FEM Mesh

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Create a FEM Mesh

There are different possibilities to create a FEM Mesh in FreeCAD:

  • The FreeCAD FEM mesh Netgen tool MeshNetgenFromShape by GUI usage or by Python
  • The FreeCAD FEM mesh GMSH tool MeshGmshFromShape by GUI usage or by Python
  • Python directly means make the FEM Mesh by Hand
  • Import a FEM Mesh

Objects created in PartDesign and Part are supported, as well as simple copies of those bodies. There are two meshers available to the user: Netgen and GMSH. Netgen is included in FreeCAD. For GMSH an external binary needs to be installed. Refer to FEM Install

Mesher Overview

implemented

of interest

FEM Mesh Elements in FreeCAD

FreeCAD supports various element types. There is an external blog link which explains about the differences and when to use which element type: https://www.comsol.com/blogs/meshing-your-geometry-various-element-types/

Import and Export of FEM Mesh Elements
Element Element FreeCAD API FreeCAD GUI med unv inp frd txt xml
Med CalculiX Python FEM Mesh SMESH IDEAS/FreeCAD Abaqus/CalculiX Result Mesh Z88 Fenics
Name Name create elements view elements import/export import/export import/export import import/export import/export
seg 2 B31 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg
seg 3 B32 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg ni -
tria 3 S3 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg - Edit OK.svg
tria 6 S6 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg -
quad 4 S4 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg - Edit OK.svg
quad 8 S8 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg -
tetra 4 C3D4 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg
tetra 10 C3D10 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg -
pyra 5 - Edit OK.svg Edit OK.svg Edit OK.svg - - - - -
pyra 13 - Edit OK.svg Edit OK.svg Edit OK.svg - - - - -
hexa 8 C3D8 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg (-) [format allows it, but not readable/writable by fenics]
hexa 20 C3D20 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg -
penta 6 C3D6 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg  ? -
penta 15 C3D15 Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg Edit OK.svg  ? -
  • "ni" means the element type is not implemented in FreeCAD but the format would support it.
  • "-" means the format specification does not support this element type, thus FreeCAD can not support it.
  • "?" it is not known if the format supports this element type.

FEM Element Types

General

More informations about the FEM element types and their data structure inside FreeCAD can be find on FEM Element Types.

Segment element

Segments.gif

Triangle element

Triangles.gif

Quadratic element

Quadrangles.gif

Tetrahedron element

Tetraedres.gif

Pyramid element

Pyramides.gif

Hexahedron element

Hexaedres.gif

Pentahedron element

Pentaedres.gif

Scripting

Create a FEM Mesh totally py python

Creating a mesh with one Tet-10 Elements

import FreeCAD, Fem
# create a empty mesh
m = Fem.FemMesh()
#create the nodes
m.addNode(0,1,0)
m.addNode(0,0,1)
m.addNode(1,0,0)
m.addNode(0,0,0)
m.addNode(0,0.5,0.5)
m.addNode(0.5,0.03,.5)
m.addNode(0.5,0.5,0.03)
m.addNode(0,0.5,0)
m.addNode(0.03,0,0.5)
m.addNode(0.5,0,0)
# add the volume with the created nodes
m.addVolume([1,2,3,4,5,6,7,8,9,10])

Fem.show(m)

If you want to have predefined element and node numbering:

m.addNode(0.0,1.0,0.0,1)
m.addVolume([1,2,3,4,5,6,7,8,9,10],1)


Visual handling

Highlight some nodes on the view:

import FreeCAD, Fem

m = Fem.FemMesh()

m.addNode(0,1,0)
m.addNode(0,0,1)
m.addNode(1,0,0)
m.addNode(0,0,0)
m.addNode(0,0.5,0.5)
m.addNode(0.5,0.03,.5)
m.addNode(0.5,0.5,0.03)
m.addNode(0,0.5,0)
m.addNode(0.03,0,0.5)
m.addNode(0.5,0,0)
m.addVolume([1,2,3,4,5,6,7,8,9,10])

Fem.show(m)
Gui.ActiveDocument.ActiveObject.HighlightedNodes = [1,2,3]

Postprocessing colors and displacement: Highlight some nodes on the view:

