Understanding what NetGen is doing!

When using FreeCAD 0.17 it is not that difficult to make a simulation of something pressuring a cube that is fixed to the ground. I’t a simple case where we follow the typical simulation procedure… Make drawing, define boundary conditions, generate mesh, solve and get results.

Simulation Process Steps
Simulation Process Steps

I can understand that I need boundary conditions since these are the essence of the problem. But the mesh seems out of place. Or not… It is the building block of the finite element method where we describe a complex geometry into multiple small connected elements. The mesher will transform the solid in building blocks that represent the geometry we wish to study. We can use a mirrad of element types (block shapes) and the mathematical formulations they hold. NetGen should not be any different it can have tetrahedrons, hexahedrons, … and each specific nodes required…

But a question which came to my mind was how would the element shape originator and the element formulation originator work. Are they the same?Why I make this question? In freeCAD I generate a mesh with NetGen or Gmsh, however I solve it with Calculix and not the solver from NGSolve or Gmsh.

Before attempting a solution, a mesh is generated and thus the shape of the elements is defined and from the images they look tetrahedrons.

Paper Clip tetrahedron Mesh
Paper Clip tetrahedron Mesh
Paper Clip Circular section Mesh
Paper Clip Circular section Mesh

I found an answer to my questions in a paper written by one of the Authors of NetGen: Joachim Schöberl: An advancing front 2D/3D-mesh generator based on abstract rules.

The mesh is generated according to a specific sequence from a geometry. First special points are gathered on the corners of the target geometry, next edges have to be detected to then create a surface mesh that follows specific element shape rules; the final step is to create a volume mesh from the surface mesh and another specific rules necessary for element quality.

The output should be a cloud of nodes, elements and their connectivity to each other. From the paper it looks like it is purely connected to the geometry but then what connects to the differential equations we wish to solve? For instance how do I say a line is a beam? Or how do I create a body shell which basically is a shell with thickness.

Here comes the solver part. In case of calculix with NetGen used in this example all tetrahedrons should have a specific element type which will define the physics involved being structural, thermal, electric. In this case structural.

Indirectly the program gives a hint of the element type suggesting structural loads and forces in the boundary conditions or for a thermal case (not this one), the appropriate thermal boundary conditions.

As an example I am picking a Cube made in FreeCAD using NetGen mesher and Calculix solver. Before entering the solving process I generated the .inp file which contains the mesh, the boundary conditions and the material data to perform the simulation.

Somewhere in the .inp file you will find the following:


The element type name used is C3D10, as expected expected since normally the solver has a ton of element types, and there should also be in the Calculix solver a similar variety  like for instance Ansys with Solid187 (https://www.sharcnet.ca/Software/Ansys/17.0/en-us/help/ans_elem/Hlp_E_SOLID187.html), Solid186 or Solid226; for a list see this reference:


More details about C3D10 element can be seen in:


And a list off all Calculix elements can be seen here:



