FEM: Esempio di capacità di due palline

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This page is a translated version of the page FEM Example Capacitance Two Balls and the translation is 14% complete.
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Base ExampleCommandModel.png Tutorial
Analisi agli elementi finiti
Livello di difficoltà
Tempo di esecuzione
Sudhanshu Dubey
Versione di FreeCAD
0.19 o superiore
Files di esempio


Questo esempio ha lo scopo di mostrare come simulare il sesto esempio di Elmer GUI Tutorials, Equazione elettrostatica - Capacità di due palline , utilizzando i nuovi Esempi di FEM. Illustra come impostare l'esempio, studiarne le varie parti, risolverlo usando il solver Elmer e visualizzare i risultati usando Clip Filter.

Two balls result 2.png


  • A compatible version of FreeCAD designated in the tutorial overview.
    Use the Help → About FreeCAD to see the version of FreeCAD installed
  • No external software is needed for loading the example, viewing the mesh and geometry as well as for visualizing the results.
  • For solving the FEA, the solver software Elmer must be installed on your computer. See Elmer Solver for how to install Elmer.

Set up the example

Load FEM Workbench

  • Start FreeCAD, the Start Workbench should be loaded
  • Switch to Workbench FEM.svg FEM workbench.

Load the example

  • Go to Utilities → FEM Examples.svg Open FEM examples.
  • When the GUI opens, find and open "Electrostatics Capacitance Two Balls". You can easily find the example in All or in Solvers → Elmer. For opening the example, either double click on it or select it and click Setup.

Two balls selection.png

Understanding the Simulation Case

This case presents the solution of the capacitance of perfectly conducting balls in free space. A voltage difference between the balls results to electric charge being introduced to the system. The balls have also self-capacitance that comes from the voltage difference with the far field. Therefore a symmetric capacitance matrix with of size 2 × 2 needs to be solved. The capacitances may be computed from two different voltage configurations.

Understanding the Model

  • The model contains three spheres.
  1. The two smaller ones are the perfectly conducting balls.
  2. The bigger one is to simulate the surrounding air.
  • The two smaller spheres are fused together and then that fusion is is cut from the bigger sphere.

Two balls model full.png

Analysis container and its objects

  • There are at least the 7 objects needed to make this electrostatic analysis.
  • FEM Analysis.png analysis container
  1. FEM SolverElmer.svg Elmer solver
  2. FEM EquationElectrostatic.svg Electrostatic equation
  3. FEM MaterialFluid.svg a fluid material (to represent the surrounding air)
  4. FEM ConstraintElectrostaticPotential.svg electrostatic constraint (3 of them)
  5. Fem-thermomechanical-analysis.svgConstant Vaccum Permittivity
  6. FEM MeshGmshFromShape.svg a Gmsh FEM mesh
  7. FEM MeshRegion.svg Mesh region (for the smaller spheres)

Two balls analysis.png

Running the FEA

  • In Tree view double click on the solver object FEM SolverElmer.svg.
  • Click on Write file in the same task window. Watch the log window until it prints "write completed."
  • Click on Run. Since this is a small analysis it should take a few seconds to run so wait till you see "ELMER SOLVER FINISHED AT" in the output.
  • Click on Close in the task window after the run is finished.
  • Two new result objects should be created, FEM PostPipelineFromResult.svg SolverElmerResult and TextDocument.svg SolverElmerOutput.
  • If you get an error message on solver binary or similar when triggering the analysis check installation of Elmer Solver.

Visualizing Results

  • Be sure the analysis is activated.
  • Be sure the analysis still contains the result object, if not just re-run the solver.
  • Make sure the mesh is invisible. If not, select the mesh object press Space to toggle the visibility.
  • Double click on the FEM PostPipelineFromResult.svg SolverElmerResult to load in the task panel.
  • Change the "Mode" to "Surface" and the "Field" to "potential". Press Ok.
  • You will notice that the colour of the sphere has changed to blue and that the gradient on the right is showing values from 0 to +1. It should look something like this:

Two balls potential.png

Post Processing the Result

  • While we have successfully visualised the potential result, currently we are only seeing the zero potential in the air surrounding the two balls. To view the potential on the balls we need to apply a clip filter.
  • In the tree view select the FEM PostPipelineFromResult.svg SolverElmerResult and then from the tool bar click on the FEM PostFilterClipRegion.svg Post Create Clip Filter.
  • This will open the task panel with the clip filter configurations. Select "Plane" in the "Create" menu and check the "Cut Cells" box. After that click Apply.

Two balls postcreate.png

  • Then choose the same configurations (Surface and potential) as you have while visualising the results. Click Ok. Toggle the visibility of FEM PostPipelineFromResult.svg SolverElmerResult using Space and you should see something like this:

Two balls result.png

  • Now we can clearly see that potential distribution in and around the balls.

Finding the Capacitance

  • Our actual focus is to find the capacitance which is contained in the TextDocument.svg SolverElmerOutput.
  • Double click on TextDocument.svg SolverElmerOutput to open it. Scroll down till you find:
StatElecSolve: Capacitance matrix computation performed (i,j,C_ij)
StatElecSolve:   1  1    5.08013E+00
StatElecSolve:   1  2    1.70071E+00
StatElecSolve:   2  2    5.07960E+00
  • Here, our desired result is C12 = 1.70071. This value is close to the 1.691 given in the Elmer GUI Tutorials. We can get an even closer value by making a finer Mesh Region but this activity is left for the user. Also, the user is advised to play with the Clip Filter to get a visual result similar to the first picture of this tutorial.