# set the volume 1 to red
Gui.ActiveDocument.ActiveObject.ElementColor= {1:(1,0,0)}
# set the node 1 and 2 to a certain Color and interpolate the survace
Gui.ActiveDocument.ActiveObject.NodeColor= {1:(1,0,0),2:(1,0,0)}
# set the node 1 and 2 to a certain displacement
Gui.ActiveDocument.ActiveObject.NodeDisplacement= {1:FreeCAD.Vector(1,0,0),2:FreeCAD.Vector(1,0,0)}
# double the factor of the displacement shown
Gui.ActiveDocument.ActiveObject.animate(2.0)

Script one Element of each supported Element Type

import Fem
#################################################
# Beams
# 2 node line --> seg2 ##########################
seg2 = Fem.FemMesh()
seg2.addNode( 0,  0, 0, 1)
seg2.addNode(10,  0, 0, 2)
seg2.addEdge(1, 2)
seg2
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","seg2")
obj.FemMesh = seg2
obj.Placement.Base = (0,110,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"


# 3 node line --> seg3 ##########################

seg3 = Fem.FemMesh()
seg3.addNode( 0,  0, 0, 1)
seg3.addNode(10,  0, 0, 2)
seg3.addNode( 5,  0, 0, 3)
seg3.addEdge([1, 2, 3])
seg3
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","seg3")
obj.FemMesh = seg3
obj.Placement.Base = (30,110,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"


#################################################
# Shells
# 3 node triangle --> tria3 #####################
tria3 = Fem.FemMesh()
tria3.addNode( 0,  0, 0, 1)
tria3.addNode( 6, 12, 0, 2)
tria3.addNode(12,  0, 0, 3)
tria3.addFace([1,  2,  3])
tria3
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","tria3")
obj.FemMesh = tria3
obj.Placement.Base = (0,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
# add Face with element number
elemtria3 = Fem.FemMesh()
nds = tria3.Nodes
for n in nds:
    elemtria3.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemtria3.addFace([1,  2,  3], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemtria3")
obj.FemMesh = elemtria3
obj.Placement.Base = (200,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
elemtria3.Faces


# 6 node triangle --> tria 6 ####################
tria6 = Fem.FemMesh()
tria6.addNode( 0,  0, 0, 1)
tria6.addNode( 6, 12, 0, 2)
tria6.addNode(12,  0, 0, 3)
tria6.addNode( 3,  6, 0, 4)
tria6.addNode( 9,  6, 0, 5)
tria6.addNode( 6,  0, 0, 6)
tria6.addFace([1,  2, 3,  4, 5, 6])
tria6
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","tria6")
obj.FemMesh = tria6
obj.Placement.Base = (30,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
# add Face with element number
elemtria6 = Fem.FemMesh()
nds = tria6.Nodes
for n in nds:
    elemtria6.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemtria6.addFace([1,  2,  3,  4, 5, 6], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemtria6")
obj.FemMesh = elemtria6
obj.Placement.Base = (230,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
elemtria6.Faces


# 4 node quad --> quad4 #########################
quad4 = Fem.FemMesh()
quad4.addNode( 0, 10, 0, 1)
quad4.addNode(10, 10, 0, 2)
quad4.addNode(10,  0, 0, 3)
quad4.addNode( 0,  0, 0, 4)
quad4.addFace([1,  2,  3, 4])
quad4
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","quad4")
obj.FemMesh = quad4
obj.Placement.Base = (60,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
# add Face with element number
elemquad4 = Fem.FemMesh()
nds = quad4.Nodes
for n in nds:
    elemquad4.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemquad4.addFace([1,  2,  3,  4], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemquad4")
obj.FemMesh = elemquad4
obj.Placement.Base = (260,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
elemquad4.Faces


# 8 node quad --> quad8 #########################
quad8 = Fem.FemMesh()
quad8.addNode( 0, 10, 0, 1)
quad8.addNode(10, 10, 0, 2)
quad8.addNode(10,  0, 0, 3)
quad8.addNode( 0,  0, 0, 4)
quad8.addNode( 5, 10, 0, 5)
quad8.addNode(10,  5, 0, 6)
quad8.addNode( 5,  0, 0, 7)
quad8.addNode( 0,  5, 0, 8)
quad8.addFace([1,  2,  3, 4, 5, 6, 7, 8])
quad8
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","quad8")
obj.FemMesh = quad8
obj.ViewObject.BackfaceCulling = False
obj.Placement.Base = (90,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Face with element number
elemquad8 = Fem.FemMesh()
nds = quad8.Nodes
for n in nds:
    elemquad8.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemquad8.addFace([1,  2,  3,  4, 5, 6, 7, 8], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemquad8")
obj.FemMesh = elemquad8
obj.Placement.Base = (290,80,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
elemquad8.Faces


