Steady-state current conduction analysis determines the current density and electric potential (voltage) distribution caused by direct current (DC) or potential drop. You can apply two types of loads in this analysis: voltage and electric current. Refer to Electromagnetics in the Mechanical APDL Theory Reference for more information.
A steady-state current conduction analysis is assumed to be linear. That is, the electric current is proportional to the applied voltage.
The procedure for doing a steady-state current conduction analysis consists of three main steps:
The next few topics discuss what you must do to perform these steps.
To build the model, you start by specifying the jobname and a title for your analysis, using the following commands or GUI paths:
If you are using the GUI, the next step is to set preferences for an electric analysis:
You must set the preference to Electric to ensure that the elements needed for your analysis will be available. (The GUI filters element types based on the preference you choose.)
Once you have set the Electric preference, use the preprocessor (PREP7) to define the element types, the material properties, and the model geometry. These tasks are common to most analyses. The Modeling and Meshing Guide explains them in detail.
You can use the following types of elements in a steady-state current conduction analysis:
Table 12.9: Elements Used in a Steady-State Analysis
| Element | Dimens. | Type |
|---|---|---|
| LINK68 | 3D | Two node thermal /electric line |
| PLANE230 | 2D | Eight node electric quadrilateral |
| SOLID5 | 3D | Eight node structural/thermal/magnetic/electric hexahedral |
| SOLID98 | 3D | Ten node structural/thermal/magnetic/electric tetrahedral |
| SOLID231 | 3D | Twenty node electric hexahedral |
| SOLID232 | 3D | Ten node electric tetrahedral |
| SHELL157 | 3D | Four node thermal/electric shell |
| MATRIX50 | 3D | Superelement |
You must specify electric resistivity values RSVX, RSVY, and RSVZ using the MP command. These properties may be constant or temperature dependent.
In this step, you define the analysis type and options, apply loads to the model, specify load step options, and initiate the finite element solution. The next few topics explain how to perform the following tasks:
To specify the analysis type, do either of the following:
In the GUI, choose menu path and choose a Steady-state analysis.
If this is a new analysis, issue the command ANTYPE,STATIC,NEW.
If you want to restart a previous analysis (for example, to specify additional loads), issue the command ANTYPE,STATIC,REST. You can restart an analysis only if you previously completed a steady-state analysis, and the files Jobname.emat, Jobname.esav, and Jobname.db from the previous run are available.
Next, you define which solver you want to use. You can use the sparse solver (default), the Jacobi Conjugate Gradient (JCG) solver, the Incomplete Cholesky Conjugate Gradient (ICCG) solver, or the Preconditioned Conjugate Gradient solver (PCG).
To select an equation solver, use either of the following:
You can apply loads to a steady-state analysis either on the solid model (keypoints, lines, and areas) or on the finite element model (nodes and elements). You can specify several types of loads:
Electric currents (AMPS) are concentrated nodal loads that you usually specify at model boundaries (the label AMPS is just a load label; it does not indicate the units of measurement). A positive value of current indicates current flowing into the node. For a uniform current density distribution, couple the appropriate nodes in the VOLT degree of freedom, and apply the full current at one of the nodes.
To apply current, use one of the following:
Voltages are DOF constraints that you usually specify at model boundaries to apply a known voltage. A typical approach specifies a zero voltage at one end of the conductor (the "ground" end) and a desired voltage at the other end.
To apply voltage, use the following command or GUI path:
You can also apply current and voltage loads using the independent current and voltage source options of CIRCU124. For more information, refer to Electric Circuit Analysis.
Optionally, you can use other commands to apply loads to a steady-state analysis, and you also can specify output controls as load step options. For information about using these commands to apply loads and about the load step options available for steady-state analysis, see Alternative Analysis Options and Solution Methods.
In this step, you initiate the solution for all load steps using one of the following:
The program writes results from a steady-state current conduction analysis to the results file, Jobname.rth (or to Jobname.rst if other degrees of freedom are available besides VOLT). Results include the data listed below:
Primary data: Nodal voltages (VOLT).
Derived data:
You can review analysis results in POST1, the general postprocessor. To access the postprocessor, choose one of the following:
For a complete description of all postprocessing functions, see the Basic Analysis Guide.
To review results in POST1, the database must contain the same model for which the solution was calculated. Also, the results file (Jobname.rth or Jobname.rst) must be available.
To read results at the desired time point into the database, use either of the following:
If you specify a time value for which no results are available, the program performs linear interpolation to calculate the results at that time.
To identify the results data you want, use a combination of a label and a sequence number or component name.
