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# Amira Abdel-Rahman
# (c) Massachusetts Institute of Technology 2020
# Topology Optimization Implementation in Julia from various sources
# based on https://paulino.ce.gatech.edu/conferences/papers/11pereira_anefficientandcompact.pdf and http://www.topopt.mek.dtu.dk/apps-and-software and https://github.com/blademwang11/Topopt/blob/master/top.jl
#######################################2d##################################################################
function topologyOptimization(nelx,nely,volfrac,rmin,penal)
anim=Animation()
display("Minimum compliance problem with OC")
display("ndes: $nelx x $nely")
display("volfrac: $volfrac rmin: $rmin penal: $penal")
# 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 * ones(Float64,nely,nelx)
xold=copy(x)
xPhys=copy(x)
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=zeros(Float64,(nely,nelx))
# FE: Build the index vectors for the for coo matrix format.
KE=lk()
nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
# DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)
U = zeros(2*(nely+1)*(nelx+1),1)
fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))
alldofs = 1:(2*(nely+1)*(nelx+1))
freedofs = setdiff(alldofs,fixeddofs)
# Prepare filter
iH = ones(convert(Int,nelx*nely*(2*(ceil(rmin)-1)+1)^2),1)
jH = ones(Int,size(iH))
sH = zeros(size(iH))
k = 0;
for i1 = 1:nelx
for j1 = 1:nely
e1 = (i1-1)*nely+j1
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (i2-1)*nely+j2
k = k+1
iH[k] = e1
jH[k] = e2
sH[k] = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2))
end
end
end
end
H = sparse(vec(iH),vec(jH),vec(sH))
Hs = sum(H,dims=2)
###################################################
loop = 0
change = 1
maxIter=1000
# Start iteration
for i =1:maxIter
if (change > 0.01)
# Start iteration
loop += 1
# FE-ANALYSIS
sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)
K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
@timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
# Objective function and sensitivity analysis
ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx)
c = sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce))
dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce
dv = ones(nely,nelx)
dc[:] = H*(dc[:]./Hs)
dv[:] = H*(dv[:]./Hs)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
l1 = 0; l2 = 1e9; move = 0.2; xnew = 0
while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.((0.0.-dc)./dv./lmid)))))
xPhys[:] = (H*xnew[:])./Hs
if sum(xPhys[:]) > volfrac*nelx*nely
l1 = lmid
else
l2 = lmid
end
end
change = maximum(abs.(xnew[:].-x[:]))
x = xnew
m=mean(xPhys[:])
display(" It:$loop Obj:$c Vol:$m ch:$change ")
if loop<20||mod(loop,10)==0
xxx=1 .- clamp.(xPhys,0,1)
display(heatmap(xxx,xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal))
heatmap(xxx,xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0),aspect_ratio=:equal)
frame(anim)
end
xPhys = copy(x)
end
end
return xPhys,anim
end
#########################################################################################################
function CompliantTopologyOptimization(nelx,nely,volfrac,rmin,penal,maxIter,Load,Support,Spring,DOut)
anim=Animation()
display("Minimum compliance problem with OC")
display("ndes: $nelx x $nely")
display("volfrac: $volfrac rmin: $rmin penal: $penal")
# Max and min stiffness
Emin=1e-9
Emax=1.0
change = 1
# dofs:
ndof = 2*(nelx+1)*(nely+1)
# Allocate design variables (as array), initialize and allocate sens.
x=volfrac * ones(Float64,nely,nelx)
xold=copy(x)
xPhys=copy(x)
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=zeros(Float64,(nely,nelx))
