2-D 8-Node
Electrostatic Solid
PLANE121 Element Description
PLANE121 is a 2-D, 8-node, charge-based electric element. The element has one degree of freedom, voltage, at each node. The 8-node 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 2-D electrostatic and time-harmonic quasistatic electric field analyses. Various printout options are also available. See PLANE121 in the Mechanical APDL Theory Reference for more details about this element.
PLANE121 Input Data
The geometry, node locations, and the coordinate system for this element are shown in Figure 121.1: PLANE121 Geometry. The element is defined by eight nodes and orthotropic material properties. A triangular-shaped element may be formed by defining the same node number for nodes K, L and O.
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= CHRG) 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.
Element loads are described in Nodal Loading. Surface charge densities may be input as surface loads at the element faces as shown by the circled numbers in Figure 121.1: PLANE121 Geometry. Charge densities may be input as element body loads at the nodes. If the node I charge density CHRGD(I) is input, and all others are unspecified, they default to CHRGD(I). If all corner node charge densities are specified, each midside node charge density defaults to the average charge density of its adjacent corner nodes.
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 "PLANE121 Input Summary". A general description of element input is given in Element Input. For axisymmetric applications see Harmonic Axisymmetric Elements.
PLANE121 Input Summary
- Nodes
I, J, K, L, M, N, O, P
- Degrees of Freedom
VOLT
- Real Constants
THK - Thickness (used only if KEYOPT(3) = 3)
- Material Properties
MP command: PERX, PERY, LSST, RSVX, RSVY
EMUNIT command: EPZRO
- Surface Loads
- Surface charge densities --
CHRGS face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)
- Body Loads
- Temperature --
T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P)
- Volume charge densities --
CHRGD(I), CHRGD(J), CHRGD(K), CHRGD(L), CHRGD(M), CHRGD(N), CHRGD(O), CHRGD(P)
- Special Features
- KEYOPT(3)
Element behavior:
- 0 --
Plane
- 1 --
Axisymmetric
- 3 --
Plane with thickness input, specified via real constant THK.
- KEYOPT(4)
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
- KEYOPT(5)
Extra element output:
- 0 --
Basic element printout
- 1 --
Repeat basic solution for all integration points
- 2 --
Nodal fields printout
- KEYOPT(6)
Electric charge reaction sign:
- 0 --
Positive
- 1 --
Negative
PLANE121 Output Data
The solution output associated with the element is in two forms:
Nodal degrees of freedom included in the overall nodal solution
Additional element output as shown in Table 121.1: PLANE121 Element Output Definitions
Several items are illustrated in Figure 121.2: PLANE121 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.
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 121.1: PLANE121 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | Y | Y |
| NODES | Nodes - I, J, K, L, M, N, O, P | Y | Y |
| MAT | Material number | Y | Y |
| VOLU: | Volume | Y | Y |
| XC, YC | Location where results are reported | Y | 2 |
| TEMP | Temperatures T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) | Y | Y |
| LOC | Output location (X, Y) | 1 | 1 |
| PERX, PERY | Electric relative permittivity | 1 | 1 |
| EF:X, Y | Electric field components | 1 | 1 |
| EF:SUM | Vector magnitude of EF | 1 | 1 |
| D:X, Y | Electric flux density components | 1 | 1 |
| D:SUM | Vector magnitude of D | 1 | 1 |
| JS:X, Y, SUM | Current density components (in the global Cartesian coordinate system) and vector magnitude [3] | 1 | 1 |
| JT:X, Y, SUM | Conduction current density components and magnitude [3] | 1 | 1 |
| JHEAT: | Joule heat generation rate per unit volume [4] [5] [6] | 1 | 1 |
| SENE: | Stored electric energy [6] | 1 | 1 |
| FMAG:X, Y | Electrostatic force [7] | - | 1 |
| CHRGD | Applied charge density | - | Y |
The solution value is output only if calculated (based upon input data). The element solution is at the centroid.
Available only at centroid as a *GET item.
For a time-harmonic analysis, 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.
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.
Calculated Joule heat generation rate per unit volume (JHEAT) may be made available for a subsequent thermal analysis with companion elements [LDREAD].
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.
Use the EMFT macro to calculate the force distribution over the body. See the discussion on Electrostatic Forces in the Low-Frequency Electromagnetic Analysis Guide.
Note: For axisymmetric solutions with KEYOPT(4) = 0, the X and Y directions correspond to the radial and axial directions, respectively.
Table 121.3: PLANE121 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 121.3: PLANE121 Item and Sequence Numbers:
- Name
output quantity as defined in the Table 121.1: PLANE121 Element Output Definitions
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
PLANE121 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 121.2: PLANE121 Output, 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 potential varies linearly, rather than parabolically, along that face. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information about the use of midside nodes.
This element is only compatible with elements having a VOLT DOF and an electric charge reaction solution. Electric charge reactions must all be positive or negative. KEYOPT(6) sets the electric charge reaction sign. See Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide for more information.