FreeCAD 2D Axisymmetric FEM Modeling Guide

This guide provides a step-by-step overview of setting up and running a two-dimensional (2D) axisymmetric Finite Element Method (FEM) simulation using FreeCAD and the integrated CalculiX solver. By reducing a rotationally symmetric 3D component to a 2D planar cross-section, you can dramatically decrease computational time while maintaining high analytical accuracy. The process covers profile modeling, coordinate alignment, material and element property definition, meshing with Gmsh, boundary condition application, and result evaluation.

1. Model the 2D Cross-Section

  1. Open FreeCAD and switch to the Sketcher Workbench.
  2. Create a new sketch on the X-Y Plane.
  3. Draw half of the cross-section of your rotationally symmetric body.
  4. Crucial Alignment Rules for CalculiX:
    • The axis of revolution must be the Y-axis (\(X = 0\)).
    • The entire geometry must exist in the positive X domain (\(X \ge 0\)). No part of the sketch may cross into negative X coordinates.
  5. Close the sketch, switch to the Part Workbench, and use the Make face from wires tool (or use a Part Design Body with a planar face) to convert the closed profile into a 2D surface.

2. Set Up the FEM Analysis Container

  1. Switch to the FEM Workbench.
  2. Click the Analysis container button (yellow capital 'A' icon) to initialize the simulation tree.
  3. Select your 2D face object and click FEM mesh from shape by Gmsh.
  4. In the Gmsh task panel:
    • Set the Element dimension to 2D.
    • Set the element order to Second order (quadratic elements, such as 8-node quadrilaterals or 6-node triangles, yield superior accuracy for axisymmetric stress calculations).
    • Define the max and min element sizes appropriate for your geometry.
  5. Click Apply, then OK to generate the planar surface mesh.

3. Assign 2D Axisymmetric Element Properties

  1. In the FEM Workbench toolbar, select Element geometry 2D (represented by a 2D sheet icon).
  2. In the properties panel, change the Element Type dropdown to Axisymmetric.
  3. Select your 2D planar face as the geometry reference and click OK. This signals CalculiX to expand the 2D elements mathematically into 3D rings during matrix formulation.

4. Assign Material and Loads

  1. Click Material for solid to open the material properties panel.
  2. Choose a preset material (e.g., Steel-Generic) or define your own Young's modulus and Poisson's ratio, then ensure your geometry is added to the selection list.
  3. Apply structural boundary conditions:
    • Constraint Fixed / Displacement: Select edges to restrain. Edges lying precisely along the Y-axis (\(X = 0\)) can be allowed to slide axially while being constrained radially (\(X\)-direction displacement = 0 mm) to respect the axis of symmetry.
    • Constraint Pressure / Force: Select the target boundary edges to apply internal or external pressure loads.

5. Configure and Run the Solver

  1. Double-click the SolverCalculiX object inside the Analysis container.
  2. In the solver properties, ensure the analysis type is set to Static.
  3. In the Task panel:
    • Click Write .inp file to generate the CalculiX input deck.
    • Click Run CalculiX to execute the simulation.

6. Post-Processing

  1. Once the solver finishes with no errors, a results object will appear in the tree view.
  2. Double-click the results object or use the Post Pipeline from Result tool to view scalar fields such as von Mises stress, radial displacement, or axial displacement directly mapped on the 2D planar profile.