https://github.com/jorgedelossantos/nusa
A Python library for structural analysis using the finite element method
https://github.com/jorgedelossantos/nusa
beam finite-element-analysis ipynb structural-analysis truss
Last synced: 5 months ago
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A Python library for structural analysis using the finite element method
- Host: GitHub
- URL: https://github.com/jorgedelossantos/nusa
- Owner: JorgeDeLosSantos
- License: mit
- Created: 2016-01-24T06:58:13.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2020-10-07T19:10:50.000Z (over 4 years ago)
- Last Synced: 2024-12-15T15:19:47.675Z (5 months ago)
- Topics: beam, finite-element-analysis, ipynb, structural-analysis, truss
- Language: Python
- Homepage: https://numython.github.io/stories/nusa/
- Size: 6.89 MB
- Stars: 125
- Watchers: 16
- Forks: 31
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
A Python library for structural analysis using the finite element method, designed for academic purposes.
## Versions
* **0.1.0** (16/11/2016)
* **0.2.0** (14/07/2019)
* **0.3.dev0** Development version
## Requirements
* NumPy
* Matplotlib
* Tabulate
* [GMSH](http://gmsh.info/)
## Installation
From PyPI (0.2.0 version):
```
$ pip install nusa
```
or from this repo (development version):
```
$ pip install git+https://github.com/JorgeDeLosSantos/nusa.git
```
## Elements type supported
* Spring
* Bar
* Truss
* Beam
* Linear triangle (currently, only plane stress)
## Mini-Demos
### Linear Triangle Element
```python
from nusa import *
import nusa.mesh as nmsh
md = nmsh.Modeler()
a = md.add_rectangle((0,0),(1,1), esize=0.1)
b = md.add_circle((0.5,0.5), 0.1, esize=0.05)
md.substract_surfaces(a,b)
nc, ec = md.generate_mesh()
x,y = nc[:,0], nc[:,1]
nodos = []
elementos = []
for k,nd in enumerate(nc):
cn = Node((x[k],y[k]))
nodos.append(cn)
for k,elm in enumerate(ec):
i,j,m = int(elm[0]),int(elm[1]),int(elm[2])
ni,nj,nm = nodos[i],nodos[j],nodos[m]
ce = LinearTriangle((ni,nj,nm),200e9,0.3,0.1)
elementos.append(ce)
m = LinearTriangleModel()
for node in nodos: m.add_node(node)
for elm in elementos: m.add_element(elm)
# Boundary conditions and loads
minx, maxx = min(x), max(x)
miny, maxy = min(y), max(y)
for node in nodos:
if node.x == minx:
m.add_constraint(node, ux=0, uy=0)
if node.x == maxx:
m.add_force(node, (10e3,0))
m.plot_model()
m.solve()
m.plot_nsol("seqv")
```
### Spring element
**Example 01**. For the spring assemblage with arbitrarily numbered nodes shown in the figure
obtain (a) the global stiffness matrix, (b) the displacements of nodes 3 and 4, (c) the
reaction forces at nodes 1 and 2, and (d) the forces in each spring. A force of 5000 lb
is applied at node 4 in the `x` direction. The spring constants are given in the figure.
Nodes 1 and 2 are fixed.
```python
# -*- coding: utf-8 -*-
# NuSA Demo
from nusa import *
def test1():
"""
Logan, D. (2007). A first course in the finite element analysis.
Example 2.1, pp. 42.
"""
P = 5000.0
# Model
m1 = SpringModel("2D Model")
# Nodes
n1 = Node((0,0))
n2 = Node((0,0))
n3 = Node((0,0))
n4 = Node((0,0))
# Elements
e1 = Spring((n1,n3),1000.0)
e2 = Spring((n3,n4),2000.0)
e3 = Spring((n4,n2),3000.0)
# Adding elements and nodes to the model
for nd in (n1,n2,n3,n4):
m1.add_node(nd)
for el in (e1,e2,e3):
m1.add_element(el)
m1.add_force(n4, (P,))
m1.add_constraint(n1, ux=0)
m1.add_constraint(n2, ux=0)
m1.solve()
if __name__ == '__main__':
test1()
```
### Beam element
**Example 02**. For the beam and loading shown, determine the deflection at point C.
Use E = 29 x 106 psi.
```python
"""
Beer & Johnston. (2012) Mechanics of materials.
Problem 9.13 , pp. 568.
"""
from nusa import *
# Input data
E = 29e6
I = 291 # W14x30
P = 35e3
L1 = 5*12 # in
L2 = 10*12 #in
# Model
m1 = BeamModel("Beam Model")
# Nodes
n1 = Node((0,0))
n2 = Node((L1,0))
n3 = Node((L1+L2,0))
# Elements
e1 = Beam((n1,n2),E,I)
e2 = Beam((n2,n3),E,I)
# Add elements
for nd in (n1,n2,n3): m1.add_node(nd)
for el in (e1,e2): m1.add_element(el)
m1.add_force(n2, (-P,))
m1.add_constraint(n1, ux=0, uy=0) # fixed
m1.add_constraint(n3, uy=0) # fixed
m1.solve() # Solve model
# Displacement at C point
print(n2.uy)
```
## GUIs based on NuSA
* [wxTruss](https://github.com/JorgeDeLosSantos/wxtruss)
## Documentation
To build documentation based on docstrings execute the `docs/toHTML.py` script. (Sphinx required)
Tutorials (Jupyter notebooks):
Spanish version (in progress):
* [Introducción a NuSA](docs/nusa-info/es/intro-nusa.ipynb)
* [Elemento Spring](docs/nusa-info/es/spring-element.ipynb)
* [Elemento Bar](docs/nusa-info/es/bar-element.ipynb)
* [Elemento Beam](docs/nusa-info/es/beam-element.ipynb)
* [Elemento Truss](docs/nusa-info/es/truss-element.ipynb)
* [Elemento LinearTriangle](docs/nusa-info/es/linear-triangle-element.ipynb)
English version (TODO):
* [Introduction to NuSA](docs/nusa-info/en/intro-nusa.ipynb)
* [Spring element](docs/nusa-info/en/spring-element.ipynb)
* [Bar element](docs/nusa-info/en/bar-element.ipynb)
* [Beam element](docs/nusa-info/en/beam-element.ipynb)
* [Truss element](docs/nusa-info/en/truss-element.ipynb)
* [LinearTriangle element](docs/nusa-info/en/linear-triangle-element.ipynb)
## About...
```
Developer: Pedro Jorge De Los Santos
E-mail: [email protected]
```