrees of freedom)


Element coordinate system defined:

0 -- 

Element coordinate system is parallel to the global coordinate system

1 -- 

Element coordinate system is based on the element I-J side


Extra element output:

0 -- 

Basic element printout

1 -- 

Repeat basic solution for all integration points

2 -- 

Nodal stress printout

PLANE13 Output Data

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

Several items are illustrated in Figure 13.2: PLANE13 Element Output. 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.

Figure 13.2:  PLANE13 Element Output

PLANE13 Element Output

Because of different sign conventions for Cartesian and polar coordinate systems, magnetic flux density vectors point in opposite directions for planar (KEYOPT(3) = 0) and axisymmetric (KEYOPT(3) =1) analyses.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that 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 “-” indicates that the item is not available.

Table 13.1:  PLANE13 Element Output Definitions

ELElement NumberYY
NODESNodes - I, J, K, LYY
MATMaterial numberYY
XC, YCLocation where results are reportedY3
PRESP1 at nodes J, I; P2 at K, J; P3 at L, K; P4 at I, LYY
TEMPInput temperatures T(I), T(J), T(K), T(L)YY
HGENInput heat generations HG(I), HG(J), HG(K), HG(L)Y-
S:X, Y, Z, XYStresses (SZ = 0.0 for plane stress elements)11
S:1, 2, 3Principal stresses11
S:INTStress intensity11
S:EQVEquivalent stress11
EPEL:X, Y, Z, XYElastic strains11
EPEL:1, 2, 3Principal elastic strains1-
EPEL:EQVEquivalent elastic strain [4]-1
EPTH:X, Y, Z, XYAverage thermal strains11
EPTH:EQVEquivalent thermal strain [4]-1
TG:X, Y, SUMThermal gradient components and vector sum11
TF:X, Y, SUMThermal flux (heat flow rate/cross-sectional area) components and vector sum11
EF:X, YElectric field components (X, Y)11
EF:SUMVector magnitude of EF11
D:X, YElectric flux density components (X, Y)11
D:SUMVector magnitude of D11
UE, UD, UMElastic (UE), dielectric (UD), and electromechanical coupled (UM) energies11
LOCOutput location (X, Y)1-
MUX, MUYMagnetic permeability11
H:X, YMagnetic field intensity components11
H:SUMVector magnitude of H11
B:X, YMagnetic flux density components11
B:SUMVector magnitude of B11
JSZSource current density, available for static analysis only11
JTZTotal current density11
JHEAT:Joule heat generation per unit volume11
FJB(X, Y)Lorentz force components11
FMX(X, Y)Maxwell force components11
FVW(X, Y)Virtual work force components11
FMAG:X, YCombined (FJB and FMX) force components-1
FACEFace label22
AREAFace area22
NODESFace nodes2-
HFILMFilm coefficient at each node of face2-
TBULKBulk temperature at each node of face2-
TAVGAverage face temperature22
HEAT RATEHeat flow rate across face by convection22
HEAT RATE/AREAHeat flow rate per unit area across face by convection2-
HFLUXHeat flux at each node of face2-
HFAVGAverage film coefficient of the face22
TBAVGAverage face bulk temperature-2
HFLXAVGHeat flow rate per unit area across face caused by input heat flux-2
TJB(Z)Lorentz torque about global Cartesian +Z axis11
TMX(Z)Maxwell torque about global Cartesian +Z axis11
TVW(Z)Virtual work torque about global Cartesian +Z axis11

  1. Solution values are output only if calculated (based on input data).

  2. Available only if a surface load is input.

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

  4. The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by the user (MP,PRXY).

Table 13.2:  PLANE13 Miscellaneous Element Output

DescriptionNames of Items OutputOR
Integration Pt. SolutionSINT, SEQV, EPEL, S, MUX, MUY, H, HSUM, B, BSUM1-
Nodal SolutionSINT, SEQV, S, H, HSUM, B, BSUM2-

  1. Output at each integration point, if KEYOPT(5) = 1.

  2. Output at each node, if KEYOPT(5) = 2.

Note:  JT represents the total measurable current density in a conductor, including eddy current effects, and velocity effects if calculated.

For axisymmetric solutions with KEYOPT(4) = 0, the X and Y directions correspond to the radial and axial directions, respectively. The X, Y, Z, and XY stress output correspond to the radial, axial, hoop, and in-plane shear stresses, respectively.

For harmonic analysis, joule losses (JHEAT), forces (FJB(X, Y), FMX(X, Y), FVW(X, Y)), and torque (TJB(Z), TMX(Z), TVW(Z)) represent time-average values. These values are stored in the "Real" data set. The macro POWERHand> can be used to retrieve this data.

Table 13.3: PLANE13 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) of the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 13.3: PLANE13 Item and Sequence Numbers:


output quantity as defined in the Table 13.1: PLANE13 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for single-valued or constant element data


sequence number for data at nodes I, J, K, L


sequence number for solution items for element Face N

Table 13.3:  PLANE13 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

Output Quantity NameETABLE and ESOL Command Input

PLANE13 Assumptions and Restrictions

  • The element requires an iterative solution for field coupling (displacement, temperature, electric, magnetic, but not piezoelectric)

  • The area of the element must be positive.

  • The element must lie in a global X-Y plane as shown in Figure 13.1: PLANE13 Geometry and the Y-axis must be the axis of symmetry for axisymmetric analyses.

  • An axisymmetric structure should be modeled in the +X quadrants.

  • For structural and piezoelectric problems, the extra displacement and VOLT shapes are automatically deleted for triangular elements so that a constant strain element results.

  • Transient magnetic analyses should be performed in a nonlinear transient dynamic analysis.

  • A skin-effect analysis (where eddy current formation is permitted in conducting regions with impressed current loading) is performed by using KEYOPT(1) = 6, specifying a resistivity, and coupling all VOLT degrees of freedom for elements in each of such regions. This is valid for both planar and axisymmetric models.

  • Current density loading (BFE,,JS) is only valid for the AZ option (KEYOPT(1) = 0). For the VOLT, AZ option (KEYOPT(1) = 6) use F,,AMPS.

  • When this element does not have the VOLT degree of freedom (KEYOPT(1) = 4), for a harmonic or transient analysis, its behavior depends on the applied load. For a BFE,,JS load, the element acts as a stranded conductor. Without BFE,,JS loads, it acts as a solid conductor modeling eddy current effects.

    In this respect, PLANE13 is not like the 3-D elements SOLID236 and SOLID237. When SOLID236 and SOLID237 do not have the VOLT degree of freedom, they act as stranded conductors.

  • Do not constrain all VOLT DOFs to the same value in a piezoelectric analysis (KEYOPT(1) = 7). Perform a pure structural analysis instead (KEYOPT(1) = 3).

  • Permanent magnets are not permitted in a harmonic analysis.

  • If a model has at least one element with piezoelectric degrees of freedom (displacements and VOLT) activated, then all elements where a VOLT degree of freedom is needed must be one of the piezoelectric types, and they must all have the piezoelectric degrees of freedom activated. If the piezoelectric effect is not desired in any of these elements, simply define very small piezoelectric material properties for them.

  • This element may not be compatible with other elements with the VOLT degree of freedom. To be compatible, the elements must have the same reaction solution for the VOLT DOF. Elements that have an electric charge reaction solution must all have the same electric charge reaction sign. For more information, see Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide.

  • When KEYOPT(1) = 0 or 6, the element does not allow any special features and KEYOPT(3) = 2 is not applicable.

PLANE13 Product Restrictions

There are no product-specific restrictions for this element.

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