# FE: Build the index vectors for the for coo matrix format.
KE=lk()
nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
# DEFINE LOADS AND SUPPORTS
F = sparse(2 .*Load[:,1] .-2 .+ Load[:,2],ones(size(Load,1)),Load[:,3],2*(nely+1)*(nelx+1),2)
DofDOut = 2 * DOut[1] - 2 +DOut[2]; #only one
F=Array(F)
F[DofDOut,2]=-1
fixeddofs = 2 .*Support[:,1] .-2 .+ Support[:,2]
NSpring = size(Spring,1);
s = sparse(2 .*Spring[:,1] .-2 .+ Spring[:,2],ones(size(Spring,1)),Spring[:,3],2*(nely+1)*(nelx+1),2)
m=Array(s)[:,1]
S= sparse(diagm(m))
U = zeros(2*(nely+1)*(nelx+1),2)
alldofs = 1:(2*(nely+1)*(nelx+1))
freedofs = setdiff(alldofs,fixeddofs)
# Prepare filter
iH = ones(convert(Int,nelx*nely*(2*(ceil(rmin)-1)+1)^2),1)
jH = ones(Int,size(iH))
sH = zeros(size(iH))
k = 0;
for i1 = 1:nelx
for j1 = 1:nely
e1 = (i1-1)*nely+j1
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (i2-1)*nely+j2
k = k+1
iH[k] = e1
jH[k] = e2
sH[k] = max(0,rmin-sqrt((i1-i2)^2+(j1-j2)^2))
end
end
end
end
H = sparse(vec(iH),vec(jH),vec(sH))
Hs = sum(H,dims=2)
change= 1
loop = 0
changeStable=0
# Start iteration
for penal in 1.0:0.5:4
display(" Penalty: $penal")
loop = 0
for i =1:maxIter
if (change < 0.01)
changeStable+=1
display(" Change Stable for $changeStable iterations")
else
changeStable=0
end
if (changeStable<10)
# Start iteration
loop += 1
# FE-ANALYSIS
sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),64*nelx*nely,1)
K = sparse(vec(iK),vec(jK),vec(sK))+S;K = (K+K')/2
@timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
U1=U[:,1]
U2=U[:,2]
# Objective function and sensitivity analysis
#ce = reshape(sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx)
ce=reshape(-sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx)
#c = sum((Emin.+xPhys[:].^penal*(Emax-Emin)).*ce)
c=U[DofDOut,1]
dc = -penal.*(Emax-Emin).*xPhys.^(penal-1).*ce
dv = ones(nely,nelx)
dc[:] = H*(dc[:]./Hs)
dv[:] = H*(dv[:]./Hs)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
l1 = 0; l2 = 1e9; move = 0.05; xnew = 0 #move=0.2
while (l2-l1)/(l2+l1) > 1e-4 && l2>1e-40
#while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.(max.(1e-10,-dc./dv./lmid))))))
#xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.(-dc./dv./lmid)))))
xPhys[:] = (H*xnew[:])./Hs
if sum(xPhys[:]) > volfrac*nelx*nely
l1 = lmid
else
l2 = lmid
end
end
change = maximum(abs.(xnew[:].-x[:]))
x = xnew
# print result
m=mean(xPhys[:])
display(" It:$loop Obj:$c Vol:$m ch:$change ")
if loop<20||mod(loop,5)==0
xxx=vcat(xPhys[end:-1:1,:],xPhys)
xxx=1 .- xxx
display(heatmap(xxx,xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0)))
heatmap(xxx,xaxis=nothing,yaxis=nothing,legend=nothing,fc=:grays,clims=(0.0, 1.0))
frame(anim)
end
xPhys = copy(x)
end
end
end
# heatmap(xPhys, legend=false, axis=nothing, foreground_color_subplot=colorant"white",fc=:grays,clims=(0.0, 1.0))
# heatmap(xPhys, legend=false,fc=:grays,clims=(0.0, 1.0))
return xPhys,anim
end
#########################################3d################################################################
function topologyOptimization3d(nelx,nely,nelz,volfrac,rmin,penal)
anim=Animation()
display("Minimum compliance problem with OC")
display("ndes: $nelx x $nely")
display("volfrac: $volfrac rmin: $rmin penal: $penal")
# Max and min stiffness
Emin=1e-9
Emax=1.0
nu=0.3
# dofs:
ndof = 3*(nelx+1)*(nely+1)*(nelz+1)
# Allocate design variables (as array), initialize and allocate sens.
x=volfrac * ones(Float64,nely,nelx,nelz)
xold=copy(x)
xPhys=copy(x)
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=zeros(Float64,(nely,nelx,nelz))
