Feon is a python-based finite element analysis framework for education and research purpose by Dr. Pei Yaoyao at the sponsor of Hubei Univeristy of Technology!
Current:1.0.0
Numpy is a must. Matplotlib is needed for visualization. Mpmath is needed for Matrix derivation.
Using pip:
$pip install feon
Or
$python setup.py install
- sa---For structrual analysis
- ffa --- For fluid flow analysis
- derivation --- For element matrix derivation
-
Spring1D11
-
Spring2D11
-
Spring3D11
-
Link1D11
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Link2D11
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Link3D11
-
Beam1D11
-
Beam2D11
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Beam3D11
-
Tri2d11S---- Triange elements for plane stress problem
-
Tri2D11 ---- Triange elements for plane strain problem
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Tetra3D11
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Quad2D11S
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Quad2D11
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Plate3D11 ---Midline plate
-
Brick3D11
We name the elements with "Name" + "dimension" + 'order" + "type", type 1 means elastic .
A Truss promblem
# -*- coding: utf-8 -*-
# ------------------------------------
# Author: YAOYAO PEI
# E-mail: yaoyao.bae@foxmail.com
# License: Hubei University of Technology License
# -------------------------------------
from feon.sa import *
from feon.tools import pair_wise
from feon.sa.draw2d import *
import matplotlib.pyplot as plt
from matplotlib.ticker import MultipleLocator
if __name__ == "__main__":
#material property
E = 210e6 #elastic modulus
A1 = 31.2e-2 #cross-section area of hanging bars
A2 = 8.16e-2 #cross-section area of others
#create nodes and elements
nds1 = []
nds2 = []
for i in range(13):
nds1.append(Node(i,0))
for i in range(11):
nds2.append(Node(i+1,-1))
els = []
for e in pair_wise(nds1):
els.append(Link2D11((e[0],e[1]),E,A1))
for e in pair_wise(nds2):
els.append(Link2D11((e[0],e[1]),E,A1))
for i in range(6):
els.append(Link2D11((nds1[i],nds2[i]),E,A2))
for i in xrange(6):
els.append(Link2D11((nds2[i+5],nds1[i+7]),E,A2))
for i in range(11):
els.append(Link2D11((nds1[i+1],nds2[i]),E,A2))
#create FEA system
s = System()
#add nodes and elements into the system
s.add_nodes(nds1,nds2)
s.add_elements(els)
#apply boundry condition
s.add_node_force(nds1[0].ID,Fy = -1000)
s.add_node_force(nds1[-1].ID,Fy = -1000)
for i in range(1,12):
s.add_node_force(nds1[i].ID,Fy = -1900)
s.add_fixed_sup(nds1[0].ID)
s.add_rolled_sup(nds1[-1].ID,"y")
#solve the system
s.solve()
#show results
disp = [np.sqrt(nd.disp["Ux"]**2+nd.disp["Uy"]**2) for nd in s.get_nodes()]
eforce = [el.force["N"][0][0] for el in s.get_elements()]
fig = plt.figure()
ax = fig.add_subplot(211)
ax.yaxis.get_major_formatter().set_powerlimits((0,1))
ax2 = fig.add_subplot(212)
ax2.yaxis.get_major_formatter().set_powerlimits((0,1))