You can now review the results by obtaining graphics displays and tabular listings. To obtain these, use the following:
To gain access to certain element results data that are not otherwise directly accessible, you must use the following commands or menu paths after you have read the results into the database:
POST1 performs many other postprocessing functions, including mapping results onto a path and load case combinations. For more information, see the Basic Analysis Guide manual.
A key parameter from an electric solution is conductance. For multiple conductor systems, this involves extracting self and mutual conductance terms so that equivalent circuit lumped conductors can be defined for use in circuit simulators. The GMATRIX command macro has been developed to extract self and mutual conductance terms for multiple conductor systems.
See the Mechanical APDL Theory Reference for more details.
GMATRIX works with the following elements:
Finite element simulation can readily compute and extract a "Ground" conductance matrix of conductance values that relate the current on one conductor with the conductor's voltage drop (to ground). Figure 12.1: Three Conductor System illustrates a three-conductor system (one conductor is ground). The following two equations relate currents on electrodes 1 and 2, I1 and I2, with the voltage drops for the electrodes, V1 and V2:
where Gg represents a matrix of conductances referred to as "ground conductances". These ground conductances do not represent lumped conductances typically used in a circuit simulator because they do not relate the conductances between conductors. However, the GMATRIX command macro can convert the ground conductance matrix to a lumped conductance matrix which is suitable for use in circuit simulators. Figure 12.2: Lumped Conductor Equivalence of Three Conductor System illustrates the lumped conductances between the conductors. The following two equations then relate the currents with the voltage drops:
In the equations above, conductance is in Siemens (1/Ω).
where Gl represents a matrix of conductances referred to as "lumped conductances".
The GMATRIX command macro will perform multiple simulations and extract both the ground conductance matrix values and the lumped conductance matrix values. To prepare for GMATRIX, you must group the conductor nodes into node components. Do not apply any loads to the model (voltages, current, etc.). The component name applied to the conductor nodes must contain a common prefix, followed by a numerical suffix progressing from 1 to the highest numbered conductor in the system. The last numbered conductor in the system must be the ground conductor (the conductor whose potential is assumed to be zero). The procedure for using GMATRIX is as follows:
Build and mesh the solid model with electric elements. Conductors are assumed to be perfect conductors and hence do not require a finite element mesh within the conductor domain. Only the surrounding conductive regions require a mesh. The resulting nodes on the boundary of the conductors represent the nodes that will be grouped into node components.
Select the nodes on the surface of the each conductor and group them into node components:
Command(s): CMGUI:Share a command prefix for the component names, and use a numerical value sequencing from 1 to the highest numbered conductor. For example, in Figure 12.2: Lumped Conductor Equivalence of Three Conductor System, three node components would be defined for each set of conductor nodes. Using a prefix "cond", the node component names would be "cond1", "cond2", and "cond3". The last component, "cond3", would be the nodes representing the ground.
Enter the SOLUTION processor:
Command(s): SOLUGUI:Select an equation solver (sparse or ICCG solver recommended):
Command(s): EQSLVGUI:Invoke the GMATRIX macro:
Command(s): GMATRIXGUI:The GMATRIX command macro requires the following input:
A symmetry factor (
SYMFAC). If there is no symmetry in the model, the symmetry factor is 1 (default). If you wish to model only a portion of the model by taking advantage of symmetry, use the symmetry factor as a multiplier to obtain the correct conductance.The node component prefix name (
Condname). This is the prefix of the node component names used to define the conductor node components. In the above example, the prefix name is "cond". The command macro requires that you put single quotes around the prefix name when entering the character string. Thus, the input for this example would be 'cond'. In the GUI, the single quotes are automatically handled by the program.The number of conductor node components (
NUMCOND). Insert the total number of conductor node components. In the above example, you would use "3".Enter a name for the stored matrix of conductance values (
Matrixname). The command macro stores the computed ground and lumped matrix values in a 3D array vector where the "i" and "j" columns represent the conductor indices, the "k" column indicates ground (k = 1) or lumped (k = 2) terms. The default name is GMATRIX. For example, the command macro stores the ground terms in GMATRIX(i,j,1) and the lumped terms in GMATRIX(i,j,2). The command macro also creates a text file containing the matrix values and stores it in a file with the stored matrix name and a .TXT extension.
Do not apply inhomogeneous loads before using the GMATRIX command. Inhomogeneous loads are those created by:
GMATRIX executes a series of solutions to compute self and mutual conductance between conductors. The solutions, which are stored in the results file, are available for postprocessing, if desired. At the end of the execution, the command macro presents a summary table.