# FE: Build the index vectors for the for coo matrix format.
KE=lk_H8(nu)
nele = nelx*nely*nelz
nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
# USER-DEFINED LOAD DOFs
m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
il=m[1]
jl=m[2]
kl=m[3]
loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
loaddof = 3 .*loadnid[:] .- 1;
# USER-DEFINED SUPPORT FIXED DOFs
m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
iif=m[1]
jf=m[2]
kf=m[3]
fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
# DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
U = zeros(ndof,1)
alldofs = 1:ndof
freedofs = setdiff(1:ndof,fixeddof)
# Prepare filter
#iH = ones(convert(Int,nele*(2*(ceil(rmin)-1)+1)^2),1)
#jH = ones(Int,size(iH))
#sH = zeros(size(iH))
iH=[]
jH=[]
sH=[]
k = 0
for k1 = 1:nelz
for i1 = 1:nelx
for j1 = 1:nely
e1 = (k1-1)*nelx*nely + (i1-1)*nely+j1
for k2 = max(k1-(ceil(rmin)-1),1):min(k1+(ceil(rmin)-1),nelz)
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (k2-1)*nelx*nely + (i2-1)*nely+j2;
k = k+1;
append!(iH, e1 )
append!(jH, e2 )
append!(sH, max(0.0,rmin-sqrt((i1-i2)^2+(j1-j2)^2+(k1-k2)^2) ))
end
end
end
end
end
end
iH=reshape(iH,length(iH),1)
jH=reshape(jH,length(jH),1)
sH=reshape(convert(Array{Float64}, sH),length(sH),1)
H = sparse(vec(iH),vec(jH),vec(sH))
Hs = sum(H,dims=2)
###################################################
loop = 0
change = 1
maxIter=1000
# Start iteration
for i =1:maxIter
if (change > 0.01)
# Start iteration
loop += 1
# FE-ANALYSIS
sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),24*24*nelx*nely*nelz,1)
K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
@timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
# Objective function and sensitivity analysis
ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx,nelz)
c = sum(sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce)))
dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce
dv = ones(nely,nelx,nelz)
dc[:] = H*(dc[:]./Hs)
dv[:] = H*(dv[:]./Hs)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
l1 = 0; l2 = 1e9; move = 0.2; xnew = 0
while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.((0.0.-dc)./dv./lmid)))))
xPhys[:] = (H*xnew[:])./Hs
if sum(xPhys[:]) > volfrac*nelx*nely
l1 = lmid
else
l2 = lmid
end
end
change = maximum(abs.(xnew[:].-x[:]))
x = xnew
m=mean(xPhys[:])
display(" It:$loop Obj:$c Vol:$m ch:$change ")
if mod(loop,2)==0
display(topplot3d(xPhys))
topplot3d(xPhys)
frame(anim)
end
xPhys = copy(x)
end
end
return xPhys,anim
end
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#########################################3d KE################################################################
function topologyOptimization3dKE(nelx,nely,nelz,volfrac,rmin,penal,CE)
anim=Animation()
display("Minimum compliance problem with OC")
display("ndes: $nelx x $nely")
display("volfrac: $volfrac rmin: $rmin penal: $penal")
# Max and min stiffness
Emin=1e-9
Emax=1.0
nu=0.3
# dofs:
ndof = 3*(nelx+1)*(nely+1)*(nelz+1)
# Allocate design variables (as array), initialize and allocate sens.
x=volfrac * ones(Float64,nely,nelx,nelz)
xold=copy(x)
xPhys=copy(x)
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=zeros(Float64,(nely,nelx,nelz))
