Releases · ZibraMax/FEM

22 Dec 15:51

ZibraMax

v1.0.34

507e06e

The Border Update

There are new features, I forgot how many. Sorry, Changelog coming soon…

Assets 2

22 Dec 16:02

ZibraMax

v.1.0.34.1

fb238d8

The Border Update Latest

Latest

There are new features, I forgot how many. Sorry, Changelog coming soon…

Assets 2

30 Jul 22:49

ZibraMax

v1.0.33

259184e

The Quality of Life Update pt 2

JSON file now saves information about solver process (eigenvalues, iteration error, etc.)
Regions 2D are treated as border elements

Assets 2

04 May 18:27

ZibraMax

v1.0.32

26d52c1

The Memory Update

Save memoy with sparse matrix!

Docs now behave like first intended

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

From source:

git clone https://github.com/ZibraMax/FEM
cd FEM
python -m venv .venv
python -m pip install build
python -m build
python -m pip install -e .[docs] # Basic instalation with docs

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable Poisson equation
2D 1 Variable second order PDE
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strees Orthotropic
2D 2 Variable Plane Strain
3D 3 variables per node isotropic elasticity

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strain

Steps:

Create geometry
Create Border Conditions (Point and regions supported)
Solve!
For example: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Geometry import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

#Save geometry to .json file
geometry.exportJSON('I_test.json')

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Geometry import Geometry #Import Geometry tools

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

#Load geometry with file.
geometry = Geometry.importJSON('I_test.json')

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Numpy: Numpy data
- Matplotlib: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class in the Elasticity2D.py file.

Roadmap

2D elastic plate theory
Transient analysis (Core modification)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

References

J. N. Reddy. Introduction to the Finite Element Method, Third Edition (McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto, 2006). https://www.accessengineeringlibrary.com/content/book/9780072466850

Jonathan Richard Shewchuk, (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator

Ramirez, F. (2020). ICYA 4414 Modelación con Elementos Finitos [Class handout]. Universidad de Los Andes.

License

MIT

Assets 2

04 May 18:20

ZibraMax

v1.0.31

9eb20df

The Memory Update

Save memoy with sparse matrix!

Docs now behave like first intended

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Full Docs

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable Poisson equation
2D 1 Variable second order PDE
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strees Orthotropic
2D 2 Variable Plane Strain
3D 3 variables per node isotropic elasticity

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strain

Steps:

Create geometry
Create Border Conditions (Point and regions supported)
Solve!
For example: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Geometry import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

#Save geometry to .json file
geometry.exportJSON('I_test.json')

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Geometry import Geometry #Import Geometry tools

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

#Load geometry with file.
geometry = Geometry.importJSON('I_test.json')

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Numpy: Numpy data
- Matplotlib: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class in the Elasticity2D.py file.

Roadmap

2D elastic plate theory
Transient analysis (Core modification)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

Examples

References

Jonathan Richard Shewchuk, (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator

Ramirez, F. (2020). ICYA 4414 Modelación con Elementos Finitos [Class handout]. Universidad de Los Andes.

License

MIT

Assets 2

20 Feb 01:29

ZibraMax

v1.0.30

489fd7b

The Region and Docs Update

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Full Docs

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable Poisson equation
2D 1 Variable second order PDE
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strees Orthotropic
2D 2 Variable Plane Strain
3D 3 variables per node isotropic elasticity

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strain

Steps:

Create geometry
Create Border Conditions (Point and regions supported)
Solve!
For example: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Geometry import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

#Save geometry to .json file
geometry.exportJSON('I_test.json')

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Geometry import Geometry #Import Geometry tools

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

#Load geometry with file.
geometry = Geometry.importJSON('I_test.json')

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Numpy: Numpy data
- Matplotlib: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class in the Elasticity2D.py file.

Roadmap

2D elastic plate theory
Transient analysis (Core modification)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

Example index:

Example 1: Preliminar geometry test
Example 2: 2D Torsion 1 variable per node. H section-Triangular Quadratic.
Example 3: 2D Torsion 1 variable per node. Square section-Triangular Quadratic.
Example 4: 2D Torsion 1 variable per node. Mesh from internet-Square Lineal.
Example 5: 2D Torsion 1 variable per node. Creating and saving mesh-Triangular Quadratic.
Example 6: 1D random differential equation 1 variable per node. Linear Quadratic.
Example 7: GiD Mesh import test — Serendipity elements
Example 8: Plane Stress 2 variable per node. Plate in tension — Serendipity.
Example 9: Plane Stress 2 variable per node. Simple Supported Beam — Serendipity.
Example 10: Plane Stress 2 variable per node. Cantilever Beam — Triangular Quadratic.
Example 11: Plane Stress 2 variable per node. Fixed-Fixed Beam — Serendipity.
Example 12: Plane Strain 2 variable per node. Embankment from GiD — Serendipity.
Example 13: Plane Strain 2 variable per node. Embankment — Triangular Quadratic.
Example 14: Plane Stress 2 variable per node. Cantilever Beam — Serendipity.
Example 15: Profile creation tool. Same as Example 14
Example 16: Non-Local Plane Stress. [WIP]
Example 17: 1D Heat transfer.
Example 18: 2D border elements creation.
Example 19: Apply loads on regions. loadOnRegion method on Test 11
Example 20: Reddy's Example 11.7.1 Ed 3
Example 21: Exam...

Assets 2

20 Feb 00:09

ZibraMax

v1.0.29

ca6f7e3

The Region Update

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Full Docs

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable Poisson equation
2D 1 Variable second order PDE
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strees Orthotropic
2D 2 Variable Plane Strain
3D 3 variables per node isotropic elasticity

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strain

Steps:

Create geometry
Create Border Conditions (Point and regions supported)
Solve!
For example: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Geometry import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

#Save geometry to .json file
geometry.exportJSON('I_test.json')

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Geometry import Geometry #Import Geometry tools

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

#Load geometry with file.
geometry = Geometry.importJSON('I_test.json')

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Numpy: Numpy data
- Matplotlib: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class in the Elasticity2D.py file.

Roadmap

2D elastic plate theory
Transient analysis (Core modification)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

Example index:

Example 1: Preliminar geometry test
Example 2: 2D Torsion 1 variable per node. H section-Triangular Quadratic.
Example 3: 2D Torsion 1 variable per node. Square section-Triangular Quadratic.
Example 4: 2D Torsion 1 variable per node. Mesh from internet-Square Lineal.
Example 5: 2D Torsion 1 variable per node. Creating and saving mesh-Triangular Quadratic.
Example 6: 1D random differential equation 1 variable per node. Linear Quadratic.
Example 7: GiD Mesh import test — Serendipity elements
Example 8: Plane Stress 2 variable per node. Plate in tension — Serendipity.
Example 9: Plane Stress 2 variable per node. Simple Supported Beam — Serendipity.
Example 10: Plane Stress 2 variable per node. Cantilever Beam — Triangular Quadratic.
Example 11: Plane Stress 2 variable per node. Fixed-Fixed Beam — Serendipity.
Example 12: Plane Strain 2 variable per node. Embankment from GiD — Serendipity.
Example 13: Plane Strain 2 variable per node. Embankment — Triangular Quadratic.
Example 14: Plane Stress 2 variable per node. Cantilever Beam — Serendipity.
Example 15: Profile creation tool. Same as Example 14
Example 16: Non-Local Plane Stress. [WIP]
Example 17: 1D Heat transfer.
Example 18: 2D border elements creation.
Example 19: Apply loads on regions. loadOnRegion method on Test 11
Example 20: Reddy's Example 11.7.1 Ed 3
Example 21: Exam...

Assets 2

07 Feb 05:28

ZibraMax

v1.0.28

11d0396

The elastic update

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Full Docs

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable Poisson equation
2D 1 Variable second order PDE
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strees Orthotropic
2D 2 Variable Plane Strain
3D 3 variables per node isotropic elasticity

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams
1D 3 Variable Non-linear Euler Bernoulli Beams
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
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: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Mesh.Delaunay import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

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

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Mesh.Geometry import Geometry #Import Geometry tools

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

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

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Numpy: Numpy data
- Matplotlib: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class in the Elasticity2D.py file.

Roadmap

2D elastic plate theory
Geometry class modification for hierarchy with 1D, 2D and 3D geometry child classes
Transient analysis (Core modification)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

Example index:

Example 1: Preliminar geometry test
Example 2: 2D Torsion 1 variable per node. H section-Triangular Quadratic.
Example 3: 2D Torsion 1 variable per node. Square section-Triangular Quadratic.
Example 4: 2D Torsion 1 variable per node. Mesh from internet-Square Lineal.
Example 5: 2D Torsion 1 variable per node. Creating and saving mesh-Triangular Quadratic.
Example 6: 1D random differential equation 1 variable per node. Linear Quadratic.
Example 7: GiD Mesh import test — Serendipity elements
Example 8: Plane Stress 2 variable per node. Plate in tension — Serendipity.
Example 9: Plane Stress 2 variable per node. Simple Supported Beam — Serendipity.
Example 10: Plane Stress 2 variable per node. Cantilever Beam — Triangular Quadratic.
Example 11: Plane Stress 2 variable per node. Fixed-Fixed Beam — Serendipity.
Example 12: Plane Strain 2 variable per node. Embankment from GiD — Serendipity.
Example 13: Plane Strain 2 variable per node. Embankment — Triangular Quadratic.
Example 14: Plane Stress 2 variable per node. Cantilever Beam — Serendipity.
Example 15: Profile creation tool. Same as Example 14
Example 16: Non-Local Plane Stress. [WIP]
Example 17: 1D Heat transfer.
Example 18: 2D border elements creation.
Example 19: Apply loads on segments. loadOnSegment method on Test 11

<img src="https://raw.githubusercontent.com/ZibraMax/FEM/mas...

Assets 2

02 Jun 19:46

ZibraMax

v1.0.26

aa793b7

The Torsion Update

A Python FEM implementation.

