21 Mar 17:34

ZibraMax

510bfaf

1D and 2D FULL FEM implementation with docs

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()

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
1D and 2D heat transfer
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)
UNIT TESTING
NUMERICAL VALIDATION
Non Local 2D?

Test index:

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

Assets 2

21 Mar 17:13

ZibraMax

v1.0.5

13ea64a

1D and 2D FULL FEM implementation with docs

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

21 Mar 03:42

ZibraMax

v1.0.2

328f93c

1D and 2D FULL FEM implementation

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()

Roadmap

Beam bending by Euler Bernoulli and Timoshenko equations
2D elastic plate theory
1D and 2D heat transfer
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)
UNIT TESTING
NUMERICAL VALIDATION
Non Local 2D?

Test index:

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

References

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

Assets 4

21 Mar 04:01

ZibraMax

V1.0.3

9b7453e

1D and 2D FULL FEM implementation

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()

Roadmap

Beam bending by Euler Bernoulli and Timoshenko equations
2D elastic plate theory
1D and 2D heat transfer
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)
UNIT TESTING
NUMERICAL VALIDATION
Non Local 2D?

Test index:

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

References

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

Assets 2

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Creating equation classes

Steps

Roadmap

Test index:

References

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Roadmap

Test index:

References

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Roadmap

Test index:

References

Releases: ZibraMax/FEM

1D and 2D FULL FEM implementation with docs

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Creating equation classes

Steps

Roadmap

Test index:

References

1D and 2D FULL FEM implementation with docs

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

1D and 2D FULL FEM implementation

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Roadmap

Test index:

References

1D and 2D FULL FEM implementation

FEM

Tutorial

Using pre implemented equations

Steps:

Example without geometry file (Test 2):

Example with geometry file (Test 2):

Roadmap

Test index:

References