# FE: Build the index vectors for the for coo matrix format.
# KE=lk_H8(nu)
KE = elementMatVec3D(0.5, 0.5, 0.5, CE);
nele = nelx*nely*nelz
nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
# USER-DEFINED LOAD DOFs
m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
il=m[1]
jl=m[2]
kl=m[3]
loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
loaddof = 3 .*loadnid[:] .- 1;
# USER-DEFINED SUPPORT FIXED DOFs
m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
iif=m[1]
jf=m[2]
kf=m[3]
fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
# DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
U = zeros(ndof,1)
alldofs = 1:ndof
freedofs = setdiff(1:ndof,fixeddof)
# Prepare filter
#iH = ones(convert(Int,nele*(2*(ceil(rmin)-1)+1)^2),1)
#jH = ones(Int,size(iH))
#sH = zeros(size(iH))
iH=[]
jH=[]
sH=[]
k = 0
for k1 = 1:nelz
for i1 = 1:nelx
for j1 = 1:nely
e1 = (k1-1)*nelx*nely + (i1-1)*nely+j1
for k2 = max(k1-(ceil(rmin)-1),1):min(k1+(ceil(rmin)-1),nelz)
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (k2-1)*nelx*nely + (i2-1)*nely+j2;
k = k+1;
append!(iH, e1 )
append!(jH, e2 )
append!(sH, max(0.0,rmin-sqrt((i1-i2)^2+(j1-j2)^2+(k1-k2)^2) ))
end
end
end
end
end
end
iH=reshape(iH,length(iH),1)
jH=reshape(jH,length(jH),1)
sH=reshape(convert(Array{Float64}, sH),length(sH),1)
H = sparse(vec(iH),vec(jH),vec(sH))
Hs = sum(H,dims=2)
###################################################
loop = 0
change = 1
maxIter=1000
# Start iteration
for i =1:maxIter
if (change > 0.01)
# Start iteration
loop += 1
# FE-ANALYSIS
sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),24*24*nelx*nely*nelz,1)
K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
@timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
# Objective function and sensitivity analysis
ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx,nelz)
c = sum(sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce)))
dc = -penal*(Emax-Emin)*xPhys.^(penal-1).*ce
dv = ones(nely,nelx,nelz)
dc[:] = H*(dc[:]./Hs)
dv[:] = H*(dv[:]./Hs)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
l1 = 0; l2 = 1e9; move = 0.2; xnew = 0
while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.((0.0.-dc)./dv./lmid)))))
xPhys[:] = (H*xnew[:])./Hs
if sum(xPhys[:]) > volfrac*nelx*nely
l1 = lmid
else
l2 = lmid
end
end
change = maximum(abs.(xnew[:].-x[:]))
x = xnew
m=mean(xPhys[:])
display(" It:$loop Obj:$c Vol:$m ch:$change ")
if mod(loop,5)==0
display(topplot3d(xPhys))
topplot3d(xPhys)
frame(anim)
end
xPhys = copy(x)
end
end
return xPhys,anim
end
#########################################################################################################
function compliantOptimization3d(nelx,nely,nelz,volfrac,rmin,penal,maxIter=500,getProblem=inverter)
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anim=Animation()
display("Compliance sythesyz problem with OC")
display("ndes: $nelx x $nely x $nelz")
display("volfrac: $volfrac rmin: $rmin penal: $penal")
# Max and min stiffness
Emin=1e-9
Emax=1.0
nu=0.3
# dofs:
ndof = 3*(nelx+1)*(nely+1)*(nelz+1)
# Allocate design variables (as array), initialize and allocate sens.
x=volfrac * ones(Float64,nely,nelx,nelz)
xold=copy(x)
xPhys=copy(x)
g=0 # must be initialized to use the NGuyen/Paulino OC approach
dc=zeros(Float64,(nely,nelx,nelz))
