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TopOptSIMP-Sigmund.py
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TopOptSIMP-Sigmund.py
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# -*- coding: utf-8 -*-
"""
Topology Optimization code of Sigmund in Python
Created on Fri Apr 08 11:33:51 2011
@author: gkumar
"""
import pylab as py
import numpy as ny
import matplotlib.pyplot as plt
from scipy.sparse import lil_matrix
def top(nelx,nely,volfrac,penal,rmin,problem):
# INITIALIZE
x = py.zeros((nely,nelx))
x[0:nely,0:nelx] = volfrac
loop = 0
change = 1.0
dc = py.zeros((nely,nelx))
j = 0
#START ITERATION
while change > 0.01 :
j = j+1
print j
loop = loop + 1
xold = x
# FE-ANALYSIS
U=FE(nelx,nely,x,penal,problem);
# OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
KE = lk()
c = 0.0
for ely in range(nely):
for elx in range(nelx):
n1 = (nely+1)*elx+ely;
n2 = (nely+1)*(elx+1) +ely;
Ue = U[[2*n1,2*n1+1, 2*n2,2*n2+1, 2*n2+2,2*n2+3, 2*n1+2,2*n1+3],0]
c = c + (x[ely,elx]**penal) * py.inner(Ue,py.inner(KE,Ue))
dc[ely,elx] = -penal*x[ely,elx]**(penal-1)*py.inner(Ue,py.inner(KE,Ue))
# FILTERING OF SENSITIVITIES
dc = check(nelx,nely,rmin,x,dc);
# DESIGN UPDATE BY THE OPTIMALITY CRITERIA METHOD
x = OC(nelx,nely,x,volfrac,dc);
# PRINT RESULTS
change = py.absolute(x-xold).max();
su= py.sum(x)/(nelx*nely)
print 'Loop :',loop,' Vol.: ',su,' Change: ', change
py.imshow(x,cmap = py.cm.gray)
py.show()
''' title(['v=' num2str(volfrac) '; J = ' num2str(c) '; Iterations = ' num2str(loop)]);'''
''' OPTIMALITY CRITERIA UPDATE '''
def OC(nelx,nely,x,volfrac,dc) :
l1 = 0; l2 = 100000; move = 0.2;
while (l2-l1 > 1e-4):
lmid = 0.5*(l2+l1)
xnew = py.maximum(1e-3,py.maximum(x-move,py.minimum(1.0,py.minimum(x+move,x*py.sqrt(-dc/lmid)))));
if sum(xnew) - volfrac*nelx*nely > 0:
l1 = lmid
else:
l2 = lmid
return xnew
''' MESH-INDEPENDENCY FILTER '''
def check(nelx,nely,rmin,x,dc):
dcn=py.zeros((nely,nelx));
for i in range(1,nelx+1):
for j in range(1,nely+1):
sumx=0.0
for k in range(py.maximum(i-py.floor(rmin),1),py.minimum(i+py.floor(rmin),nelx)+1):
for l in range(py.maximum(j-py.floor(rmin),1),py.minimum(j+py.floor(rmin),nely)+1):
fac = rmin-py.sqrt((i-k)**2+(j-l)**2)
sumx = sumx+py.maximum(0,fac)
dcn[j-1,i-1] = dcn[j-1,i-1] + py.maximum(0,fac)*x[l-1,k-1]*dc[l-1,k-1]
dcn[j-1,i-1] = dcn[j-1,i-1]/(x[j-1,i-1]*sumx)
return dcn
''' FE-ANALYSIS '''
def FE(nelx,nely,x,penal,problem):
KE = lk()
K = py.zeros((2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1)))
#K = lil_matrix((2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1)))
#F = lil_matrix((2*(nely+1)*(nelx+1),1))
F = py.zeros((2*(nely+1)*(nelx+1),1))
U = py.zeros((2*(nely+1)*(nelx+1),1))
#U = lil_matrix((2*(nely+1)*(nelx+1),1))
#print 'K', K, 'F', F, 'U', U
for elx in range(nelx):
for ely in range(nely):
n1 = (nely+1)*elx+ely
n2 = (nely+1)* (elx+1)+ely
#print 'n', n1, n2
edof = [2*n1,2*n1+1, 2*n2,2*n2+1, 2*n2+2,2*n2+3, 2*n1+2,2*n1+3]
#print 'edof', edof
E =x[ely,elx]**penal
#print E*KE, K+.01