ax.set_xlabel(r"$Node ID$")
ax.set_ylabel(r"$Disp/m$")
ax.set_ylim([-0.05,0.05])
ax.set_xlim([-1,27])
ax.xaxis.set_minor_locator(MultipleLocator(1))
ax.plot(range(len(disp)),disp,"r*-")
ax2.set_xlabel(r"$Element ID$")
ax2.set_xlim([-1,46])
ax2.set_ylabel(r"$N/kN$")
ax2.set_ylim(-40000,40000)
ax2.xaxis.set_minor_locator(MultipleLocator(1))
for i in range(len(eforce)):
ax2.plot([i-0.5,i+0.5],[eforce[i],eforce[i]],"ks-",ms = 3)
plt.show()
draw_bar_info(els[5])
Frame with hinged node problem
# -*- coding: utf-8 -*-
# ------------------------------------
# Author: YAOYAO PEI
# E-mail: yaoyao.bae@foxmail.com
# License: Hubei University of Technology License
# -------------------------------------
from feon.sa import *
from feon.tools import pair_wise
#define beamlink element
class BeamLink2D11(StructElement):
def __init__(self,nodes,E,A,I):
StructElement.__init__(self,nodes)
self.E = E
self.A = A
self.I = I
#define node degree of freedom, left node has three dofs
#while the right node has only two
def init_unknowns(self):
self.nodes[0].init_unknowns("Ux","Uy","Phz")
self.nodes[1].init_unknowns("Ux","Uy")
self._ndof = 3
#transformative matrix
def calc_T(self):
TBase = _calc_Tbase_for_2d_beam(self.nodes)
self._T = np.zeros((6,6))
self._T[:3,:3] = self._T[3:,3:] = TBase
#stiffness matrix
def calc_ke(self):
self._ke = _calc_ke_for_2d_beamlink(E = self.E,A = self.A,I = self.I,L = self.volume)
def _calc_ke_for_2d_beamlink(E = 1.0,A = 1.0,I = 1.0,L = 1.0):
a00 = E*A/L
a03 = -a00
a11 = 3.*E*I/L**3
a12 = 3.*E*I/L**2
a14 = -a11
a22 = 3.*E*I/L
T = np.array([[a00, 0., 0., a03, 0.,0.],
[ 0., a11, a12, 0., a14, 0.],
[ 0., a12, a22, 0.,-a12, 0.],
[a03, 0., 0., a00, 0., 0.],
[ 0., a14, -a12, 0., a11, 0.],
[ 0., 0., 0., 0., 0., 0.]])
return T
def _calc_Tbase_for_2d_beam(nodes):
x1,y1 = nodes[0].x,nodes[0].y
x2,y2 = nodes[1].x,nodes[1].y
le = np.sqrt((x2-x1)**2+(y2-y1)**2)
lx = (x2-x1)/le
mx = (y2-y1)/le
T = np.array([[lx,mx,0.],
[-mx,lx,0.],
[0.,0.,1.]])
return T
if __name__ == "__main__":
#materials
E = 210e6
A = 0.005
I = 10e-5
#nodes and elements
n0 = Node(0,0)
n1 = Node(0,3)
n2 = Node(4,3)
n3 = Node(4,0)
n4 = Node(4,5)
n5 = Node(8,5)
n6 = Node(8,0)
e0 = Beam2D11((n0,n1),E,A,I)
e1 = BeamLink2D11((n1,n2),E,A,I)
e2 = Beam2D11((n2,n3),E,A,I)
e3 = Beam2D11((n2,n4),E,A,I)
e4 = Beam2D11((n4,n5),E,A,I)
e5 = Beam2D11((n5,n6),E,A,I)
#system
s = System()
s.add_nodes([n0,n1,n2,n3,n4,n5,n6])
s.add_elements([e0,e1,e2,e3,e4,e5])
s.add_node_force(1,Fx = -10)
s.add_node_force(5,Fx = -10)
s.add_fixed_sup(0,3,6)
s.solve()
print n2.disp
print e1.force
Embedded wall problem
# -*- coding: utf-8 -*-
# ------------------------------------
# Author: YAOYAO PEI
# E-mail: yaoyao.bae@foxmail.com
# License: Hubei University of Technology License
# -------------------------------------
from feon.sa import *
from feon.tools import pair_wise
import matplotlib.pyplot as plt
from feon.sa.draw2d import *