** written by FreeCAD inp file writer for CalculiX,Abaqus meshes
** Nodes
*Node, NSET=Nall
1, 10, 10, 0
2, 10, 10, 10
3, 10, 0, 0
4, 10, 0, 10
5, 0, 10, 0
6, 0, 10, 10
7, 0, 0, 0
8, 0, 0, 10
9, 0, 5, 10
10, 5, 10, 10
11, 10, 5, 10
12, 5, 0, 10
13, 0, 5, 0
14, 5, 10, 0
15, 10, 5, 0
16, 5, 0, 0
17, 10, 10, 5
18, 0, 10, 5
19, 10, 0, 5
20, 0, 0, 5
21, 5, 5, 10
22, 5, 5, 0
23, 5, 10, 5
24, 5, 0, 5
25, 10, 5, 5
26, 0, 5, 5
** Volume elements
<span style="color: #0000ff;"><strong>*Element, TYPE=C3D10, ELSET=Evolumes</strong></span>
25, 7, 4, 6, 8, 24, 21, 26, 20, 12, 9
26, 7, 6, 4, 1, 26, 21, 24, 22, 23, 25
27, 5, 7, 1, 6, 13, 22, 14, 18, 26, 23
28, 4, 7, 1, 3, 24, 22, 25, 19, 16, 15
29, 4, 2, 1, 6, 11, 17, 25, 21, 10, 23
** Define element set Eall
** Element sets for materials and FEM element type (solid, shell, beam, fluid)
** written by write_element_sets_material_and_femelement_type function
** Node sets for fixed constraint
** written by write_node_sets_constraints_fixed function
** FemConstraintFixed
** Materials
** written by write_materials function
** Young's modulus unit is MPa = N/mm2
** FreeCAD material name: 1C60
** SolidMaterial
*MATERIAL, NAME=SolidMaterial
210000, 0.300
** Sections
** written by write_femelementsets function
*SOLID SECTION, ELSET=SolidMaterialSolid, MATERIAL=SolidMaterial
** At least one step is needed to run an CalculiX analysis of FreeCAD
** written by write_step_begin function
** Fixed Constraints
** written by write_constraints_fixed function
** FemConstraintFixed
** Node loads Constraints
** written by write_constraints_force function
** FemConstraintForce
** node loads on shape: Box:Face4
** Outputs --&amp;gt; frd file
** written by write_outputs_types function
S, E
** outputs --&amp;gt; dat file
** written by write_step_end function
** CalculiX Input file
** written by write_footer function
** written by --&amp;gt; FreeCAD 0.17.12321 (Git)
** written on --&amp;gt; Sun Oct 8 21:43:43 2017
** file name --&amp;gt;
** analysis name --&amp;gt; Analysis
** Units
** Geometry (mesh data) --&amp;gt; mm
** Materials (Young's modulus) --&amp;gt; N/mm2 = MPa
** Loads (nodal loads) --&amp;gt; N


The Paper Clip

A paper clip as simple as it is. It always is handy when we need to join paper sheets together. A soft metal wire is bended in such a way that when we insert a few paper sheets in-between the bended profile, it will act as a spring load pressing the paper sheets together.

Paper Clip
Paper Clip

The mesher used in this case was NetGen with standard options:

Max Size: 1000
Growth Rate: 0.3
Nbr. Segments per Edge: 1
Nbr. Segments per Radius: 2

Resulting Mesh:

Node count: 80181
Triangle count: 25166
Tetrahedron count: 39417

Paper Clip tetrahedron Mesh
Paper Clip tetrahedron Mesh

But what did NetGen actually do? It did a mesh but many questions should now start to appear. Some questions came to my mind, like what elements did it used, what is the general quality of the elements like for instance:

  • Element quality criteria;
  • Aspect ratio
  • Jacobean
  • Warping factor
  • Maximum corner angle
  • Skewness
  • Orthogonal quality

Also I wonder what element types are used and where can I find documentation. I will try to understand this better in my next posts…

Salome 8.2 Meshing

The salome mesh environment also presents many options. It reminds me a bit of LSPrepost in the LS-Dyna product from LSTC or Hyper mesh with some differences. On the example I am showing I fused all the parts toguether since I didn’t know at the time if I could define contacts. The mesh generation algorithm’s come from NetGen it would be nice to see in the future Gmsh support as FreeCad is doing on it’s 0.17 version.

Salome 8 Meshing Interface
Salome 8 Meshing Interface

Meshing and viewing in Salome is quite simplistic and non visual. Tools like Ansys give us access to selecting surfaces, edges, and lines to allow us to define what we wanto to do to them. This is a limitation that NetGen, Gmsh and other open software lack. Also to troubleshoot a problem requires some knoledge of the mechanisms behind Salome and NetGen. Rendering sometimes fails to display meshed parts or displays parts of them and this was a bit anoying to me.

With the Salome package we get a geometry creation editor, a mesh generation editor and a post processor analyser but where is the solver? This was something that didn’t feel well when I started with Salome, I knew that eventually I would get into a dead end. And so it was wright! To use a solver I need Code-Aster or if I want the two packages bundled toguether we need to use Saolme-Meca where it intigrates the solver. I will get to that subject in a future post.