The procedure for doing an electrostatic analysis consists of three main steps:
Build the model.
Apply loads and obtain the solution.
Review the results.
The next few topics discuss what you must do to perform these steps. First, the text presents a general description of the tasks required to complete each step. An example follows, based on an analysis of electrostatic forces between charge spheres. The example walks you through doing the analysis by choosing items from Mechanical APDL' GUI menus, then shows you how to perform the same analysis using APDL commands.
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.
For an electrostatic analysis, you must define the permittivity (PERX) material property. It can be temperature dependent, as well as isotropic or orthotropic.
In Mechanical APDL, you must make sure that you use a consistent system of units for all the data you enter. See the EMUNIT command in the Command Reference for additional information regarding appropriate settings of free-space permeability and permittivity.
For micro-electromechanical systems (MEMS), it is best to set up problems in more convenient units since components may only be a few microns in size. For convenience, see Table 13.4: Electrical Conversion Factors for MKS to muMKSV and Table 13.5: Electrical Conversion Factors for MKS to muMSVfA.
Table 13.4: Electrical Conversion Factors for MKS to muMKSV
| Electrical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain μMKSV Unit | Dimension |
|---|---|---|---|---|---|
| Voltage | V | (kg)(m)2/(A)(s)3 | 1 | V | (kg)(μm)2/(pA)(s)3 |
| Current | A | A | 1012 | pA | pA |
| Charge | C | (A)(s) | 1012 | pC | (pA)(s) |
| Conductivity | S/m | (A)2(s)3/(kg)(m)3 | 106 | pS/μm | (pA)2(s)3/(kg)(μm)3 |
| Resistivity | Ωm | (kg)(m)3/(A)2(s)3 | 10-6 | T Ωμm | (kg)(μm)3/(pA)2(s)3 |
| Permittivity[1] | F/m | (A)2(s)4/(kg)(m)3 | 106 | pF/μm | (pA)2(s)2/(kg)(μm)3 |
| Energy | J | (kg)(m)2/(s)2 | 1012 | pJ | (kg)(μm)2/(s)2 |
| Capacitance | F | (A)2(s)4/(kg)(m)2 | 1012 | pF | (pA)2(s)4/(kg)(μm)2 |
| Electric Field | V/m | (kg)(m)/(s)3(A) | 10-6 | V/μm | (kg)(μm)/(s)3(pA) |
| Electric Flux Density | C/(m)2 | (A)(s)/(m)2 | 1 | pC/(μm)2 | (pA)(s)/(μm)2 |
Table 13.5: Electrical Conversion Factors for MKS to muMSVfA
| Electrical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain μMKSVfA Unit | Dimension |
|---|---|---|---|---|---|
| Voltage | V | (kg)(m)2/(A)(s)3 | 1 | V | (g)(μm)2/(fA)(s)3 |
| Current | A | A | 1015 | fA | fA |
| Charge | C | (A)(s) | 1015 | fC | (fA)(s) |
| Conductivity | S/m | (A)2(s)3/(kg)(m)3 | 109 | fS/μm | (fA)2(s)3/(g)(μm)3 |
| Resistivity | Ωm | (Kg)(m3/(A)2(s)3 | 10-9 | - | (g)(μm)3/(fA)2(s)3 |
| Permittivity[1] | F/m | (A)2(s)4/(kg)(m)3 | 109 | fF/μm | (fA)2(s)2/(g)(μm)3 |
| Energy | J | (kg)(m)2/(s)2 | 1015 | fJ | (g)(μm)2/(s)2 |
| Capacitance | F | (A)2(s)4/(kg)(m)2 | 1015 | fF | (fA)2(s)4/(g)(μm)2 |
| Electric Field | V/m | (kg)(m)/(s)3(A) | 10-6 | V/μm | (g)(μm)/(s)3(fA) |
| Electric Flux Density | C/(m)2 | (A)(s)/(m)2 | 103 | fC/(μm)2 | (fA)(s)/(μm)2 |
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 these tasks.
To enter the SOLUTION processor, use either of the following:
To specify the analysis type, do either of the following:
In the GUI, choose menu path and choose a Static 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 an electrostatic 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 select the sparse solver (default), Preconditioned Conjugate Gradient (PCG) solver, Jacobi Conjugate Gradient (JCG) solver, or Incomplete Cholesky Conjugate Gradient (ICCG) solver.
To select an equation solver, use either of the following:
If you choose either the JCG solver or the PCG solver, you can also specify a solver tolerance value. This value defaults to 1.0E-8.
