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1D and 2D FULL FEM implementation with docs
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@ZibraMax ZibraMax released this 21 Mar 17:13
· 387 commits to master since this release
v1.0.5
13ea64a

FEM

N dimensional FEM implementation for M variables per node problems.

Tutorial

Using pre implemented equations

Avaliable equations:

  • 1D 1 Variable ordinary diferential equation
  • 1D 2 Variable Euler Bernoulli Beams [TODO]
  • 1D 2 Variable Timoshenko Beams [TODO]
  • 2D 1 Variable Torsion
  • 2D 2 Variable Plane Strees
  • 2D 2 Variable Plane Strain

Steps:

  • Create geometry (From coordinates or GiD)
  • Create Border Conditions (Point and segment supported)
  • Solve!
  • For example: Test 2, Test 5, Test 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
import FEM #import AFEM
from FEM import Mesh #Import Meshing tools

#Define some variables with geometric properties
a = 0.3
b = 0.3
tw = 0.05
tf = 0.05

#Define material constants
E = 200000
v = 0.27
G = E / (2 * (1 + v))
phi = 1 #Rotation angle

#Define domain coordinates
vertices = [
    [0, 0],
    [a, 0],
    [a, tf],
    [a / 2 + tw / 2, tf],
    [a / 2 + tw / 2, tf + b],
    [a, tf + b],
    [a, 2 * tf + b],
    [0, 2 * tf + b],
    [0, tf + b],
    [a / 2 - tw / 2, tf + b],
    [a / 2 - tw / 2, tf],
    [0, tf],
]

#Define triangulation parameters with `_strdelaunay` method.
params = Mesh.Delaunay._strdelaunay(constrained=True, delaunay=True,
                                    a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Mesh.Delaunay1V(vertices, params)

#Save geometry to .msh file
geometry.saveMesh('I_test')

#Create torsional 2D analysis.
O = FEM.Torsion2D(geometry, G, phi)
#Solve the equation in domain.
#Post process and show results
O.solve()
plt.show()

Example with geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
import FEM #import AFEM
from FEM import Mesh #Import Meshing tools

#Define material constants.
E = 200000
v = 0.27
G = E / (2 * (1 + v))
phi = 1 #Rotation angle

#Load geometry with file.
geometry = Mesh.Geometry.loadmsh('I_test.msh')

#Create torsional 2D analysis.
O = FEM.Torsion2D(geometry, G, phi)
#Solve the equation in domain.
#Post process and show results
O.solve()
plt.show()
Assets 2
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