FEM MeshGmshFromShape/de

Beschreibung

Für eine Finite-Elemente-Analyse muss die Geometrie in ein FEM-Netz diskretisiert werden. Dieser Befehl verwendet die Software Gmsh (die auf dem System installiert sein muss) zum Erstellen des Netzes.

Abhängig vom Betriebssystem und dem Installationspaket kann Gmsh in FreeCAD enthalten sein oder auch nicht. Für weitere Informationen siehe FEM Installation.

Anwendung

1. Die Form auswählen, die analysiert werden soll. Bei der Volumen-FEM muss es sich um einen Festkörper oder Compsolid (zusammengesetzten Festkörper) handeln. Ein Compsolid ist erforderlich, wenn dein Teil aus mehreren Materialien besteht. (Ein Compsolid kann mit dem Befehl BoolescheFragmente erstellt werden).
2. Das Werkzeug durch eine der folgenden Möglichkeiten aktivieren:
   • Die Schaltfläche FEM-Netz aus Form - Gmsh drücken.
   • Den Menüeintrag Netz → FEM-Netz aus Form - Gmsh auswählen.
3. Wahlweise minimale und maximale Elementgröße anpassen (Die vorgegebene Einstellung erstellt oft zu grobe Netze). Es kann auch die dimensionale Art (1D, 2D, 3D) eingestellt (wobei die Voreinstellung From shape meistens passt) sowie die Ordnung des Elements geändert werden.
4. Die Schaltfläche Anwenden anklicken und warten, bis die Erstellung des Netzes abgeschlossen ist. eingeführt mit Version 1.0: Wahlweise die Schaltfläche Abbrechen drücken, um das Vernetzen abzubrechen.
5. Die Schaltfläche OK drücken, um die Aufgabe abschließen. Jetzt sollte sich ein neues FEMMeshGmsh-Objekt im aktiven Analysebehälter befinden. Oder die Schaltfläche Abbrechen drücken, um die Änderung oder die Erstellung des Netzobjekts abzubrechen.

Nachdem das Netz erstellt wurde, können seine Eigenschaften im Eigenschafteneditor angepasst werden. Nach dem Ändern einer Eigenschaft, muss der Gmsh-Dialog erneut geöffnet und die Schaltfläche Anwenden gedrückt werden (der Dialog kann geöffnet bleiben, während weitere Eigenschaften geändert werden).

The Gmsh version button allows you to check the details about the currently linked Gmsh binary.

Eigenschaften

• DatenAlgorithm2D: The algorithm to create 2D meshes. The different algorithms are explained here. For Delaunay, see Delaunay triangulation.
• DatenAlgorithm3D: The algorithm to create 3D meshes. The different algorithms are explained here.
• DatenCharacteristic Length Max: The maximal size of the mesh elements. If set to 0.0, the size will be set automatically. This property can also be changed in the Gmsh dialog in the field Max element size.
• DatenCharacteristic Length Min: The minimal size of the mesh elements. If set to 0.0, the size will be set automatically. This property can also be changed in the Gmsh dialog in the field Min element size.
• DatenCoherence Mesh:
  • true (default); duplicate mesh nodes will be removed
  • false
• DatenElement Dimension: The dimension of the mesh elements. This property can also be changed in the Gmsh dialog in the field Mesh element dimension.
  • From Shape (default); the dimension will be determined from the dimension of the object that is meshed
  • 1D
  • 2D
  • 3D
• DatenElement Order: The mesh element order. This property can also be changed in the Gmsh dialog in the field Mesh order. introduced in 0.20
  • 1st
  • 2nd (default)
    Note: If you use the solver Elmer you may get this error: ERROR:: GetEdgeBasis: Can't handle but linear elements, sorry. This means the solver equation cannot handle 2nd order meshes. Use either 1st order meshes then, or check the FreeCAD Wiki page for the solver equation for possible options to handle 2nd order meshes.
• DatenGeometrical Tolerance: The geometrical tolerance for the mesh to match the object edges. The default 0.0 means that Gmsh's default of 1e-8 is used.
• DatenGroups Of Nodes: All nodes and not only the elements will be saved for each physical mesh group. Physical groups are collections of mesh entities (points, curves, surfaces and volumes). They and are identified by their dimension and by a tag. For example a mesh of the same object region is internally tagged the same. So all surfaces of this region will form one physical group.
• DatenHigh Order Optimize: If and how meshes with DatenElement Order = 2nd are optimized. The optimization is done by a deformation of the element borders.
  introduced in 0.20 Gmsh supports different optimization algorithms. Elastic is an algorithm in which the mesh elements are treated as a collection of deformable viscoelastic solids. 1st order meshes cannot be optimized because their element borders are linear an cannot be deformed.
• DatenMesh Size From Curvature introduced in 0.20: The number of mesh elements per ${\displaystyle 2\pi }$ times the radius of the curvature. To get a finer mesh at small corners or holes, this value can be increased for better results