# FE: Build the index vectors for the for coo matrix format.
KE=lk_H8(nu)
nele = nelx*nely*nelz
nodenrs = reshape(1:(1+nelx)*(1+nely)*(1+nelz),1+nely,1+nelx,1+nelz)
edofVec = reshape(3*nodenrs[1:end-1,1:end-1,1:end-1].+1,nelx*nely*nelz,1)
edofMat = repeat(edofVec,1,24).+repeat([0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1 3*(nely+1)*(nelx+1).+[0 1 2 3*nely.+[3 4 5 0 1 2] -3 -2 -1]],nelx*nely*nelz,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(24,1))',24*24*nele,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,24))',24*24*nele,1))
# # USER-DEFINED LOAD DOFs
# m= Matlab.meshgrid(nelx:nelx, 0:0, 0:nelz)
# il=m[1]
# jl=m[2]
# kl=m[3]
# loadnid = kl.*(nelx+1).*(nely+1).+il.*(nely+1).+(nely+1 .-jl)
# loaddof = 3 .*loadnid[:] .- 1;
# # USER-DEFINED SUPPORT FIXED DOFs
# m= Matlab.meshgrid(0:0,0:nely,0:nelz)# Coordinates
# iif=m[1]
# jf=m[2]
# kf=m[3]
# fixednid = kf.*(nelx+1).*(nely+1) .+iif .*(nely .+1) .+(nely .+1 .-jf) # Node IDs
# fixeddof = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
# # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
# F= sparse(loaddof,fill(1,length(loaddof)),fill(-1,length(loaddof)),ndof,1);
# U = zeros(ndof,1)
# alldofs = 1:ndof
# freedofs = setdiff(1:ndof,fixeddof)
# USER-DEFINED LOAD DOFs
# il = [0 nelx]; jl = [nely nely]; kl = [0 0];
# loadnid = kl .*(nelx+1) .*(nely+1) .+il .*(nely .+1) .+(nely+1 .-jl);
# loaddof = 3 .*loadnid[:] .- 2;
# din = loaddof[1]; dout = loaddof[2];
# F = sparse(loaddof,[1;2],[1;-1],ndof,2);
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# # USER-DEFINED SUPPORT FIXED DOFs
# # Top face
# m = Matlab.meshgrid(0:nelx,0:nelz)
# iif=m[1]
# kf=m[2]
# fixednid = kf .*(nelx+1) .*(nely+1) .+iif .*(nely+1) .+1;
# fixeddof_t = 3 .*fixednid[:] .-1;
# # Side face
# m = Matlab.meshgrid(0:nelx,0:nely)
# iif=m[1]
# jf=m[2]
# fixednid = iif .*(nely+1) .+(nely+1 .-jf);
# fixeddof_s = 3*fixednid[:];
# # Two pins
# iif = [0;0]; jf = [0;1]; kf = [nelz;nelz];
# fixednid = kf .*(nelx+1) .*(nely .+1) .+iif .*(nely .+1) .+(nely+1 .-jf)
# fixeddof_p = [3 .*fixednid[:]; 3 .*fixednid[:].-1; 3 .*fixednid[:].-2] # DOFs
# # Fixed DOFs
# fixeddof = union(fixeddof_t,fixeddof_s);
# fixeddof = union(fixeddof, fixeddof_p);
# fixeddof = sort(fixeddof);
# # Displacement vector
# U = zeros(ndof,2);
# freedofs = setdiff(1:ndof,fixeddof)
U,F,freedofs,din,dout=getProblem(nelx,nely,nelz)
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# Prepare filter
#iH = ones(convert(Int,nele*(2*(ceil(rmin)-1)+1)^2),1)
#jH = ones(Int,size(iH))
#sH = zeros(size(iH))
iH=[]
jH=[]
sH=[]
k = 0
for k1 = 1:nelz
for i1 = 1:nelx
for j1 = 1:nely
e1 = (k1-1)*nelx*nely + (i1-1)*nely+j1
for k2 = max(k1-(ceil(rmin)-1),1):min(k1+(ceil(rmin)-1),nelz)
for i2 = max(i1-(ceil(rmin)-1),1):min(i1+(ceil(rmin)-1),nelx)
for j2 = max(j1-(ceil(rmin)-1),1):min(j1+(ceil(rmin)-1),nely)
e2 = (k2-1)*nelx*nely + (i2-1)*nely+j2;
