def initBeams(dim):
tapered = teb.taperedElasticaBeam()
tapered.setBeamDimensions(L=dim['L'], Lt=dim['Lt'], t=dim['t'],
w=dim['w'], E=dim['E'])
tapered.setShearLoad(shearLoad=dim['shearLoad'])
tapered.setEndAngle(endAngle=dim['endAngle'])
untapered = teb.taperedElasticaBeam()
untapered.setBeamDimensions(L=dim['L'], Lt=1, t=dim['t'],
w=dim['w'], E=dim['E'])
untapered.setShearLoad(shearLoad=dim['shearLoad'])
untapered.setEndAngle(endAngle=dim['endAngle'])
return (tapered, untapered)
def main():
toRadians = np.pi/180
endAngleDeg = np.array([40, 50, 60], dtype=int)
L = 60e-6
Lt = 120e-1
t = 20e-6
w = 20e-6
E = 1e6
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L=L, Lt=Lt, t=t, w=w, E=E)
fig = initFigure()
colors = initColors()
elasticaLegends = []
eulerLegends = []
for (offset, value) in enumerate(endAngleDeg):
elastica(beam=beam, endAngle=value*toRadians, fig=fig,
legend=elasticaLegends, color=colors[offset])
euler(beam=beam, endAngle=value*toRadians, fig=fig,
legend=eulerLegends, color=colors[offset])
addChartJunk(beam=beam, figure=fig, endAngle=endAngleDeg,
elasticaLegends=elasticaLegends, eulerLegends=eulerLegends)
saveFile(fig=fig['fig'])
def main():
numPointLoads = 100
pointLoad = np.linspace(.1e-6,18e-6,numPointLoads)
L = 60e-6
Lt = 120e-1
t = 20e-6
w = 20e-6
E = 1e6
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L=L, Lt=Lt, t=t, w=w, E=E)
dateCode = datetime.now().strftime('%Y%m%d%H%M')
for i, j in zip(pointLoad, range(numPointLoads)):
elasticaLegends = []
eulerLegends = []
fig = initFigure()
elastica(beam=beam, pointLoad=i, fig=fig, legend=elasticaLegends, color='b')
euler(beam=beam, pointLoad=i, fig=fig, legend=eulerLegends, color='r')
addChartJunk(beam=beam, figure=fig, pointLoad=i,
elasticaLegends=elasticaLegends, eulerLegends=eulerLegends)
saveFile(fig=fig['fig'], imageNumber=j, dateCode=dateCode)
mpl.close()
def main():
pointLoad = [1e-6, 5e-6, 10e-6]
L = 60e-6
Lt = 120e-1
t = 20e-6
w = 20e-6
E = 1e6
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L=L, Lt=Lt, t=t, w=w, E=E)
fig = initFigure()
colors = initColors()
elasticaLegends = []
eulerLegends = []
for (index, value) in enumerate(pointLoad):
elastica(beam=beam, pointLoad=value, fig=fig,
legend=elasticaLegends, color=colors[index])
euler(beam=beam, pointLoad=value, fig=fig,
legend=eulerLegends, color=colors[index])
addChartJunk(beam=beam, figure=fig, pointLoad=pointLoad,
elasticaLegends=elasticaLegends, eulerLegends=eulerLegends)
saveFile(fig=fig['fig'])
def beamLoop(E,t,w,L,Lt,ax,label):
beam = teb.taperedElasticaBeam()
lengthInContact = sp.linspace(0,10,11) * 1e-6
frictionFactor = 1
shearForce = lengthInContact * frictionFactor
shearForce = sp.zeros(len(lengthInContact))
endAngle = sp.pi / 2
curvature = sp.zeros(len(lengthInContact))
print(label)
for i, thisLength in enumerate(lengthInContact):
beam.setBeamDimensions(L - thisLength, Lt, t, w, E)
beam.setEndAngle(endAngle)
beam.setShearLoad(shearForce[i])
beam.calculateSlopeFunction()
beam.calculateDisplacements()
curvature[i] = beam.slopeDerivative[-1]
print('length =', thisLength*1e6, 'um')
#print('curvature =', curvature[i], '1/m')
print('radius =', 1/curvature[i]*1e6, 'um')
tipThick = beam.thickness(L-thisLength)
print('tip thick =', tipThick*1e6, 'um')
print()
ax.plot(lengthInContact*1e6,1/curvature*1e6,label = label)
def main():
E = 2e6 # modulus of pdms
t = 19e-6 # thickness of beam
w = 19e-6 # width of beam
L = 52e-6 # length of beam
Lt = 60e-6 # length of taper
#Lt = 1000000e-6 # length of taper
thisBeam = teb.taperedElasticaBeam()
lengthInContact = sp.linspace(0,10,11) * 1e-6