for i in range(8):
for j in range(8):
#print edof[i],edof[j]
K[edof[i],edof[j]]=K[edof[i],edof[j]]+E*KE[i,j]
#K[edof,:][:,edof] = K[edof,:][:,edof] + E*KE
#print 'KXX',K[edof,:][:,edof]
#py.transpose(K)
#print 'Final', K
''' DEFINE LOADS AND SUPPORTS
Left fixed, right tip load'''
if (problem == 1):
forcedDof = [2*(nelx+1)*(nely+1)-nely-1] # y force
fixeddofs = py.arange(2*(nely+1))# left edge
#print forcedDof, fixeddofs
elif (problem == 2):
forcedDof = 2*(nelx+1)*(nely+1) -1
fixeddofs = py.arange(2*(nely+1))
elif (problem == 3):
forcedDof = py.array([2*(nelx+1)*(nely+1)-nely-1, 5*20*2+20-1]) # y force
fixeddofs = py.arange(2*(nely+1)) # left edge
F[forcedDof,0] = -1.0
alldofs = py.arange(2*(nely+1)*(nelx+1))
freedofs = list(set(alldofs) - set(fixeddofs))
#K = K.todense
#print K[freedofs,:][:,freedofs]
#print F[freedofs,:]
U[freedofs,:] = py.solve(K[freedofs,:][:,freedofs], F[freedofs,:]);
U[fixeddofs,:]= 0;
#input('abc')
#print 'U',py.shape(U), U
return U
''' ELEMENT STIFFNESS MATRIX '''
def lk():
E = 1.0
nu = 0.3
k=py.array([ 1./2.-nu/6.,1./8.+nu/8., -1./4.-nu/12., -1./8.+3.*nu/8., -1./4.+nu/12., -1./8.-nu/8. ,nu/6. , 1./8.-3.*nu/8.])
KE = E/(1-nu**2)*py.array([[ k[0], k[1], k[2], k[3], k[4], k[5] ,k[6], k[7]], [k[1], k[0], k[7], k[6], k[5], k[4], k[3], k[2]],[k[2], k[7], k[0], k[5], k[6], k[3], k[4], k[1]],[k[3], k[6], k[5], k[0], k[7], k[2], k[1], k[4]],[k[4], k[5], k[6], k[7,], k[0], k[1], k[2], k[3]], [k[5], k[4], k[3], k[2], k[1], k[0], k[7], k[6]],[k[6], k[3], k[4], k[1], k[2],k[7], k[0], k[5]], [k[7], k[2], k[1], k[4], k[3], k[6], k[5], k[0]]])
return KE
''' %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''
def findContourValueWithArea(field,desiredVolFrac):
#% Surround the matrix by a very low region to get closed contours
#% But we have to go thru hoops to get the corner contours to come
#% out correctly. Change sign of field, etc, etc.
[nely,nelx] = py.shape(field)
for value in py.arange(0.4,0.7,0.01):
vf = computeAreaInContour(field,value)/(nelx*nely);
if (vf > desiredVolFrac):
break;
return value
'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''
def computeAreaInContour(field,value):
field = -field
value = -value;
valMin = field.min()
[M,N] = py.shape(field);
bufferedField = valMin*py.ones((M+2,N+2));
#print bufferedField
bufferedField[1:-1,1:-1] = field;
print 'field' ,bufferedField
[c,d] = py.shape(bufferedField)
[X,Y] = py.mgrid[0:c,0:d]
cs = plt.contour(X,Y,bufferedField,[value]);
plt.show()
p =cs.collections[0].get_paths()
s = py.size(p)
a = 0.0;
for i in range(s):
p0 = cs.collections[0].get_paths()[i].vertices
a = a + area(p0)
#print 'p', p, 'p0', p0, 'size' , py.size(cs.collections[0].get_paths())
#ar = area(p0);
#print 'area', ar
return a;
def area(p):
return 0.5 * abs(sum(x0*y1 - x1*y0 for ((x0, y0), (x1, y1)) in segments(p)))
def segments(p):
return zip(p, p[1:] + [p[0]])
nelx = 30;nely = 15; volfrac = 0.5;
penal = 3;
rmin = 1.5;
problem = 1;
top(nelx,nely,volfrac,penal,rmin,problem)