#################################################
# Volumes
# 4 node tetrahedron --> tetra4 #################
tetra4 = Fem.FemMesh()
tetra4.addNode( 6, 12, 18, 1)
tetra4.addNode( 0,  0, 18, 2)
tetra4.addNode(12,  0, 18, 3)
tetra4.addNode( 6,  6,  0, 4)
tetra4.addVolume([1,  2,  3, 4])
tetra4
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","tetra4")
obj.FemMesh = tetra4
obj.Placement.Base = (0,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elemtetra4 = Fem.FemMesh()
nds = tetra4.Nodes
for n in nds:
    elemtetra4.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemtetra4.addVolume([1,  2,  3, 4], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemtetra4")
obj.FemMesh = elemtetra4
obj.Placement.Base = (200,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elemtetra4.Volumes


# 10 node tetrahedron --> tetra10 ###############
tetra10 = Fem.FemMesh()
tetra10.addNode( 6, 12, 18, 1)
tetra10.addNode( 0,  0, 18, 2)
tetra10.addNode(12,  0, 18, 3)
tetra10.addNode( 6,  6,  0, 4)

tetra10.addNode( 3,  6, 18, 5)
tetra10.addNode( 6,  0, 18, 6)
tetra10.addNode( 9,  6, 18, 7)

tetra10.addNode( 6,  9,  9, 8)
tetra10.addNode( 3,  3,  9, 9)
tetra10.addNode( 9,  3,  9,10)
tetra10.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
tetra10
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","tetra10")
obj.FemMesh = tetra10
obj.Placement.Base = (30,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elemtetra10 = Fem.FemMesh()
nds = tetra10.Nodes
for n in nds:
    elemtetra10.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemtetra10.addVolume([1,  2,  3, 4, 5, 6, 7, 8, 9, 10], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemtetra10")
obj.FemMesh = elemtetra10
obj.Placement.Base = (230,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elemtetra10.Volumes


# 8 node Hexahedron --> hexa8 ###################
hexa8 = Fem.FemMesh()
hexa8.addNode( 0, 10, 10, 1)
hexa8.addNode( 0,  0, 10, 2)
hexa8.addNode(10,  0, 10, 3)
hexa8.addNode(10, 10, 10, 4)
hexa8.addNode( 0, 10,  0, 5)
hexa8.addNode( 0,  0,  0, 6)
hexa8.addNode(10,  0,  0, 7)
hexa8.addNode(10, 10,  0, 8)
hexa8.addVolume([1, 2, 3, 4, 5, 6, 7, 8])
hexa8
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","hexa8")
obj.FemMesh = hexa8
obj.Placement.Base = (60,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elemhexa8 = Fem.FemMesh()
nds = hexa8.Nodes
for n in nds:
    elemhexa8.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemhexa8.addVolume([1,  2,  3, 4, 5, 6, 7, 8], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemhexa8")
obj.FemMesh = elemhexa8
obj.Placement.Base = (260,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elemhexa8.Volumes


# 20 node Hexahedron --> hexa20 #################
hexa20 = Fem.FemMesh()
hexa20.addNode( 0, 10, 10,  1)
hexa20.addNode( 0,  0, 10,  2)
hexa20.addNode(10,  0, 10,  3)
hexa20.addNode(10, 10, 10,  4)
hexa20.addNode( 0, 10,  0,  5)
hexa20.addNode( 0,  0,  0,  6)
hexa20.addNode(10,  0,  0,  7)
hexa20.addNode(10, 10,  0,  8)

hexa20.addNode( 0,  5, 10,  9)
hexa20.addNode( 5,  0, 10, 10)
hexa20.addNode(10,  5, 10, 11)
hexa20.addNode( 5, 10, 10, 12)

hexa20.addNode( 0,  5,  0, 13)
hexa20.addNode( 5,  0,  0, 14)
hexa20.addNode(10,  5,  0, 15)
hexa20.addNode( 5, 10,  0, 16)

hexa20.addNode( 0, 10,  5, 17)
hexa20.addNode( 0,  0,  5, 18)
hexa20.addNode(10,  0,  5, 19)
hexa20.addNode(10, 10,  5, 20)
hexa20.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])
hexa20
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","hexa20")
obj.FemMesh = hexa20
obj.Placement.Base = (90,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elemhexa20 = Fem.FemMesh()
nds = hexa20.Nodes
for n in nds:
    elemhexa20.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elemhexa20.addVolume([1,  2,  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elemhexa20")
obj.FemMesh = elemhexa20
obj.Placement.Base = (290,50,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elemhexa20.Volumes