Effect of Mesh Size From Curvature'; left: set to 12, right: deactivated

• DatenOptimize Netgen: Whether the mesh will be optimized using the 3D mesh generator Netgen to improve the quality of tetrahedral elements. Note: since Netgen can only create tetrahedral elements, this option is ignored for meshes whose DatenElement Dimension is not 3D.
• DatenRecombination Algorithm introduced in 0.20: The algorithm used for DatenRecombine 3D All and also for DatenRecombine All. For more info, see section Element Recombination and for technical details see the Gmsh documentation.
• DatenRecombine 3D All introduced in 0.20: Applies a recombination 3D-algorithm to all volumes. Tetrahedra will be recombined into prisms, hexahedra or pyramids if possible.
• DatenRecombine All: Applies a recombination algorithm to all surfaces. Triangles will be recombined into quadrangles when possible.
• DatenOptimize Std Optimizes the mesh to improve the quality of tetrahedral elements.
• DatenSecond Order Linear: Option if second order nodes (if DatenElement Order set to 2nd) and/or mesh refinement points are created by linear interpolation.
  • true; linear interpolation is used
  • false (default); curvilinear interpolation is used
• DatenSubdivision Algorithm introduced in 1.0: allows the creation of quadrilateral and hexahedral elements by subdivision
  • None; doesn't use any subdivision algorithm
  • All Quadrangles; creates quadrilateral elements by subdivision
  • All Hexahedra; creates hexahedral elements by subdivision
  • Barycentric; creates triangular elements by barycentric subdivision

Hinweise

Nonpositive Jacobians

When you get a meshing error about nonpositive Jacobians, you can try out the following strategies:

• Set DatenSecond Order Linear to true but keep DatenElement Order at 2nd.
• Set DatenElement Order to 1st.
• Use a smaller element size by reducing the DatenCharacteristic Length Max.
• If solver ccxtools is used and the run button is used (not the task panel) the nodes of nonpositive jacobian elements will be green.

Mesh Growth

At edges and small geometric entities, the mesh has to be smaller than in areas without edges. So the mesh element size grows away from the edges. The growing strategy of Gmsh is to grow between edges of different sizes. So the growing fails when an area has the same sized edges like for example this tube:

Failing mesh growing because the cylindrical area is surrounded by the same edges

To enable a sensible mesh growing, you must in this case add an edge to the area. In the example, this would be a circle in the middle of the cylinder. The circle is added as part of a BooleanFragments compound (to form a CompSolid), see the project file of the example.

Sensible mesh growing due to the additional edge in the middle of the cylindrical area

Element Recombination

Elements can be recombined in two ways, on the surface of objects so that triangles will be recombined into quadrangles if possible and in the volume of objects so that tetrahedra will be recombined into prisms, hexahedra or pyramids if possible. Thinking about the geometry, it becomes clear that the recombination result depends strongly on the geometry of the body and that recombining a 3D body only at the surface will mostly lead to strange results.

To illustrate this, look at the image below. A cuboid body is meshed using the standard settings (tetrahedra, 2nd order mesh). This is the subimage at the upper left. The image at the upper right shows the result, when additionally the elements are recombined only at the surface of the body. The result is bad because the changed surface elements don't fit to the unchanged volume elements. So DatenRecombine All alone usually only makes sense for 2D meshes.
When we use now also DatenRecombine 3D All, the result is better, see the lower left subimage. However, the result doesn't show a great difference compared to the mesh without recombinations. Since our body is a cuboid, it is therefore sensible to use a recombination algorithm that tries to create cuboids as well. And this result is shown in the subimage at the lower right.

The Simple recombination algorithm will leave some triangles in the mesh in case the recombining leads to badly shaped quads. In such cases use a full-quad recombination algorithm, which will automatically perform a coarser mesh followed by the recombination, smoothing and subdividing. See forum topic

Effect of mesh element recombination.
Upper left: standard mesh.
Upper right: recombination only at the surface using the Simple algorithm.
Lower left: recombination at the surface and in the volume using the Simple algorithm.
Lower right: recombination at the surface and in the volume using the Simple full-quad algorithm