These loads specify flux-parallel, flux-normal, far-field, and periodic boundary conditions, as well as an imposed external magnetic field. The following table shows the value of volt required for each type of boundary condition:
| Boundary Condition | Value of VOLT |
|---|---|
| Flux-parallel | None required (naturally occurring). |
| Flux-normal | Specify a constant value of VOLT using the D command (. |
| Far-field | For 2D analysis, use INFIN110 elements. For 3D analysis, use INFIN47 or INFIN111 elements. |
| Imposed external field | Apply nonzero values of VOLT. Use . |
Flux-parallel boundary conditions force the flux to flow parallel to a surface, while flux-normal boundary conditions force the flux to flow normal to a surface. You do not need to specify far-field zero boundary conditions if you use far-field elements to represent the "infinite" boundary of the model. For an imposed external field, specify the appropriate nonzero value of VOLT.
You can apply loads to an electrostatic 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:
These loads are DOF constraints that you usually specify at model boundaries to apply a known voltage. To apply voltage, use one of the following:
These are concentrated nodal-force loads. To apply them, use the following command or GUI path:
These are surface loads you can apply at nodes or elements. To apply them, use the following command or GUI path:
Infinite surface flags are not actual loads, but they are used to indicate which surface of an infinite element faces toward the open (infinite) domain. Applying the INF label to an element face turns the flag on for that face. To apply infinite surface flags, choose one of the following:
These are body loads you can apply at nodes or elements. To apply volume charge densities, use the commands or GUI path shown below:
Alternatively, you can apply volume charge densities to lines, areas, and volumes of the solid model by using the BFL, BFA, and BFV commands, respectively. You can then transfer the specified volume charge densities from the solid model to the finite element model by using either the BFTRAN command or the SBCTRAN command.
For an electrostatic analysis, you can optionally use other commands to apply loads to a current conduction analysis, and you also can specify output controls as load step options. For further information, see Alternative Analysis Options and Solution Methods.
Use the SAVE_DB button on the Toolbar to save a backup copy of the database. This enables you to retrieve your model should your computer fail while the analysis is in progress. To retrieve a model, re-enter Mechanical APDL and use one of the following:
In this step, you initiate the solution for all loads steps using one of the following:
If you wish to apply any additional loading conditions (load steps), repeat the appropriate steps described in the foregoing.
To leave the SOLUTION processor, use either of the following:
The program writes results from an electrostatic analysis to the results file, Jobname.rth. Results include the data listed below:
Primary data: Nodal voltages (VOLT)
Derived data:
Nodal and element electric field (EFX, EFY, EFZ, EFSUM)
Nodal electric flux density (DX, DY, DZ, DSUM)
Nodal electrostatic forces (FMAG: components X, Y, Z, SUM)
Nodal reaction current segment (CSGZ)
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) 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, Mechanical APDL performs linear interpolation to calculate the results at that time.
To gain access to derived results, you must use one of the following commands or menu paths after you have read the results into the database:
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.
For contour displays, use either of the following methods:
For vector (arrow) displays, use either of the following methods:
You can find details on how to graphically display a charged particle traveling in a magnetic field in Charged Particle Traces and Controlling Charged Particle Trace Displays in the Basic Analysis Guide. See Electromagnetic Particle Tracing in the Mechanical APDL Theory Reference for more details.
To produce tabular data listings, use any of the following:
POST1 performs many other postprocessing functions, including mapping results onto a path and load case combinations. For more information, see the Basic Analysis Guide.
You can summarize total electrostatic force and torque on a given set of nodes from the data available in the database in postprocessing. Use the EMFT macro for these calculations. The EMFT macro is available only for PLANE121, SOLID122, and SOLID123 elements.
Three types of magnetic forces are usually available:
Current segment force: Force from the finite element boundary domain. Forces and fields here are typically normal to the capacitor surface. To list these forces:
Reluctance force: Force due to a change in material properties. Here, the direction of the field may be arbitrary with regard to the force. To list this force:
Select the nodes at the interface between the body of interest and the adjacent air elements.
Select all elements.
Issue EMFT.
This method may use a truncated portion of the body of interest if the body extends past the FE boundary.
Body forces (including Lorentz forces): This method uses the entire body of interest:
Select the nodes of the body of interest and all elements.
Issue EMFT.
Note: In models that use symmetry, you must select nodes and elements carefully. You need to select the surface nodes on the surfaces interior to the body and then select the elements adjacent to those nodes.
Force results will be reported in the coordinate system specified by RSYS. However, if using a coordinate system other than global Cartesian (RSYS ≠ 0), torque results will take into account the coordinate system shift and rotation only.