FEM Mesh: Difference between revisions

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Create a finite element mesh

Finite element analysis (FEA) is performed on a mesh composed of multiple triangular and quadrilateral finite elements that subdivide an original body. The more refined the mesh is, the more accurate the numerical results will be, but also the computation time will be larger. A balance between the size of the mesh, and computation time and accuracy of results is an important characteristic of a well defined finite element analysis.

There are different possibilities to set up a mesh in the FEM Workbench:

The Gmsh tool from the graphical user interface.
The Netgen tool from the graphical user interface.
Importing a mesh from another program. In particular, Gmsh and Netgen can be used by themselves outside of FreeCAD to mesh solid bodies like Step files.
Manually creating the mesh through Python scripting.

The Gmsh and Netgen tools support meshing bodies created with the Part Workbench and PartDesign Workbench, as well as simple copies of those solids. In general, any workbench that generates solid objects, like the Arch Workbench, can be used as the basis from which to create meshes. Notice that a mesh used for FEA is different from a mesh created or imported from the Mesh Workbench.

The FEM Workbench calls the external tool Gmsh to obtain a mesh from a solid body created with any workbench in FreeCAD; it can also import a mesh created externally

(1) Solid body created with PartDesign; (2) mesh produced by the Gmsh tool inside the FEM Workbench (all triangles); and (3) mesh produced externally by Gmsh, exported to Abaqus format .inp, and then imported into FreeCAD (all quadrangles)

The Gmsh and Netgen tools are convenience tools to quickly mesh a body, and thus don't expose the full capabilities of these programs; they normally create triangular meshes, which may not be ideal for some types of analysis. If you'd like to have more control of the created mesh (use only quadrilaterals, precise element number and size, variable resolution of the mesh, etc.), you should use these programs externally, produce a mesh file in a supported format (.inp, .unv, .vtk, .z88), and import this file into FreeCAD.

Previously, Netgen was included with FreeCAD and could be used immediately. Now, both Netgen and Gmsh should be installed before they can be used by the FEM Workbench. Refer to FEM Install for instructions.

Meshing software

Meshing software operates on solid bodies that can be in different formats, like Step and Brep. These programs can be used independently of FreeCAD, and typically have many options to control the meshing algorithms, element size, and boundary conditions.

The FEM Workbench has developed simple communication interfaces to use Gmsh and Netgen directly inside FreeCAD. Other programs don't have an interface, but this could change in the future if there is interest from the community, and if those applications are easy to integrate. The meshing software can be compiled and distributed together with FreeCAD only if its license is compatible with the LGPL2 license; otherwise, the program has to be used as an external binary, like Gmsh (GPL2) is used.

Interface implemented in FreeCAD

Gmsh: main website, code repository
Netgen: main website, code repository

No interface in FreeCAD

ENigMA, forum thread, code repository
libMesh, main website, code repository, forum thread; it's a very active project, and it's C++ only
PythonOCC, main website
SnappyHexMesh, main website
Tetgen, main website

Mesh elements in FreeCAD

FreeCAD supports various element types. The following article explains the difference between them, and when should be used: Meshing Your Geometry: When to Use the Various Element Types.

Import and export of 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
seg 3	B32							NI
tria 3	S3
tria 6	S6
quad 4	S4
quad 8	S8
tetra 4	C3D4
tetra 10	C3D10
hexa 8	C3D8								() the format allows it, but it's not readable or writable by FEniCS
hexa 20	C3D20
penta 6	C3D6							?
penta 15	C3D15							?
pyra 5
pyra 13

"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 cannot support it.
"?" means it is not known if the format supports this element type.

FEM element types

More information on the elements, and their data structure inside FreeCAD can be found in FEM Element Types.

Segment element

Triangle element

Quadrangle element

Tetrahedron element

Hexahedron element

Pentahedron element (prism)

Pyramid element

Scripting

Create a FEM mesh completely in Python

See also: FreeCAD Scripting Basics.

The Python API allows the user to define a finite element mesh by directly adding individual nodes, and defining edges, faces, and volumes.

The mesh itself is of type Fem::FemMesh, which needs to be attached to a proper document object of type Fem::FemMeshObject.

App.ActiveDocument.Mesh_object.TypeId = Fem::FemMeshObject
                              .
                              .
                              .FemMesh.TypeId = Fem::FemMesh

Creating a mesh with one Tet-10 element

Create an empty FemMesh, populate it with nodes, create the volume, and finally call Fem.show() to create the document object with the corresponding mesh.

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, 0.5)
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)
obj = FreeCAD.ActiveDocument.ActiveObject

If you want to have predefined node and element numbering, pass the appropriate ID to the node and volume methods.