# 6 node pentahedron --> penta6 #################
penta6 = Fem.FemMesh()
penta6.addNode(10,10,10, 1)
penta6.addNode( 0, 0,10, 2)
penta6.addNode(20, 0,10, 3)
penta6.addNode(10,10, 0, 4)
penta6.addNode( 0, 0, 0, 5)
penta6.addNode(20, 0, 0, 6)
penta6.addVolume([1, 2, 3, 4, 5, 6])
penta6
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","penta6")
obj.FemMesh = penta6
obj.Placement.Base = (0,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elempenta6 = Fem.FemMesh()
nds = penta6.Nodes
for n in nds:
    elempenta6.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elempenta6.addVolume([ 1,  2,  3, 4, 5, 6], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elempenta6")
obj.FemMesh = elempenta6
obj.Placement.Base = (200,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elempenta6.Volumes


# 15 node pentahedron --> penta15 ###############
penta15 = Fem.FemMesh()
penta15.addNode(10,10,10, 1)
penta15.addNode( 0, 0,10, 2)
penta15.addNode(20, 0,10, 3)
penta15.addNode(10,10, 0, 4)
penta15.addNode( 0, 0, 0, 5)
penta15.addNode(20, 0, 0, 6)

penta15.addNode( 5, 5,10, 7)
penta15.addNode(10, 0,10, 8)
penta15.addNode(15, 5,10, 9)

penta15.addNode( 5, 5, 0,10)
penta15.addNode(10, 0, 0,11)
penta15.addNode(15, 5, 0,12)

penta15.addNode(10,10, 5,13)
penta15.addNode( 0, 0, 5,14)
penta15.addNode(20, 0, 5,15)
penta15.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])
penta15
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","penta15")
obj.FemMesh = penta15
obj.Placement.Base = (40,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elempenta15 = Fem.FemMesh()
nds = penta15.Nodes
for n in nds:
    elempenta15.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elempenta15.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elempenta15")
obj.FemMesh = elempenta15
obj.Placement.Base = (240,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elempenta15.Volumes


# 5 node pyramid --> pyra5 ######################
pyra5 = Fem.FemMesh()
pyra5.addNode( 0,20, 0, 1)
pyra5.addNode(20,20, 0, 2)
pyra5.addNode(20, 0, 0, 3)
pyra5.addNode( 0, 0, 0, 4)
pyra5.addNode(10,10,10, 5)
pyra5.addVolume([1, 2, 3, 4, 5])
pyra5
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","pyra5")
obj.FemMesh = pyra5
obj.Placement.Base = (80,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elempyra5 = Fem.FemMesh()
nds = pyra5.Nodes
for n in nds:
    elempyra5.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elempyra5.addVolume([1,  2,  3, 4, 5], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elempyra5")
obj.FemMesh = elempyra5
obj.Placement.Base = (280,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elempyra5.Volumes


# 13 node pyramid --> pyra13 ####################
pyra13 = Fem.FemMesh()
pyra13.addNode( 0,20, 0, 1)
pyra13.addNode(20,20, 0, 2)
pyra13.addNode(20, 0, 0, 3)
pyra13.addNode( 0, 0, 0, 4)
pyra13.addNode(10,10,10, 5)

pyra13.addNode(10,20, 0, 6)
pyra13.addNode(20,10, 0, 7)
pyra13.addNode(10, 0, 0, 8)
pyra13.addNode( 0,10, 0, 9)

pyra13.addNode( 5,15, 5,10)
pyra13.addNode(15,15, 5,11)
pyra13.addNode(15, 5, 5,12)
pyra5 = Fem.FemMesh()
pyra13.addNode( 5, 5, 5,13)
pyra13.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])
pyra13
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","pyra13")
obj.FemMesh = pyra13
obj.Placement.Base = (120,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
# add Volume with element number
elempyra13 = Fem.FemMesh()
nds = pyra13.Nodes
for n in nds:
    elempyra13.addNode(nds[n].x, nds[n].y, nds[n].z, n)

elempyra13.addVolume([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 88)
obj = App.ActiveDocument.addObject("Fem::FemMeshObject","elempyra13")
obj.FemMesh = elempyra13
obj.Placement.Base = (320,0,0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
elempyra13.Volumes