3-D 20-Node Electric Solid

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SOLID231 Element Description

SOLID231 is a 3-D 20-node, current-based electric element. The element has one degree of freedom, voltage, at each node. It can tolerate irregular shapes without much loss of accuracy. SOLID231 elements have compatible voltage shapes and are well suited to model curved boundaries.

This element is based on the electric scalar potential formulation and it is applicable to the following low frequency electric field analyses: steady-state electric conduction, time-harmonic quasistatic and transient quasistatic. See SOLID231 - 3-D 20-Node Electric Solid in the Mechanical APDL Theory Reference for more details about this element.

Figure 231.1:  SOLID231 Geometry

SOLID231 Geometry

SOLID231 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 231.1: SOLID231 Geometry. The element is defined by 20 node points and the material properties. The type of units (MKS or user defined) is specified through the EMUNIT command. EMUNIT also determines the value of EPZRO. The EMUNIT defaults are MKS units and EPZRO = 8.854 x 10-12 Farad/meter. A prism-shaped element may be formed by defining duplicate K, L, and S; A and B; and O, P, and W node numbers. A pyramid-shaped element and a tetrahedral-shaped element may also be formed as shown in Figure 231.1: SOLID231 Geometry.

Orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Properties not input default as described in the Material Reference.

Nodal loads are defined with the D (Lab = VOLT) and F (Lab = AMPS) commands. The temperature (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.

A summary of the element input is given in "SOLID231 Input Summary". A general description of element input is given in Element Input.

SOLID231 Input Summary


I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A, B

Degrees of Freedom


Real Constants


Material Properties



Surface Loads


Body Loads
Temperature --

T(I), T(J), ..., T(Z), T(A), T(B)

Special Features

Birth and death



SOLID231 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 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 231.1:  SOLID231 Element Output Definitions

ELElement NumberYY
NODESNodes - I, J, K, L, M, N, O, PYY
MATMaterial numberYY
XC, YC, ZCLocation where results are reportedY2
TEMPTemperatures T(I), T(J), ..., T(Z), T(A), T(B)YY
LOCOutput location (X, Y, Z)1-
EF:X, Y, Z, SUMElectric field components and vector magnitude11
JC:X, Y, Z, SUMNodal conduction current density components and vector magnitude11
JS:X, Y, Z, SUM Current density components (in the global Cartesian coordinate system) and vector magnitude [3]-1
JT:X, Y, Z, SUMElement conduction current density components and magnitude [3]-1
JHEAT:Joule heat generation rate per unit volume [4] [5] [6]-1
SENE:Stored electric energy [6]-1
D:X, Y, Z, SUMElectric flux density components and vector magnitude-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. JS represents the sum of element conduction and displacement current densities. JT represents the element conduction current density. The element displacement current density (JD) can be derived from JS and JT as JD = JS-JT. JS can be used as a source current density for a subsequent magnetostatic analysis with companion elements [LDREAD].

  4. For a time-harmonic analysis, calculated Joule heat generation rate per unit volume (JHEAT) includes conduction heating and dielectric heating due to the loss tangent.

  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 a time-harmonic analysis, Joule losses (JHEAT) and stored energy (SENE) represent time-average values. These values are stored in both the real and imaginary data sets.

Table 231.2: SOLID231 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 The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 231.2: SOLID231 Item and Sequence Numbers:


output quantity as defined in Table 231.1: SOLID231 Element Output Definitions


predetermined Item label for ETABLE command


sequence number for single-valued or constant element data

Table 231.2:  SOLID231 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

SOLID231 Assumptions and Restrictions

  • The element must not have a zero volume or a zero length side. This occurs most frequently when the element is not numbered properly. Elements may be numbered either as shown in Figure 231.1: SOLID231 Geometry or in an opposite fashion.

  • An edge with a removed midside node implies that the potential varies 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.

  • Degeneration to the form of pyramid should be used with caution. The element sizes, when degenerated, should be small in order to minimize the field gradients. Pyramid elements are best used as filler elements in meshing transition zones.

  • This element is only compatible with elements having a VOLT degree of freedom and an electric current reaction solution. See Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide) for more information.

  • The solenoidal current density is required for a solution, or for any postprocessing operations.

SOLID231 Product Restrictions

There are no product-specific restrictions for this element.

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