To create an actual document object, instead of Fem.show() you can also use the document addObject() method; then attach the created mesh to this object's FemMesh attribute.

a = Fem.FemMesh()

a.addNode(0,    1,    0,    1)
a.addNode(0,    0,    1,    2)
a.addNode(1,    0,    0,    3)
a.addNode(0,    0,    0,    4)
a.addNode(0,    0.5,  0.5,  5)
a.addNode(0.5,  0.03, 0.5,  6)
a.addNode(0.5,  0.5,  0.03, 7)
a.addNode(0,    0.5,  0,    8)
a.addNode(0.03, 0,    0.5,  9)
a.addNode(0.5,  0,    0,   10)

a.addVolume([1,2,3,4,5,6,7,8,9,10], 1)
obj_2 = FreeCAD.ActiveDocument.addObject("Fem::FemMeshObject")
obj_2.Placement.Base = FreeCAD.Vector(2, 0, 0)
obj_2.FemMesh = a

Visual properties

Once a FemMesh object has been created with Fem.show(), some of its visual properties can be changed by modifying the different attributes of its ViewObject. This can be useful to postprocess the mesh after a finite element solution has been obtained.

Highlight some nodes in the mesh

Fem.show(m)
obj = FreeCAD.ActiveDocument.ActiveObject

obj.ViewObject.HighlightedNodes = [1, 2, 3]

The individual elements of a mesh can be modified by passing a dictionary with the appropriate key:value pairs.

Set volume 1 to red

obj.ViewObject.ElementColor = {1:(1,0,0)}

Set nodes 1, 2 and 3 to a certain color; the faces between the nodes acquire an interpolated color.

obj.ViewObject.NodeColor = {1:(1,0,0), 2:(0,1,0), 3:(0,0,1)}

Displace the nodes 1 and 2 by the magnitude and direction defined by a vector.

obj.ViewObject.NodeDisplacement = {1:FreeCAD.Vector(0,1,0), 2:FreeCAD.Vector(1,0,0)}

Double the factor of the displacement shown. (Note to editors: removed in newer versions?)

obj.ViewObject.animate(2.0)

Scripting examples of each supported element type

Beam, 2 node line, seg2 (linear)

import Fem

seg2 = Fem.FemMesh()
seg2.addNode( 0, 0, 0, 1)
seg2.addNode(10, 0, 0, 2)
seg2.addEdge(1, 2)
print(seg2)

obj = FreeCAD.ActiveDocument.addObject("Fem::FemMeshObject", "seg2")
obj.FemMesh = seg2
obj.Placement.Base = FreeCAD.Vector(0, 110, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"

Beam, 3 node line, seg3 (quadratic)

import Fem

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])
print(seg3)

obj = App.ActiveDocument.addObject("Fem::FemMeshObject", "seg3")
obj.FemMesh = seg3
obj.Placement.Base = FreeCAD.Vector(30, 110, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"

Shell, 3 node triangle, tria3 (linear)

import Fem

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])
print(tria3)

obj = App.ActiveDocument.addObject("Fem::FemMeshObject", "tria3")
obj.FemMesh = tria3
obj.Placement.Base = FreeCAD.Vector(0, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False

Add a face with the element number.

elemtria3 = Fem.FemMesh()
nodes = tria3.Nodes
for n in nodes:
    elemtria3.addNode(nodes[n].x, nodes[n].y, nodes[n].z, n)

elemtria3.addFace([1, 2, 3], 88)

obj = App.ActiveDocument.addObject("Fem::FemMeshObject", "elemtria3")
obj.FemMesh = elemtria3
obj.Placement.Base = FreeCAD.Vector(200, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
print(elemtria3.Faces)

Shell, 6 node triangle, tria6 (quadratic)

import Fem

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])
print(tria6)

obj = App.ActiveDocument.addObject("Fem::FemMeshObject", "tria6")
obj.FemMesh = tria6
obj.Placement.Base = FreeCAD.Vector(30, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False

Add a face with the element number.

elemtria6 = Fem.FemMesh()
nodes = tria6.Nodes
for n in nodes:
    elemtria6.addNode(nodes[n].x, nodes[n].y, nodes[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 = FreeCAD.Vector(230, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
print(elemtria6.Faces)

Shell, 4 node quadrangle, quad4 (linear)

import Fem

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])
print(quad4)

obj = FreeCAD.ActiveDocument.addObject("Fem::FemMeshObject", "quad4")
obj.FemMesh = quad4
obj.Placement.Base = FreeCAD.Vector(60, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False

Add a face with the element number.

elemquad4 = Fem.FemMesh()
nodes = quad4.Nodes
for n in nodes:
    elemquad4.addNode(nodes[n].x, nodes[n].y, nodes[n].z, n)

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

Shell, 8 node quadrangle, quad8 (quadratic)

import Fem

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])
print(quad8)

obj = App.ActiveDocument.addObject("Fem::FemMeshObject", "quad8")
obj.FemMesh = quad8
obj.Placement.Base = FreeCAD.Vector(90, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False

Add a face with the element number.

elemquad8 = Fem.FemMesh()
nodes = quad8.Nodes
for n in nodes:
    elemquad8.addNode(nodes[n].x, nodes[n].y, nodes[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 = FreeCAD.Vector(290, 80, 0)
obj.ViewObject.DisplayMode = "Faces, Wireframe & Nodes"
obj.ViewObject.BackfaceCulling = False
print(elemquad8.Faces)