N dimensional FEM implementation for M variables per node problems.

Installation

Use the package manager pip to install AFEM.

pip install AFEM

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Full Docs

Tutorial

Using pre implemented equations

Avaliable equations:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams [TODO]
1D 2 Variable Timoshenko Beams [TODO]
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
2D 2 Variable Plane Strees
2D 2 Variable Plane Strain

Numerical Validation:

1D 1 Variable ordinary diferential equation
1D 1 Variable 1D Heat with convective border
1D 2 Variable Euler Bernoulli Beams [TODO]
1D 2 Variable Timoshenko Beams [TODO]
2D 1 Variable Torsion
2D 1 Variable 2D Heat with convective borders
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: Example 2, Example 5, Example 11-14

Example without geometry file (Test 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM Torsion class
from FEM.Mesh.Delaunay import Delaunay #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 = Delaunay._strdelaunay(constrained=True, delaunay=True,
                                                                        a='0.00003', o=2)
#**Create** geometry using triangulation parameters. Geometry can be imported from .msh files.
geometry = Delaunay(vertices, params)

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

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

Example with geometry file (Example 2):

import matplotlib.pyplot as plt #Import libraries
from FEM.Torsion2D import Torsion2D #import AFEM
from FEM.Mesh.Geometry import Geometry #Import Geometry tools

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

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

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

Creating equation classes

Note: Don't forget the docstring!

Steps

Create a Python flie and import the libraries:
```
from .Core import *
from tqdm import tqdm
import numpy as np
import matplotlib.pyplot as plt
```
- Core: Solver
- Core: Numpy data
- Core: Matplotlib graphs
- Tqdm: Progressbars

Create a Python class with Core inheritance

class PlaneStress(Core):
    def __init__(self,geometry,*args,**kargs):
    #Do stuff
    Core.__init__(self,geometry)

It is important to manage the number of variables per node in the input geometry.

Define the matrix calculation methods and post porcessing methods.
```
def elementMatrices(self):
def postProcess(self):
```

The elementMatrices method uses gauss integration points, so you must use the following structure:

for e in tqdm(self.elements,unit='Element'):
    _x,_p = e.T(e.Z.T) #Gauss points in global coordinates and Shape functions evaluated in gauss points
    jac,dpz = e.J(e.Z.T) #Jacobian evaluated in gauss points and shape functions derivatives in natural coordinates
    detjac = np.linalg.det(jac)
    _j = np.linalg.inv(jac) #Jacobian inverse
    dpx = _j @ dpz #Shape function derivatives in global coordinates
    for k in range(len(e.Z)): #Iterate over gauss points on domain
        #Calculate matrices with any finite element model
    #Assign matrices to element

A good example is the PlaneStress class

Roadmap

Beam bending by Euler Bernoulli and Timoshenko equations
2D elastic plate theory
Geometry class modification for hierarchy with 1D, 2D and 3D geometry child classes
Transient analysis (Core modification)
Elasticity in 3D (3D meshing and post process)
Non-Lineal analysis for 1D equation (All cases)
Non-Lineal for 2D equation (All cases)
Testing and numerical validation (WIP)

Example index:

Example 1: Preliminar geometry test
Example 2: 2D Torsion 1 variable per node. H section-Triangular Quadratic.
Example 3: 2D Torsion 1 variable per node. Square section-Triangular Quadratic.
Example 4: 2D Torsion 1 variable per node. Mesh from internet-Square Lineal.
Example 5: 2D Torsion 1 variable per node. Creating and saving mesh-Triangular Quadratic.
Example 6: 1D random differential equation 1 variable per node. Linear Quadratic.
Example 7: GiD Mesh import test — Serendipity elements
Example 8: Plane Stress 2 variable per node. Plate in tension — Serendipity.
Example 9: Plane Stress 2 variable per node. Simple Supported Beam — Serendipity.
Example 10: Plane Stress 2 variable per node. Cantilever Beam — Triangular Quadratic.
Example 11: Plane Stress 2 variable per node. Fixed-Fixed Beam — Serendipity.
Example 12: Plane Strain 2 variable per node. Embankment from GiD — Serendipity.
Example 13: Plane Strain 2 variable per node. Embankment — Triangular Quadratic.
Example 14: Plane Stress 2 variable per node. Cantilever Beam — Serendipity.
Example 15: Profile creation tool. Same as Example 14
Example 16: Non-Local Plane Stress. [WIP]
Example 17: 1D Heat transfer.
Example 18: 2D border elements creation.
Example 19: Apply loads on segments. loadOnSegment method on Test 11

<img src="https://raw.githubusercontent.com/ZibraMax/FEM/master/Examples/ex...

Assets 2

Releases: ZibraMax/FEM

The Border Update

The Border Update

The Quality of Life Update pt 2

The Memory Update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

References

License

The Memory Update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

References

License

The Region and Docs Update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

Example index:

The Region Update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

Example index:

The elastic update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

Example index:

The Quality of Life Update

Installation

Contributing

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Example 2):

Creating equation classes

Steps

Roadmap

Example index:

The Torsion Update

Installation