A Python library for structural analysis using the finite element method, designed for academic purposes.
- 0.1.0 (16/11/2016)
- 0.2.0 (14/07/2019)
- 0.3.dev0 Development version
- NumPy
- Matplotlib
- Tabulate
- GMSH
From PyPI (0.2.0 version):
$ pip install nusa
or from this repo (development version):
$ pip install git+https://github.com/JorgeDeLosSantos/nusa.git
- Spring
- Bar
- Truss
- Beam
- Linear triangle (currently, only plane stress)
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")
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.
# -*- 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()Example 02. For the beam and loading shown, determine the deflection at point C. Use E = 29 x 106 psi.
"""
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)To build documentation based on docstrings execute the docs/toHTML.py script. (Sphinx required)
Tutorials (Jupyter notebooks):
Spanish version (in progress):
- Introducción a NuSA
- Elemento Spring
- Elemento Bar
- Elemento Beam
- Elemento Truss
- Elemento LinearTriangle
English version (TODO):
Developer: Pedro Jorge De Los Santos
E-mail: [email protected]
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent