Сетки конечных элементов
Создать FEM Mesh
Существуют различные возможности для создания FEM Mesh во FreeCAD:
- Инструмент Netgen для сетки FreeCAD FEM MeshNetgenFromShape с использованием графического интерфейса или Python
- Инструмент GMSH для сетки FreeCAD FEM MeshGmshFromShape с использованием графического интерфейса или Python
- Python напрямую означает создание сетки FEM вручную
- Импорт сетки FEM
Поддерживаются объекты, созданные в PartDesign и Part, а также простые копии этих тел. Пользователю доступны два Mesh: Netgen и GMSH. Netgen включен в FreeCAD. Для GMSH необходимо установить внешний двоичный файл. Обратитесь к FEM Install
Mesher Overview
implemented
- Netgen
- Gmsh
of interest
- PythonOCC
- Tetgen
- SnappyHexMesh
- ENigMA
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/
- "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
Triangle element
Quadratic element
Tetrahedron element
Pyramid element
Hexahedron element
Pentahedron element
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
- Materials: Solid, Fluid, Nonlinear mechanical, Reinforced (concrete); Material editor
- Element geometry: Beam (1D), Beam rotation (1D), Shell (2D), Fluid flow (1D)
Constraints
- Electromagnetic: Electrostatic potential, Current density, Magnetization
- Geometrical: Plane rotation, Section print, Transform
- Mechanical: Fixed, Displacement, Contact, Tie, Spring, Force, Pressure, Centrif, Self weight
- Thermal: Initial temperature, Heat flux, Temperature, Body heat source
- Overwrite Constants: Constant vacuum permittivity
- Solve: CalculiX Standard, Elmer, Mystran, Z88; Equations: Deformation, Elasticity, Electrostatic, Electricforce, Magnetodynamic, Magnetodynamic 2D, Flow, Flux, Heat; Solver: Solver control, Solver run
- Results: Purge, Show; Postprocessing: Apply changes, Pipeline from result, Warp filter, Scalar clip filter, Function cut filter, Region clip filter, Contours filter, Line clip filter, Stress linearization plot, Data at point clip filter, Filter function plane, Filter function sphere, Filter function cylinder, Filter function box
- Additional: Preferences; FEM Install, FEM Mesh, FEM Solver, FEM CalculiX, FEM Concrete; FEM Element Types
- Getting started
- Installation: Download, Windows, Linux, Mac, Additional components, Docker, AppImage, Ubuntu Snap
- Basics: About FreeCAD, Interface, Mouse navigation, Selection methods, Object name, Preferences, Workbenches, Document structure, Properties, Help FreeCAD, Donate
- Help: Tutorials, Video tutorials
- Workbenches: Std Base, Arch, Assembly, CAM, Draft, FEM, Inspection, Mesh, OpenSCAD, Part, PartDesign, Points, Reverse Engineering, Robot, Sketcher, Spreadsheet, Start, Surface, TechDraw, Test Framework, Web
- Hubs: User hub, Power users hub, Developer hub