k = k+1;
append!(iH, e1 )
append!(jH, e2 )
append!(sH, max(0.0,rmin-sqrt((i1-i2)^2+(j1-j2)^2+(k1-k2)^2) ))
end
end
end
end
end
end
iH=reshape(iH,length(iH),1)
jH=reshape(jH,length(jH),1)
sH=reshape(convert(Array{Float64}, sH),length(sH),1)
H = sparse(vec(iH),vec(jH),vec(sH))
Hs = sum(H,dims=2)
###################################################
loop = 0
change = 1
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# Start iteration
for i =1:maxIter
if (change > 0.01)
# Start iteration
loop += 1
# FE-ANALYSIS
sK = reshape(KE[:]*(Emin.+xPhys[:]'.^penal*(Emax-Emin)),24*24*nelx*nely*nelz,1)
K = sparse(vec(iK),vec(jK),vec(sK))
K[din,din] = K[din,din] + 0.1
K[dout,dout] = K[dout,dout] + 0.1
K = (K+K')/2
# @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
@timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
U1 = U[:,1]
U2 = U[:,2]
# Objective function and sensitivity analysis
#ce = reshape(sum((U[edofMat]*KE).*U[edofMat],dims=2),nely,nelx,nelz)
ce = reshape(sum((U1[edofMat]*KE).*U2[edofMat],dims=2),nely,nelx,nelz);
#c = sum(sum(sum((Emin.+xPhys.^penal*(Emax-Emin)).*ce)))
c = U[dout,1]
dc = penal*(Emax-Emin)*xPhys.^(penal-1).*ce
dv = ones(nely,nelx,nelz)
dc[:] = H*(dc[:]./Hs)
dv[:] = H*(dv[:]./Hs)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES AND PHYSICAL DENSITIES
#l1 = 0; l2 = 1e9; move = 0.2; xnew = 0
l1 = 0; l2 = 1e9; move = 0.1;xnew = 0
#while (l2-l1)/(l1+l2) > 1e-3
while (l2-l1)/(l1+l2) > 1e-4 && l2 > 1e-40
lmid = 0.5*(l2+l1)
#xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*sqrt.((0.0.-dc)./dv./lmid)))))
xnew = max.(0,max.(x.-move,min.(1,min.(x.+move,x.*(max.(1e-10,-dc./dv./lmid)).^0.3))));
xPhys[:] = (H*xnew[:])./Hs
if sum(xPhys[:]) > volfrac*nelx*nely
l1 = lmid
else
l2 = lmid
end
end
change = maximum(abs.(xnew[:].-x[:]))
x = xnew
m=mean(xPhys[:])
display(" It:$loop Obj:$c Vol:$m ch:$change ")
if mod(loop,5)==0
display(topplot3d(xPhys))
topplot3d(xPhys)
frame(anim)
end
xPhys = copy(x)
end
end
return xPhys,anim
end
#############################################multimaterial############################################################
#Based on: https://link.springer.com/article/10.1007/s00158-013-0999-1
function multitop(nx,ny,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf)
anim=Animation()
alpha = zeros(Float64,nx*ny,p)
for i = 1:p
alpha[:,i] .= v[i]
end
# MAKE FILTER
H,Hs = make_filter(nx,ny,rf)
obj=0
change_out = 2*tol_out; iter_out = 0;
while (iter_out < iter_max_out) && (change_out > tol_out)
alpha_old = copy(alpha)
for a = 1:p
for b = a+1:p
obj,alpha = bi_top(a,b,nx,ny,p,v,e,q,alpha,H,Hs,iter_max_in);
end
end
iter_out = iter_out + 1;
change_out = norm(alpha[:].-alpha_old[:],Inf);
display("Iter:$iter_out Obj.:$obj change:$change_out");
# UPDATE FILTER
if (change_out < tol_f) && (rf>3)
tol_f = 0.99*tol_f; rf = 0.99*rf;
H,Hs = make_filter(nx,ny,rf);
end
# SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
if mod(iter_out,5)==0
I = make_bitmap(p,nx,ny,alpha);
display(RGB.(I[:,:,1],I[:,:,2],I[:,:,3]))
I = permutedims(I, [3, 1, 2])
img = colorview(RGB, I)
heatmap(img,xaxis=nothing,yaxis=nothing,aspect_ratio=:equal)
frame(anim)
end
end
return anim,alpha
end
function bi_top(a,b,nx,ny,p,v,e,q,alpha_old,H,Hs,maxIter)
alpha = copy(alpha_old)
nu = 0.3;
# PREPARE FINITE ELEMENT ANALYSIS
A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
nelx=nx
nely=ny
nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
# DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)
U = zeros(2*(nely+1)*(nelx+1),1)
fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))
alldofs = 1:(2*(nely+1)*(nelx+1))
freedofs = setdiff(alldofs,fixeddofs)
o=0;alpha_a=0
# inner iteration
for i =0: (maxIter-1)
# FE-ANALYSIS
E = e[1]*alpha[:,1].^q
for phase = 2:p
E = E + e[phase]*alpha[:,phase].^q;
end
sK = reshape(KE[:]*E[:]',64*nelx*nely,1)
K = sparse(vec(iK),vec(jK),vec(sK)); K = (K+K')/2
@timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
# Objective function and sensitivity analysis
ce = sum((U[edofMat]*KE).*U[edofMat],dims=2)
o = sum(sum(E.*ce))
# FILTERING OF SENSITIVITIES
dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
dc = min.(dc,0.0)
# UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
move = 0.2;
r = ones(nx*ny,1)
for k = 1:p
#if (k ~= a) && (k ~= b)
if (k != a) && (k != b)
# display("k $k a $a b $b")
r = r .- alpha[:,k]
end
end
l = max.(0,alpha[:,a] .-move)
u = min.(r,alpha[:,a] .+move)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
l1 = 0; l2 = 1e9
while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
alpha_a = max.(l,min.(u,alpha[:,a].*sqrt.(-dc./lmid)));
if sum(alpha_a) > nx*ny*v[a]
l1 = lmid
else
l2 = lmid
end
end
alpha[:,a] = alpha_a
alpha[:,b] = r .-alpha_a
end
return o,alpha
end
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function multitop_compliant(nx,ny,tol_out,tol_f,iter_max_in,iter_max_out,p,q,e,v,rf,Load,Support,Spring,DOut)
anim=Animation()
alpha = zeros(Float64,nx*ny,p)
for i = 1:p
alpha[:,i] .= v[i]
end
# MAKE FILTER
H,Hs = make_filter(nx,ny,rf)
obj=0
change_out = 2*tol_out; iter_out = 0;
while (iter_out < iter_max_out) && (change_out > tol_out)
alpha_old = copy(alpha)
for a = 1:p
for b = a+1:p
obj,alpha = bi_top_compliant(a,b,nx,ny,p,v,e,q,alpha,H,Hs,iter_max_in);
end
end
iter_out = iter_out + 1;
change_out = norm(alpha[:].-alpha_old[:],Inf);
display("Iter:$iter_out Obj.:$obj change:$change_out");
# UPDATE FILTER
if (change_out < tol_f) && (rf>3)
tol_f = 0.99*tol_f; rf = 0.99*rf;
H,Hs = make_filter(nx,ny,rf);
end
# SCREEN OUT TEMPORAL TOPOLOGY EVERY 5 ITERATIONS
if mod(iter_out,5)==0
I = make_bitmap_compliant(p,nx,ny,alpha);
display(RGB.(I[:,:,1],I[:,:,2],I[:,:,3]))
I = permutedims(I, [3, 1, 2])
img = colorview(RGB, I)
