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Example:Timoshenko Locking - Revision history
2026-04-18T12:47:16Z
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Fotis at 22:48, 28 May 2007
2007-05-28T22:48:28Z
<p></p>
<p><b>New page</b></p><div><pre><br />
u=[]<br />
r=[2,3,4,5,10,20,50,100,500,1000]<br />
for beam in ['EULER','TIM2F','TIM2R','TIM3F','TIM3R']:<br />
t=[]<br />
for ratio in r:<br />
print 'Solving for type %s and r=%4i.'%(beam,ratio)<br />
domain.dim(2)<br />
material.uniElastic(1,1000,0.)<br />
section.rect(1,1.0,20./ratio)<br />
<br />
# nodes<br />
node.add(1,0.,0.)<br />
for i in range(20): <br />
node.add(2*i+2,i+0.5, 0.)<br />
node.add(2*i+3,i+1.0, 0.)<br />
<br />
# beams<br />
for i in range(20):<br />
if beam=='EULER':<br />
element.beam2e(i+1,2*i+1,2*i+3,1,1)<br />
elif beam=='TIM2F':<br />
element.beam2t(i+1,2*i+1,2*i+3,1,1,2)<br />
elif beam=='TIM2R':<br />
element.beam2t(i+1,2*i+1,2*i+3,1,1,1)<br />
elif beam=='TIM3F':<br />
element.beam3t(i+1,2*i+1,2*i+3,2*i+2,1,1,3)<br />
elif beam=='TIM3R':<br />
element.beam3t(i+1,2*i+1,2*i+3,2*i+2,1,1,3)<br />
<br />
node.fix(1,1)<br />
node.fix(1,2)<br />
node.fix(1,6)<br />
<br />
lc.define(1)<br />
load.node(21,2,1.0)<br />
<br />
analysis.static()<br />
analysis.run(1,1)<br />
<br />
t.append(node.data(41)['disp'][1])<br />
domain.clear()<br />
u.append(t)<br />
<br />
# Results<br />
for i in range(1,5):<br />
for j in range(len(r)):<br />
u[i][j]=u[i][j]/u[0][j]<br />
for j in range(len(r)):<br />
u[0][j]=1.0<br />
print <br />
print "====================================================="<br />
print "|Ratio |Tip Displacement (normalized) |"<br />
print "-----------------------------------------------------"<br />
print "| | EULER |TIM2F | TIM2R | TIM3F | TIM3R |"<br />
print "====================================================="<br />
for i in range(len(r)):<br />
print '|%9.3f|'%(r[i]),<br />
for j in range(5):<br />
print ' %6.4f'%(u[j][i]),<br />
print '|'<br />
print "====================================================="<br />
<br />
<br />
import pylab<br />
from numpy import array<br />
x=array(r)<br />
y1=array(u[0])<br />
y2=array(u[1])<br />
y3=array(u[2])<br />
y4=array(u[3])<br />
y5=array(u[4])<br />
pylab.semilogx(x,y1,'k',x,y2,'r:o',x,y3,'r-',x,y4,'g:o',x,y5,'g-')<br />
pylab.legend(('Euler-Bernulli', 'Timoshenko 2 nodes, 2 Gauss-points', 'Timoshenko 2 nodes, 1 Gauss-point','Timoshenko 3 nodes, 3 Gauss-points', 'Timoshenko 3 nodes, 2 Gauss-points'),<br />
'upper right', shadow=True)<br />
pylab.xlabel('log (L/h)')<br />
pylab.ylabel('w/wEB')<br />
pylab.grid(True)<br />
pylab.show()<br />
</pre><br />
<br />
[[Category:Examples]]</div>
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