FEM and Blender

Introduction

• 

  The door canopy with 22.5 degree supports.

• 

  The original idea with 45 deg supports.

• Blender
  • 3D print add-on (Check all)
  • BFEX - Blender FEA Exporter https://github.com/MiguelDLM/BFEX
  • Blendmsh https://github.com/senthurayyappan/blendmsh
  • quad remesher https://www.youtube.com/watch?v=kfQfU_cDRWE
  • Fix meshes https://github.com/evaherbst/Blender_remeshing_guide
• FreeCAD
• Elmer https://www.elmerfem.org/blog/ Couldn't install on Arch Linux
• Gmsh https://gmsh.info/ Worked to create the mesh but not perfectly
• Netgen https://ngsolve.org/ as a part of FreeCAD.
• OpenFOAM https://www.openfoam.com/ Fluif FEM
• Paraview https://www.paraview.org/ Didn't try
• Salome Didn't try
• TetGen Didn't try

Blender and CAD

• TinyCAD https://docs.blender.org/manual/en/4.1//addons/mesh/tinycad.html
• CadSketcher https://www.cadsketcher.com/
• Parts list
  • Using a script: Selected parts only, and don't apply rotations! https://github.com/kittengue-dot/Blender-Script-Export-Part-list https://www.youtube.com/watch?v=C1RZszKlojQ

import bpy
import csv

def export_selected_mesh_dimensions_to_csv(filepath):
    """Export Parts
    Args:
        filepath (str): Le chemin du fichier CSV de sortie.
    """

    with open(filepath, 'w', newline='', encoding='utf-8') as csvfile:
        fieldnames = ['Part', 'Section X (mm)', 'Section Y (mm)', 'Length Z (mm)']
        writer = csv.DictWriter(csvfile, fieldnames=fieldnames)

        writer.writeheader()
        for obj in bpy.context.selected_objects:
            if obj.type == 'MESH':
                
                dimensions = obj.dimensions
                x = [0,0,0]
                x[0] = round(dimensions.x * 1000, 3)
                x[1] = round(dimensions.y * 1000, 3)
                x[2] = round(dimensions.z * 1000, 3)
                x.sort()

                writer.writerow({'Part': obj.name, 'X (mm)': x[0], 'Y (mm)': x[1], 'Z (mm)': x[2]})

filepath = "/home/user/Downloads/part_list.csv"  # Replace destination path

export_selected_mesh_dimensions_to_csv(filepath)

FreeCAD import

Steps:

• Export from Blender. If exporting STL, scale on export 1000x. Problems with non-manifold geometry.
  • Use Boolean to make on mesh
  • Non-manifold: Select -> Select All by Trait -> Non Manifold, also the others from there. Remove the faces and then dissolve the edges (Limited Dissolve or X > Dissolve Edges).
    • (Select Similar). This is often useful to select vertices with only one connecting edge
    • (Select Linked)
    • W > Specials > Remove doubles Doubles,
  • Check the normals outward: Edit mode, Select All, Mesh -> Normals -> Outward (Shift + N)
  • Eliminate the bolts and some holes
• FreeCAD
  • Part -> Create shape from mesh
  • Part -> MakeSolid

Some problems (see a Part check Geometry)

• Geometry is a shell -- not a solid: a shell mesh on meshing
  • Check this by right clicking on the mesh and printing mesh informations (Tasks: Node count vs Triangle count vs Tetrahedron count)
• Self intersections
  • Use Boolean in Blender for all parts (both, if two are overlapping)
  • Self intersecting meshes are considered dirty
  • Use Part -> View -> Transparency to see the intersection points, if they persist.
  • eg Netfabb cleans

FEM Calculations of the Door Canopy

Images of the displacement.

Images

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  Displacement Y

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  Y

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Results

Material: Wood-Generic

• Density 700 kg/m³
• Young's Modulus 12.00 GPa
• Poisson Ratio 0.05

Roof is done with fine mesh, no roofed with even finer mesh.

Design	Displacement magnitude		Displacement X		Displacement Y		Displacement Z		von Mises Stress		Max Principal Stress		Min Principal Stress		Max Shear Stress
	Min	Max [mm]	Min [µm]	Max [µm]	Min [µm]	Max [µm]	Min [mm]	Max [nm]	Min	Max [kPa]	Min [kPa]	Max [kPa]	Min [kPa]	Max [kPa]	Min	Max [kPa]
No Rafters	0.00	2.01	-110	320	240	100	-2.01	800.04	0.00	5847.87	-191.14	6037.13	-5486.84	285.32	0.00	2969.41
22.5° rafter	0.00	0.22	-17.67	92.32	-46.55	14.54	-0.23	164.74	0.00	2020.39	-118.97	2101.76	-1742,35	119.10	0.00	1014.03
22.5° × 2 rafters	0.00	0.16	-13.67	63.63	-35.62	9.99	-0.15	148.73	0.00	1324.45	-108.65	1142.64	-1356.50	60.92	0	672.31
45° rafter short	0.0	0.42	-21.53	58.41	-72.82	30.83	-0.42	5650	0.0	2401.54	-211.93	1492.78	-2688.61	163.16	0.0	1238.34
45° rafter long	0.0	0.29	-150	27.54	-27.47	44.55	-0.28	18000	0.0	4428.06	-452.01	3577.26	-4490.38	177.60	0.0	2328.85
No Rafters + Roof	0.00	0.20	-31.32	1.46	-12.69	15.98	-0.20	1810	0	1250.0	-184.54	1140.49	-1295.94	126.83	0.0	628.53
22.5° rafter + Roof	0.00	0.056	-13.27	4.16	-7.57	4.78	-0.055	481.98	0.00	681.47	-86.48	584.56	-709.20	48.88	0.00	348.28
22.5° × 2 rafters + Roof	0.00	0.051	-12.77	3.01	-5.27	4.28	-0.050	417.70	0.00	583.69	-84.33	397.96	-618.15	27.47	0.00	299.63
45° rafter short + Roof	0.0	0.054	-6.79	4.28	-2.05	5.69	-0.054	419.78	0.00	582.62	-67.76	411.89	-649.33	53.02	0.0	302.88
45° rafter long + Roof	0.0	0.045	-8.38	8.09	-11.90	3.60	-0.044	1010	0.0	828.26	-95.27	619.46	-865.24	62.89	0.0	421.55