endAngle = sp.pi / 2
figure = plt.figure()
# figure size and resolution
width = 9
height = 9
figure.set_figheight(height)
figure.set_figwidth(width)
ax = figure.add_axes((0.1,0.4,0.8,0.55))
bendingMoment = sp.zeros(len(lengthInContact))
curvature = sp.zeros(len(lengthInContact))
for i, thisLength in enumerate(lengthInContact):
thisBeam.setBeamDimensions(L - thisLength, Lt, t, w, E)
bendingMoment[i] = thisBeam.calculateSlopeFunctionForEndAngle(endAngle)
thisBeam.calculateDisplacements()
print(bendingMoment[i],end='\t')
curvature[i] = thisBeam.derivativeForEndAngle(0, L - thisLength,
bendingMoment[i])
print(curvature[i])
#thisBeam.plotBeam(ax,str(thisLength))
ax.plot(lengthInContact*1e6,1/curvature*1e6)
ax.set_xlabel('length in contact (microns)')
ax.set_ylabel('radius of curvature (microns)')
ax.grid()
from datetime import datetime
import os
string = ('length = '+str(L*1e6)+' microns'+'\n'+
'thickness = '+str(t*1e6)+' microns'+'\n'+
'width = '+str(w*1e6)+' microns'+'\n'+
'modulus = '+str(E/1e6)+' MPa'+'\n'+
'taper length = '+str(Lt*1e6)+' microns' +'\n'+
datetime.now().strftime('%d %b %Y - %H:%M')+'\n'+
os.path.abspath(__file__))
xPos = 0.5
yPos = 0.05
plt.figtext(xPos, yPos, string,
ha='center')
# name plot same as script
fileName = os.path.basename(__file__)
fileName = os.path.splitext(fileName)[0]
plotFileName = fileName + '.pdf'
figure.savefig(plotFileName, transparent=True)
def main():
E = 1e6 # elastic modulus of beam (Pa)
t = 20e-6 # dimension of beam in bending direction (m)
w = 20e-6 # width of beam (m)
L = 60e-6 # length of beam (m)
Lt = 1e6 # length of taper (m) at Lt beam has zero thickness
# instantiate
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L,Lt,t,w,E)
shearLoad = sp.linspace(0,5e-6,11)
energy = []
for load in shearLoad:
beam.setShearLoad(load)
beam.calculateSlopeFunction()
energy.append(beam.calculateStrainEnergy())
fig, ax = configurePlot()
ax.plot(shearLoad,energy)
fig.savefig('energy.pdf')
E = 1e6 # elastic modulus of beam (Pa)
t = 20e-6 # dimension of beam in bending direction (m)
w = 20e-6 # width of beam (m)
L = 60e-6 # length of beam (m)
Lt = 1e6 # length of taper (m) at Lt beam has zero thickness
I = t**3 * w / 12.0
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L,Lt,t,w,E)
beam.setEndAngle(sp.pi/2)
beam.calculateSlopeFunction()
energy = beam.calculateStrainEnergy()
print 'teb energy = ', energy
analyticEnergy = (sp.pi/L/2.0)**2 * E * I / 2 * L
print 'analytic energy = ',analyticEnergy
energyError = (energy-analyticEnergy)/analyticEnergy
print 'error as fraction =', energyError
def initBeam(L,Lt,w,t):
E = 1.75e6 # elastic modulus of beam (Pa)
# t = 20e-6 # dimension of beam in bending direction (m)
# w = 20e-6 # width of beam (m)
# L = 75e-5 # length of beam (m)
# Lt = 80e-6 # length of taper (m) at Lt beam has zero thickness
beam=teb.taperedElasticaBeam()
beam.setBeamDimensions(E=E, t=t, w=w, L=L, Lt=Lt)
return beam
def initBeam():
E = 200e9 # elastic modulus of beam (Pa)
t = 0.4e-3 # dimension of beam in bending direction (m)
w = 2e-2 # width of beam (m)
L = 2e-3 # length of beam (m)
Lt = 2.0151e-3 # length of taper (m) at Lt beam has zero thickness
beam=teb.taperedElasticaBeam()
beam.setBeamDimensions(E=E, t=t, w=w, L=L, Lt=Lt)
return beam
def plotBeam(Lt,suffix):
thisBeam = teb.taperedElasticaBeam()
lengthInContact = sp.linspace(0,20,11) * 1e-6
endAngle = sp.pi / 2
figure = plt.figure()
# figure size and resolution
width = 9
height = 9
figure.set_figheight(height)
figure.set_figwidth(width)
ax = figure.add_axes((0.1,0.4,0.8,0.55))