heatmap(img,xaxis=nothing,yaxis=nothing,aspect_ratio=:equal)
frame(anim)
end
end
return anim,alpha
end
function bi_top_compliant(a,b,nx,ny,p,v,e,q,alpha_old,H,Hs,maxIter,Load,Support,Spring,DOut)
alpha = copy(alpha_old)
nu = 0.3;
# PREPARE FINITE ELEMENT ANALYSIS
A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
nelx=nx
nely=ny
nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx)
edofVec = reshape(2*nodenrs[1:end-1,1:end-1].+1,nelx*nely,1)
edofMat = repeat(edofVec,1,8).+repeat([0 1 2*nely.+[2 3 0 1] -2 -1],nelx*nely,1)
iK = convert(Array{Int},reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1))
jK = convert(Array{Int},reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1))
# # DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
# F = sparse([2],[1],[-1.0],2*(nely+1)*(nelx+1),1)
# U = zeros(2*(nely+1)*(nelx+1),1)
# fixeddofs = union(1:2:2*(nely+1),2*(nelx+1)*(nely+1))
# alldofs = 1:(2*(nely+1)*(nelx+1))
# freedofs = setdiff(alldofs,fixeddofs)
# DEFINE LOADS AND SUPPORTS
F = sparse(2 .*Load[:,1] .-2 .+ Load[:,2],ones(size(Load,1)),Load[:,3],2*(nely+1)*(nelx+1),2)
DofDOut = 2 * DOut[1] - 2 +DOut[2]; #only one
F=Array(F)
F[DofDOut,2]=-1
fixeddofs = 2 .*Support[:,1] .-2 .+ Support[:,2]
NSpring = size(Spring,1);
s = sparse(2 .*Spring[:,1] .-2 .+ Spring[:,2],ones(size(Spring,1)),Spring[:,3],2*(nely+1)*(nelx+1),2)
m=Array(s)[:,1]
S= sparse(diagm(m))
U = zeros(2*(nely+1)*(nelx+1),2)
alldofs = 1:(2*(nely+1)*(nelx+1))
freedofs = setdiff(alldofs,fixeddofs)
o=0;alpha_a=0
# inner iteration
for i =0: (maxIter-1)
# FE-ANALYSIS
E = e[1]*alpha[:,1].^q
for phase = 2:p
E = E + e[phase]*alpha[:,phase].^q;
end
sK = reshape(KE[:]*E[:]',64*nelx*nely,1)
K = sparse(vec(iK),vec(jK),vec(sK));
K[din,din] = K[din,din] + 0.1;
K[dout,dout] = K[dout,dout] + 0.1;
K = (K+K')/2
# @timed U[freedofs] = K[freedofs,freedofs] \ Array(F[freedofs])
@timed U[freedofs,:] = K[freedofs,freedofs] \ Array(F[freedofs,:])
U1=U[:,1]
U2=U[:,2]
# Objective function and sensitivity analysis
# ce = sum((U[edofMat]*KE).*U[edofMat],dims=2)
ce =-sum((U1[edofMat]*KE).*U2[edofMat],dims=2)
# o = sum(sum(E.*ce))
o=U[DofDOut,1]
# FILTERING OF SENSITIVITIES
dc = 0.0 .-(q .*(e[a].-e[b]).*alpha[:,a].^(q-1)).*ce;
dc = H*(alpha[:,a].*dc)./Hs./max.(1e-3,alpha[:,a])
dc = min.(dc,0.0)
# UPDATE LOWER AND UPPER BOUNDS OF DESIGN VARIABLES
move=0.1;
r = ones(nx*ny,1)
for k = 1:p
#if (k ~= a) && (k ~= b)
if (k != a) && (k != b)
# display("k $k a $a b $b")
r = r .- alpha[:,k]
end
end
l = max.(0,alpha[:,a] .-move)
u = min.(r,alpha[:,a] .+move)
# OPTIMALITY CRITERIA UPDATE OF DESIGN VARIABLES
l1 = 0; l2 = 1e9
while (l2-l1)/(l2+l1) > 1e-4 && l2>1e-40
# while (l2-l1)/(l1+l2) > 1e-3
lmid = 0.5*(l2+l1)
alpha_a = max.(l,min.(u,alpha[:,a].*((max.(1e-10,-dc./lmid)).^0.3 )));
if sum(alpha_a) > nx*ny*v[a]
l1 = lmid
else
l2 = lmid
end
end
alpha[:,a] = alpha_a
alpha[:,b] = r .-alpha_a
end
return o,alpha
end