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郑敬润 1 year ago
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      topopt-88.py

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topopt-88.py

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# A 165 LINE TOPOLOGY OPTIMIZATION CODE BY NIELS AAGE AND VILLADS EGEDE JOHANSEN, JANUARY 2013
from __future__ import division
import numpy as np
from scipy.sparse import coo_matrix
from scipy.sparse.linalg import spsolve
from matplotlib import colors
import matplotlib.pyplot as plt
# MAIN DRIVER
def main(nelx,nely,volfrac,penal,rmin,ft,sysargv):
print("Minimum compliance problem with OC")
print("ndes: " + str(nelx) + " x " + str(nely))
print("volfrac: " + str(volfrac) + ", rmin: " + str(rmin) + ", penal: " + str(penal))
print("Filter method: " + ["Sensitivity based","Density based"][ft])
# Max and min stiffness
Emin=1e-9
Emax=1.0
# dofs:
ndof = 2*(nelx+1)*(nely+1)
# Allocate design variables (as array), initialize and allocate sens.
x=volfrac * np.ones(nely*nelx,dtype=float)
xold=x.copy()
xPhys=x.copy()
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=np.zeros((nely,nelx), dtype=float)
# FE: Build the index vectors for the for coo matrix format.
KE=lk()
edofMat=np.zeros((nelx*nely,8),dtype=int)
for elx in range(nelx):
for ely in range(nely):
el = ely+elx*nely
n1=(nely+1)*elx+ely
n2=(nely+1)*(elx+1)+ely
edofMat[el,:]=np.array([2*n1+2, 2*n1+3, 2*n2+2, 2*n2+3,2*n2, 2*n2+1, 2*n1, 2*n1+1])
# Construct the index pointers for the coo format
iK = np.kron(edofMat,np.ones((8,1))).flatten()
jK = np.kron(edofMat,np.ones((1,8))).flatten()
# Filter: Build (and assemble) the index+data vectors for the coo matrix format
nfilter=int(nelx*nely*((2*(np.ceil(rmin)-1)+1)**2))
iH = np.zeros(nfilter)
jH = np.zeros(nfilter)
sH = np.zeros(nfilter)
cc=0
for i in range(nelx):
for j in range(nely):
row=i*nely+j
kk1=int(np.maximum(i-(np.ceil(rmin)-1),0))
kk2=int(np.minimum(i+np.ceil(rmin),nelx))
ll1=int(np.maximum(j-(np.ceil(rmin)-1),0))
ll2=int(np.minimum(j+np.ceil(rmin),nely))
for k in range(kk1,kk2):
for l in range(ll1,ll2):
col=k*nely+l
fac=rmin-np.sqrt(((i-k)*(i-k)+(j-l)*(j-l)))
iH[cc]=row
jH[cc]=col
sH[cc]=np.maximum(0.0,fac)
cc=cc+1
# Finalize assembly and convert to csc format
H=coo_matrix((sH,(iH,jH)),shape=(nelx*nely,nelx*nely)).tocsc()
Hs=H.sum(1)
# BC's and support
dofs=np.arange(2*(nelx+1)*(nely+1))
fixed=np.union1d(dofs[0:2*(nely+1):2],np.array([2*(nelx+1)*(nely+1)-1]))
free=np.setdiff1d(dofs,fixed)
# Solution and RHS vectors
f=np.zeros((ndof,1))
u=np.zeros((ndof,1))
# Set load
f[1,0]=-1
# Initialize plot and plot the initial design
plt.ion() # Ensure that redrawing is possible
fig,ax = plt.subplots()
im = ax.imshow(-xPhys.reshape((nelx,nely)).T, cmap='gray',\
interpolation='none',norm=colors.Normalize(vmin=-1,vmax=0))
fig.show()
# Set loop counter and gradient vectors
loop=0
change=1
dv = np.ones(nely*nelx)
dc = np.ones(nely*nelx)
ce = np.ones(nely*nelx)
while change>0.01 and loop<2000:
loop=loop+1
# Setup and solve FE problem
sK=((KE.flatten()[np.newaxis]).T*(Emin+(xPhys)**penal*(Emax-Emin))).flatten(order='F')
K = coo_matrix((sK,(iK,jK)),shape=(ndof,ndof)).tocsc()