ax.set_aspect('equal')
for i, thisLength in enumerate(lengthInContact):
thisBeam.setBeamDimensions(L - thisLength, Lt, t, w, E)
thisBeam.calculateSlopeFunctionForEndAngle(endAngle)
thisBeam.addSlopeWithLength(endAngle, thisLength)
thisBeam.calculateDisplacements()
thisBeam.plotBeam(ax,str(thisLength))
ax.grid()
ax.legend(loc='best')
from datetime import datetime
import os
string = ('length = '+str(L*1e6)+' microns'+'\n'+
'thickness = '+str(t*1e6)+' microns'+'\n'+
'width = '+str(w*1e6)+' microns'+'\n'+
'modulus = '+str(E/1e6)+' MPa'+'\n'+
'taper length = '+str(Lt*1e6)+' microns' +'\n'+
datetime.now().strftime('%d %b %Y - %H:%M')+'\n'+
os.path.abspath(__file__))
xPos = 0.5
yPos = 0.05
plt.figtext(xPos, yPos, string,
ha='center')
# name plot same as script
fileName = os.path.basename(__file__)
fileName = os.path.splitext(fileName)[0]
plotFileName = fileName + '-' + suffix + '.pdf'
figure.savefig(plotFileName, transparent=True)
def main():
E = 1e6 # elastic modulus of beam (Pa)
t = 20e-6 # dimension of beam in bending direction (m)
w = 20e-6 # width of beam (m)
L = 60e-6 # length of beam (m)
Lt = 1e6 # length of taper (m) at Lt beam has zero thickness
# instantiate
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L,Lt,t,w,E)
shearLoad = 1e-6 # point load condition
endAngle = 3.1415/2
axialLoad = [-2.0e-6, 0.0, 2.0e-6]
beam.setShearLoad(shearLoad)
beam.setEndAngle(endAngle)
width = 6.0 # fig width
height = 6.0 # fig height
fig = plt.figure()
fig.set_figheight(height)
fig.set_figwidth(width)
ax = fig.add_axes((0.1,0.1,0.8,0.8))
#ax.set_aspect('equal')
ax.grid()
for al in axialLoad:
beam.setAxialLoad(al)
# solve psi(s) function
beam.calculateSlopeFunction()
# convert psi(s) to cartesian
beam.calculateDisplacements()
legendString = str(al)
# plot beam position
beam.plotBeam(ax,legendString)
ax.legend(loc='best')
fig.savefig('arbLoad.pdf')
def main():
degrees = np.pi/180
endAngle = np.linspace(1,89,89)
L = 60e-6
Lt = 120e-1
t = 20e-6
w = 20e-6
E = 1e6
beam = teb.taperedElasticaBeam()
beam.setBeamDimensions(L=L, Lt=Lt, t=t, w=w, E=E)
dateCode = datetime.now().strftime('%Y%m%d%H%M')
for i in endAngle:
elasticaLegends = []
eulerLegends = []
fig = initFigure()
elastica(beam=beam, endAngle=i*np.pi/180, fig=fig, legend=elasticaLegends, color='b')
euler(beam=beam, endAngle=i*np.pi/180, fig=fig, legend=eulerLegends, color='r')
addChartJunk(beam=beam, figure=fig, endAngle=i*np.pi/180,
elasticaLegends=elasticaLegends, eulerLegends=eulerLegends)
saveFile(fig=fig['fig'], endAngle=i*np.pi/180, dateCode=dateCode)
#!/usr/bin/env python import taperedElasticaBeam as teb import matplotlib as mpl import matplotlib.pyplot as plt E = 2e6 # modulus of pdms t = 19e-6 # thickness of beam w = 19e-6 # width of beam I = t**3 * w / 12.0 # moment of inertia L = 52e-6 # length of beam Lt = 60e-6 # length of taper Lt = 1000000e-6 # length of taper thisBeam = teb.taperedElasticaBeam() thisBeam.setBeamDimensions(L,Lt,t,w,E) load = 1e-5 thisBeam.applyShearLoad(load) thisBeam.printParameters() thisBeam.calculateSlopeFunction() thisBeam.calculateDisplacements() figure = plt.figure() # figure size and resolution width = 9 height = 9 figure.set_figheight(height) figure.set_figwidth(width) #ax = figure.add_subplot(121) #ax = figure.add_axes((left_margin, height/2+0.5,
def createBeams(E, t, w, I, L, Lt):
untaperedBeam = teb.taperedElasticaBeam()
taperedBeam = teb.taperedElasticaBeam()
taperedBeam.setBeamDimensions(L=L, Lt=Lt, t=t, w=w, E=E)
untaperedBeam.setBeamDimensions(L=L, Lt=1, t=t, w=w, E=E)
return (untaperedBeam, taperedBeam)