Simulation parameters

• Roof Sheet: 1200 x 900 x 22 (distance 634 mm + 20 mm) and 1200 x 700 x 22

Material: Wood-Generic

• Density 700 kg/m3
• Young's Modulus 12.00 GPa
• Poisson Ratio 0.05

Force: 1000 N, downwards (about).

Caption text

Header text	Nodes	Triangles	Tetrahedron	Header text
No Rafters	16413	5424	7786	Example
22.5° rafter	20407	6684	9775	Example
22.5° × 2 rafters	20185	6650	9627	Example
45° rafter	101200	15184	63378	Example
No Rafters + roof	138706	29970	80746	Example
22.5° rafter + roof	150122	31522	88019	Example
22.5° × 2 rafters + roof	160384	33678	94172	Example
45° rafter short + roof	143677	32766	82140	Example

Size

Name	Width	Height	Length
sivuvaaka	40.0	60.0	1200.0
sivuvaaka2	40.0	60.0	1200.0
etulyhytpysty	40.0	60.0	400.0
lyhytvino2	40.0	60.0	1207.695
pystyseina	40.0	60.0	535.61
pitkavino	40.0	60.0	740.106
lujyvino	40.0	60.0	1207.695
pystyseina2	40.0	60.0	535.61
pitkavino2	40.0	60.0	740.106
vinavase	40.0	60.0	686.624
takapalkki	40.0	60.0	1270.0
vinooikea2	40.0	60.0	771.684
takapalkki.001	40.0	60.0	1270.0
vinavase.002	40.0	60.0	686.624
vinooikea1	40.0	60.0	771.684
vinavase.004	40.0	60.0	686.624
vinooikea	40.0	60.0	771.684

Convergence tests

To ensure that the FEM simulation results converge, we try a simple simulation with different size of triangulation.

Workflow and test examples

1. Plan and sketch using Blender
2. Create the FEM model using FreeCAD
3. Do the simulations
4. Make the plans.

Below is the non working idea.

1. Make the Blender mesh and export as .obj file
2. Make the mesh using GMSH or FreeCAD, and use FreeCAD to FEM calculations

Simple Cube

Works OK with the FreeCAD, not with the Gmsh

OBJ

• 

  The imported cube has double nodes, and the color is strange.

• 

  (If normals are fixed (shift+N in edit mode) the box will look better. This is not used in the following parts).

• 

  It works flawless in the FreeCAD.

• 

  The FreeCAD FEM solver gives some results.

• 

  However, when importing to GMSH, it will produce an error.

STL

• 

  Meshing works, if the normals are done.

• 

  If the cube is exported as STL, then GMSH will work better (if not normals done).

• 

  The mesh generation does not work: "PLC Error: A segment and a facet intersect at point" and "Invalid boundary mesh (segment-facet intersection) on surface 1, intersection (0.333327,0.333327,1)". (if not normals done.)

Two Cubes

• 

  The two cubes made in Blender. The mesh looks fine, and there are none self intersecting nodes.

• 

  When importing the Obj file back to Blender, the seems to be missing some faces.

• 

  Seems that some of the normals are faced wrong way. In edit mode use (Ctrl+A) shift+N to fix this.

• 

  Tetrahedron count is more than zero! It seems to work.

• 

  The FEM results seems to be working. The force is 10 N.

The Door Canopy

Couldn't do the model using Blender and Freecad/ Gmsh.

Make it step by step.

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  First part works, though the dimensions are totally wrong. In the inset is the Blender Edit mode image of the same part.

• 

  Set the scale from Blender export (1000x). Now the stress is visible, and dimensions are correct. Nice to work with familiar units.

• 

  Already second part (or third) gives problems. The mesh cannot be generated. This is with STL export.

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  If tested using OBJ format, there will be some places without faces, and no tetrahedron in the mesh.

Gmsh

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  Gmsh makes the FEM mesh for the first part, and by refining the mesh, it will be clearer.

• 

  Gmsh can use the second part, also. Need to check if FreeCAD can read that file.

• 

  FreeCAD has also Gmsh mesh generator. That will generate the mesh, but while solving gives an error: "Nodes, but no results found in frd file. It means there only is a mesh but no results in frd file. Usually this happens if CalculiX returned no results (happens on nonpositive jacobian determinant in at least one element)"

• 

  By trying again, it works! Force is 10 N.

• 

  Changed the Force to 100 N, and the maximum size of mesh to 10. The later increased the computation time a lot, the time being about 9 s.

FreeCAD Tutorials

Good tutorials for noobies

• https://www.youtube.com/watch?v=E14m5hf6Pvo
• https://www.youtube.com/watch?v=5DoHT2lqVU4

Theory

Frame formulas: https://structx.com/frames.html

References

The human character is Nathan https://sketchfab.com/3d-models/nathan-animated-003-walking-3d-man-143a2b1ea5eb4385ae90a73657aca3bc CC Attribution.