# Remove constrained dofs from matrix
K = K[free,:][:,free]
# Solve system
u[free,0]=spsolve(K,f[free,0])
# print(f.shape, f)
# print(K.shape, K)
# print(f[free,0])
# print(u.shape, u)
# Objective and sensitivity
ce[:] = (np.dot(u[edofMat].reshape(nelx*nely,8),KE) * u[edofMat].reshape(nelx*nely,8) ).sum(1)
obj=( (Emin+xPhys**penal*(Emax-Emin))*ce ).sum()
dc[:]=(-penal*xPhys**(penal-1)*(Emax-Emin))*ce
dv[:] = np.ones(nely*nelx)
# Sensitivity filtering:
if ft==0:
dc[:] = np.asarray((H*(x*dc))[np.newaxis].T/Hs)[:,0] / np.maximum(0.001,x)
elif ft==1:
dc[:] = np.asarray(H*(dc[np.newaxis].T/Hs))[:,0]
dv[:] = np.asarray(H*(dv[np.newaxis].T/Hs))[:,0]
# Optimality criteria
xold[:]=x
(x[:],g)=oc(nelx,nely,x,volfrac,dc,dv,g)
# Filter design variables
if ft==0: xPhys[:]=x
elif ft==1: xPhys[:]=np.asarray(H*x[np.newaxis].T/Hs)[:,0]
# Compute the change by the inf. norm
change=np.linalg.norm(x.reshape(nelx*nely,1)-xold.reshape(nelx*nely,1),np.inf)
# Plot to screen
im.set_array(-xPhys.reshape((nelx,nely)).T)
fig.canvas.draw()
# Write iteration history to screen (req. Python 2.6 or newer)
print("it.: {0} , obj.: {1:.3f} Vol.: {2:.3f}, ch.: {3:.3f}".format(\
loop,obj,(g+volfrac*nelx*nely)/(nelx*nely),change))
plt.show()
# np.savetxt("./results/top88_output" + str(loop) + '.csv', xPhys.reshape((nelx,nely)).T, delimiter=',')
# np.save('results/top88_output' + str(loop) + '.npy',xPhys.reshape((nelx,nely)).T)
# plt.savefig('images/top88_output' + str(loop) + '.png')
# print(f.shape, f)
# print(K.shape, K)
# print(f[free,0])
# print(u.shape, u)
print(u.reshape(nelx+1,nely+1,2))
# Make sure the plot stays and that the shell remains
np.save('results/top88_xPhys' + '_' +str(sysargv[1]) + '_' + str(sysargv[2]) + '.npy',xPhys.reshape((nelx,nely)).T)
np.save('results/top88_u' + '_' +str(sysargv[1]) + '_' + str(sysargv[2]) + '.npy',u)
np.savetxt('results/top88_xPhys' + '_' +str(sysargv[1]) + '_' + str(sysargv[2]) + '.csv', xPhys.reshape((nelx,nely)).T, delimiter=',')
plt.savefig('results/top88_xPhys' + '_' +str(sysargv[1]) + '_' + str(sysargv[2]) + '.png')
plt.show()
print("Press any key...")
#element stiffness matrix
def lk():
E=1
nu=0.3
k=np.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)*np.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)
# Optimality criterion
def oc(nelx,nely,x,volfrac,dc,dv,g):
l1=0
l2=1e9
move=0.2
# reshape to perform vector operations
xnew=np.zeros(nelx*nely)
while (l2-l1)/(l1+l2)>1e-3:
lmid=0.5*(l2+l1)
xnew[:]= np.maximum(0.0,np.maximum(x-move,np.minimum(1.0,np.minimum(x+move,x*np.sqrt(-dc/dv/lmid)))))
gt=g+np.sum((dv*(xnew-x)))
if gt>0 :
l1=lmid
else:
l2=lmid
return (xnew,gt)
# The real main driver
if __name__ == "__main__":
# Default input parameters
nelx=180
nely=60
volfrac=0.4
rmin=5.4
penal=3.0
ft=1 # ft==0 -> sens, ft==1 -> dens
import sys
if len(sys.argv)>1: nelx =int(sys.argv[1])
if len(sys.argv)>2: nely =int(sys.argv[2])
if len(sys.argv)>3: volfrac=float(sys.argv[3])
if len(sys.argv)>4: rmin =float(sys.argv[4])
if len(sys.argv)>5: penal =float(sys.argv[5])
if len(sys.argv)>6: ft =int(sys.argv[6])
main(nelx,nely,volfrac,penal,rmin,ft,sys.argv)
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