14.5.1. Restrained beam under thermal expansionΒΆ

  1. The original model can be found here.
  2. The Pypton source code is shown below, which can be downloaded here.
  3. Make sure the numpy and matplotlib packages are installed in your Python distribution.
  4. Run the source code in your favorate Python program and should see
../_images/beamThermal.png 
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from openseespy.opensees import *

import numpy as np
import matplotlib.pyplot as plt

# define model
model('basic', '-ndm', 2, '-ndf', 3)

#define node
node(1, 0.0, 0.0)
node(2, 2.0, 0.0)
node(3, 1.0, 0.0)

#define boundary condition
fix(1, 1, 1, 1)
fix(2, 1, 1, 1)
fix(3, 0, 1, 1)

#define an elastic material with Tag=1 and E=2e11.
matTag = 1
uniaxialMaterial('Steel01Thermal', 1, 2e11, 2e11, 0.01)

#define fibred section Two fibres: fiber $yLoc $zLoc $A $matTag
secTag = 1
section('FiberThermal',secTag)
fiber(-0.025, 0.0, 0.005, matTag)
fiber(0.025, 0.0, 0.005, matTag)

#define coordinate transforamtion
#three transformation types can be chosen: Linear, PDelta, Corotational)
transfTag = 1
geomTransf('Linear', transfTag)

# beam integration
np = 3
biTag = 1
beamIntegration('Lobatto',biTag, secTag, np)

#define beam element
element('dispBeamColumnThermal', 1, 1, 3, transfTag, biTag)
element('dispBeamColumnThermal', 2, 3, 2, transfTag, biTag)

# define time series
tsTag = 1
timeSeries('Linear',tsTag)

# define load pattern
patternTag = 1
maxtemp = 1000.0
pattern('Plain', patternTag, tsTag)
eleLoad('-ele', 1, '-type', '-beamThermal', 1000.0, -0.05, 1000.0, 0.05)
#eleLoad -ele 2 -type -beamThermal 0 -0.05 0 0.05

# define analysis
incrtemp = 0.01
system('BandGeneral')
constraints('Plain')
numberer('Plain')
test('NormDispIncr', 1.0e-3,  100, 1)
algorithm('Newton')
integrator('LoadControl', incrtemp)
analysis('Static')

# analysis
nstep = 100
temp = [0.0]
disp = [0.0]
for i in range(nstep):
    if analyze(1) < 0:
        break

    temp.append(getLoadFactor(patternTag)*maxtemp)
    disp.append(nodeDisp(3,1))


plt.plot(temp,disp,'-o')
plt.xlabel('Temperature')
plt.ylabel('Nodal displacement')
plt.grid()
plt.show()