## 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.

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.

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:

TYPE=C3D10

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:

https://www.sharcnet.ca/Software/Ansys/17.0/en-us/help/ans_elem/

More details about C3D10 element can be seen in:

http://web.mit.edu/calculix_v2.7/CalculiX/ccx_2.7/doc/ccx/node33.html

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

http://web.mit.edu/calculix_v2.7/CalculiX/ccx_2.7/doc/ccx/node25.html

```** 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
*ELSET, ELSET=Eall
Evolumes

***********************************************************
** Element sets for materials and FEM element type (solid, shell, beam, fluid)
** written by write_element_sets_material_and_femelement_type function
*ELSET,ELSET=SolidMaterialSolid
Evolumes

***********************************************************
** Node sets for fixed constraint
** written by write_node_sets_constraints_fixed function
** FemConstraintFixed
*NSET,NSET=FemConstraintFixed
3,
4,
7,
8,
12,
16,
19,
20,
24,

***********************************************************
** Materials
** written by write_materials function
** Young's modulus unit is MPa = N/mm2
** SolidMaterial
*MATERIAL, NAME=SolidMaterial
*ELASTIC
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
*STEP
*STATIC

***********************************************************
** Fixed Constraints
** written by write_constraints_fixed function
** FemConstraintFixed
*BOUNDARY
FemConstraintFixed,1
FemConstraintFixed,2
FemConstraintFixed,3

***********************************************************
** written by write_constraints_force function
** FemConstraintForce
** node loads on shape: Box:Face4
1,2,-0.0000000000000E+00
2,2,-0.0000000000000E+00
5,2,-0.0000000000000E+00
6,2,-0.0000000000000E+00
10,2,-1.6666666666667E+02
14,2,-1.6666666666667E+02
17,2,-1.6666666666667E+02
18,2,-1.6666666666667E+02
23,2,-3.3333333333333E+02

***********************************************************
** Outputs --&amp;gt; frd file
** written by write_outputs_types function
*NODE FILE
U
*EL FILE
S, E
** outputs --&amp;gt; dat file
*NODE PRINT , NSET=Nall
U
*EL PRINT , ELSET=Eall
S

***********************************************************
** written by write_step_end function
*END STEP

***********************************************************
** 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
**
```

## 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.

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

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

Resulting Mesh:

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

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…

## Playing a bit with the results in the Brompton bike handlebar case

On my previous post I got to discover that the new design for the 2017 Brompton bike model is much more robust. Didn’t get to understand if it was designed on purpose or was a technical difficulty. My hunch was that they enjoyed the design and it made construction simple. However with experience they concluded that it was a problematic design and went for a new design. They could have just reduced the central bar length but instead almost removed it to a more challenging design at least for manufacturing.

FreeCAD produces nice images and this one is an undeformed vs deformed shape. Here I think it is visible that near the stem is where most of the stresses will be generated. So if you have a handlebar from a bellow 2017 model take special care to not pressure in an exaggerated manner the handlebar down.

Special thanks: I would like to thank the FreeCAD forum team and in particular Bernd for providing troubleshooting for FreeCAD  and showing how to do the deformed and undeformed image.

## The Brompton Handlebar Case II

While browsing the Internet I found some past references to Brompton Handlebar cracks near the bending elbows. I noticed my colleague Brompton had a different design and thus concluded that probably the Brompton bike team, decided to turn the  handlebar more robust.

I notice that I make some force to the ground direction when pedalling and curving, special when the road has bumps.

In wich elbow will the stress higher and the cracks be formed? I will be continuing on this subject, so please stay tuned.

## An illustration of the FEM study process

Good comercial packages integrate conveniently all steps required to get results with minimum effort. As I have been demonstrating on previous posts, since open source softwares grew up each in their single box, with specific intents at their time, integration never was a primary concern, however as they matured, naturally, synergies start to take place and each project starts to fit together to supply the integrated platform that everyone is urging for. 2017 will be a year that will bring two interesting versions os software that integrate it all, FreeCAD 0.17 and Salome-Meca 2017.

## FreeCAD 0.17 another good step forward

The new FreeCad version that will be out, will introduce quite a few big improvements on many areas, however I will be focusing on the FEM toolbar since this version has a great number of changes. Still I have to comment that when we now go to the Part design drop down menu I saw something which made me happy. I got a strange feeling that I was working with CREO or Unigraphics where we see the base planes and can start a sketch on any one of these. This little change is a huge step forward in making it easier to work with FreeCAD.

Going now to the FEM menu. What is different can you spot it?

More icons certainly are noticiable. Fluid dynamics seems to be integrated aswell as Non linear material behaviour (looks like strain hardening tangent method), part to part contact definition and thermal boundary conditions.
We can use two meshing applications just by clicking a button for NetGen or Gmsh.

The boundary conditions are easy to make just like before you select a specific entity and define it. This time around we get more types of boundaryconditions for structural, thermal and fluidic problems.

The NetGen mesh worked smoothly, got no issues.

The Gmsh mesh was also easy to use and generated a tet mesh with no issues.

There are more options to explore like mesh boundary layer which I haven’t tried it yet on this new version.

This version also boost result viewing with more result types and scoping zones.

Where to get freeCAD 0.17 with FEM? You can get binaries here:

And here more specifically here