Mesh FEM

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Revision as of 20:44, 12 April 2017 by Renatorivo (talk | contribs)

Creare una Mesh FEM

In FreeCAD ci sono diverse possibilità per creare una Mesh FEM:

  • Lo strumento Gui Mesh da forma
  • Lo strumento Gui di Python
  • Direttamente in Python, il che significa creare la Mesh FEM a mano
  • Importare una Mesh FEM

Sono supportati gli oggetti creati in Part Design e Parte, così come le copie semplici di tali corpi. Sono disponibili due mesher: Netgen e GMSH. Netgen è incluso in FreeCAD. Fare riferimento a Installare FEM. Per generare una Mesh FEM con GMSH l'utente psicofil ha fornito la Macro GMSHMesh.

Elementi Mesh FEM in FreeCAD

FreeCAD supporta vari tipi di elementi. Questo blog esterno vi spiega le differenze tra i tipi di elementi e come utilizzarli: https://www.comsol.com/blogs/meshing-your-geometry-various-element-types/

Import and Export of FEM Mesh Elements
Element Element FreeCAD API FreeCAD View med unv inp frd txt xml
Med CalculiX create by FC ViewProvider SMESH IDEAS/FreeCAD Abaqus/CalculiX Result Mesh Z88 Fenics
Name Name Python import/export import/export import/export import import/export import/export
seg 2 B31
seg 3 B32 ni ni ni -
tria 3 S3 -
tria 6 S6 -
quad 4 S4 -
quad 8 S8 -
tetra 4 C3D4
tetra 10 C3D10 -
pyra 5 - - - - - -
pyra 13 - - - - - -
hexa 8 C3D8 (-) [format allows it, but not readable/writable by fenics]
hexa 20 C3D20 -
penta 6 C3D6 ? -
penta 15 C3D15 ? -
  • "ni" significa non implementato dentro FreeCAD ma il formato e supportato.
  • "-" significa non supportato dall'interfaccia, quindi non è possibile supportarlo.
  • "?" non si sa se il formato supporta questo tipo d'elemento

Tipi di elementi FEM

Generale

Maggiori informazioni sui tipi di elementi FEM e la loro struttura dei dati all'interno di FreeCAD si trovano nella pagina Tipi di elementi FEM.

Segment element

File:Segments.gif


Triangle element

File:Triangles.gif


Quadratic element

File:Quadrangles.gif


Tetrahedron element

File:Tetraedres.gif


Pyramid element

File:Pyramides.gif


Hexahedron element

File:Hexaedres.gif


Pentahedron element

File:Pentaedres.gif


Script

Creare una Mesh FEM interamente con python

Creare una mesh con 10 nodi (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)

Se si desidera avere un elemento predefinito e la numerazione del nodo:

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


Manipolazione visiva

Evidenziare alcuni nodi nella vista:

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]

Post-elaborazione dei colori e della posizione:

# 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 di un elemento per ciascun tipo di elemento supportato

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 ##########################
# not implemented


#################################################
# 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

Ambiente FEM