if __name__ == "__main__":
#material
E1 = 2.85e6 #elastic modulus of the wall
E2 = 200e6 #elastic modulus of the bracing
k = 15000 #soil reaction coefficient
I = 0.0427 #inertia of the wall
A = 0.8 # area of the wall section
A1 = 0.003 #area of the bracing section
ka = 0.6 #active earth pressure coefficient
#create nodes
nds1 =[Node(0,-i) for i in range(10)]
nds2 = [Node(0,-(i+20)*0.5) for i in range(11)]
nds3 = [Node(-0.5,-(i+20)*0.5) for i in range(11)]
nds4 = [Node(-1.5,-2),Node(-1.5,-6)]
#create beam
els=[]
for nd in pair_wise(nds1+nds2):
els.append(Beam2D11(nd,E1,A,I))
#create soil spring
for i in range(11):
els.append(Spring2D11((nds2[i],nds3[i]),k))
#create bracing
els.append(Link2D11((nds4[0],nds1[2]),E2,A1))
els.append(Link2D11((nds4[1],nds1[6]),E2,A1))
#create FEA system
s = System()
s.add_nodes(nds1,nds2,nds3,nds4)
s.add_elements(els)
nid1 = [nd.ID for nd in nds3]
nid2 = [nd.ID for nd in nds4]
#add fixed supports
s.add_fixed_sup(nid1,nid2)
for i,el in enumerate(els[:10]):
s.add_element_load(el.ID,"tri",-18*ka)
s.add_element_load(el.ID,"q",-i*18*ka)
#add active earth pressure
for el in els[10:20]:
s.add_element_load(el.ID,"q",-180*ka)
for nd in nds1:
nd.set_disp(Uy =0)
for nd in nds2:
nd.set_disp(Uy = 0)
#solve the FEA system
s.solve()
#show results
disp = np.array([nd.disp["Ux"] for nd in nds1]+[nd.disp["Ux"] for nd in nds2])*1000
Mz = [el.force["Mz"][0][0] for el in els[:20]]
fig1,fig2,fig3 = plt.figure(),plt.figure(),plt.figure()
ax1 = fig1.add_subplot(111)
ax2 = fig2.add_subplot(111)
ax3 = fig3.add_subplot(111)
Y1 = [-i for i in range(10)]+[-(i+20)*0.5 for i in range(11)]
Y2 = [-i-0.5 for i in range(10)]+[-(i+20)*0.5-0.5 for i in range(10)]
ax1.plot(disp,Y1,"r--")
ax1.set_xlabel("$Ux/mm$")
ax1.set_ylabel("$Height/m$")
ax2.plot(Mz,Y2,"r-+")
ax2.set_xlabel("$Mz/kN.m$")
ax2.set_ylabel("$Height/m$")
for el in els[:20]:
draw_element(ax3,el,lw = 10,color = "g")
for el in els[20:31]:
draw_spring(ax3,el,color = "k")
for el in els[31:]:
draw_element(ax3,el,lw = 1.5,color = "k",marker = "s")
for nd in nds3+nds4:
draw_fixed_sup(ax3,nd,factor = (0.4,4),color ="k")
ax3.set_xlim([-2,2])
ax3.set_ylim([-16,1])
plt.show()Fuild flow problem
# -*- coding: utf-8 -*-
# ------------------------------------
# Author: YAOYAO PEI
# E-mail: yaoyao.bae@foxmail.com
# License: Hubei University of Technology License
# -------------------------------------
from feon.ffa import *
from feon.tools import pair_wise
import numpy as np
if __name__ == "__main__":
#permeability
Kxx = -2e-5
#create nodes and elements
A = np.pi*(np.linspace(0.06,0.15,7)[:-1]+0.0075)
nds = [Node(-i*0.1,0) for i in range(7)]
els = []
for i in range(6):
els.append(E1D((nds[i],nds[i+1]),Kxx,A[i]))
#create FEA system
s = System()
s.add_nodes(nds)
s.add_elements(els)
s.add_node_head(0,0.2)
s.add_node_head(6,0.1)
s.solve()
print [nd.head["H"] for nd in nds]
print [el.velocity["Vx"] for el in els]