基于matlab有限体积法的传热结构拓扑优化程序
这里写自定义目录标题
- 设计域
- 设计结果
- 代码
-
- 主代码（备注：程序没有经过优化，所以看起来比较多，请指正）
- 有限体积求解
- 敏度求解
- MMA程序更新设计变量
- 过滤函数
- 参考文献
设计域
设计结果
代码
主代码（备注：程序没有经过优化，所以看起来比较多，请指正）
clc;
clear;
Lx = 0.2; % length x-direction
Ly = 0.2; % length y -direction
cv_x=100;cv_y=100;
ni = cv_x+1; % grid points x-direction
nj = cv_y+1; % grid points y-direction
ei = cv_x+2; ej = cv_y+2; %虚拟单元
Dx = Ly/cv_x; Dy = Ly/cv_y;
dx = Dy; dy = Dy;
xcord = 0:Dx:Lx;
ycord = 0:Dy:Ly;
DV =Dx*Dy;
Ex = 0-dx/2:dx:(ei-1)*dx;
Ey = 0-dx/2:dy:(ej-1)*dy;
bT0=[1 5];bT1 =[200,200];
%%
lameda0 = 900; %900 W/m^2*K
cp = 690; %690 J/kg*K
rho = 2220; %(kg/m^3)
Tinit =293.15;
qB1 = 5E6;
maxtime = 100;
p=1.5;
T(1:ni,1:nj) = Tinit;
theta(1:ei,1:ej) = 0;
theta(2:ei-1,2:ej-1) =0.8;
volfrac=0.50;
r=0.005;
for loop = 1:300
thetaold = theta;
Elameda=lameda0*theta.^p;
T = thermalFVMout(T,Elameda,ni,nj,Dx,Dy,Tinit,qB1,rho,cp,maxtime,bT0,bT1);
c = sum(sum(T))/(ni*nj);
dc = calcdc(ni,nj,ei,ej,Dy,Dx,lameda0,T,theta,p);
dc= SensitivityFilter(Ex,Ey,ei,ej,r,dc,theta);
theta(2:ei-1,2:ej-1) = MMA(ei-2,ej-2,theta(2:ei-1,2:ej-1),volfrac,-dc(2:ei-1,2:ej-1));
change = max(max(abs(theta(2:ei-1,2:ej-1)-thetaold(2:ei-1,2:ej-1))));
disp([' It.: ' sprintf('%4i',loop) ' Obj.: ' sprintf('%10.4f',c) ...
' Vol.: ' sprintf('%6.3f',sum(sum(theta(2:ni-1,2:nj-1)))/((ni-2)*(nj-2))) ...
' ch.: ' sprintf('%6.3f',change)])
cStore(loop) =c;
% PLOT DENSITIES
% thetaAll(:,:,loop)=theta;
% TAll(:,:,loop)=T;
figure(1);
pcolor(T(1:ni,1:nj));xlabel('x');ylabel('y');title('Temperature distribution');colorbar;
filename = ['C:\Users\DELL018\Desktop\Thermal30C01\T\T_',num2str(loop),];
saveas(gcf,filename,'bmp');
figure(2);
pcolor(theta(2:ei-1,2:ej-1));shading interp;xlabel('x');ylabel('y');title('Theta distribution');colorbar;
filename = ['C:\Users\DELL018\Desktop\Thermal30C01\Theta\T_',num2str(loop),];
saveas(gcf,filename,'bmp');
figure(3); colormap(flipud(gray)); imagesc(theta(2:ei-1,2:ej-1)); axis equal; axis tight;colorbar;
filename = ['C:\Users\DELL018\Desktop\Thermal30C01\Theta02\T_',num2str(loop),];
saveas(gcf,filename,'bmp');
figure(4);
plot(cStore);
end
% figure(1);
% pcolor(T(2:ni-1,2:nj-1));xlabel('x');ylabel('y');title('Theta distribution');colorbar;
% figure(2);
% pcolor(theta(3:ei-2,3:ej-2));shading interp;xlabel('x');ylabel('y');title('Theta distribution');colorbar;
save('dataAll','T','theta','cStore');
有限体积求解
function T = thermalFVMout(T,Elameda,ni,nj,Dx,Dy,Tinit,qB1,rho,cp,maxtime,bT0,bT1)
DV =Dx*Dy;
dx = Dx;
dy = Dy;
dt = 0.01;%传热时间
volfrac = 0.5;
lamedaEW(1:ni+1,1:nj)=0;
lamedaNS(1:ni,1:nj+1)=0;
for i=1:ni+1
for j = 1:nj
if j == 1
lamedaEW(i,j) = Elameda(i,j+1);
elseif j==nj
lamedaEW(i,j) = Elameda(i,j);
else
lamedaEW(i,j) = (Elameda(i,j)+Elameda(i,j+1))*0.5;
end
end
end
for j=1:nj+1
for i = 1:ni
if i == 1
lamedaNS(i,j) = Elameda(i+1,j);
elseif i==ni
lamedaNS(i,j) = Elameda(i,j);
else
lamedaNS(i,j) = (Elameda(i,j)+Elameda(i+1,j))*0.5;
end
end
end
for i=2:ni-1
for j=2:nj-1
aE(i,j) = Dy/(dx/lamedaEW(i+1,j));
aW(i,j) = Dy/(dx/lamedaEW(i,j));
aN(i,j) = Dx/(dy/lamedaNS(i,j+1));
aS(i,j) = Dx/(dy/lamedaNS(i,j));
aP0 = rho*cp*Dx*Dy/dt;
SP(i,j) = 0;
SC(i,j) = 0;
b(i,j) = 0;
SC(i,j) = qB1;
aP(i,j) = aE(i,j)+aW(i,j)+aN(i,j)+aS(i,j)+aP0-SP(i,j)*Dx*Dy;
end
end
T(1:ni,1:nj) = Tinit;
maxres = 1.0e-6;
maxit = 100;
time=0;
omega=1;
while (time < (maxtime+dt/2))
Told=T;
sumres = 1;
counter = 0;
while (sumres>maxres&counter=bT0(1))&&(j<=bT0(2))
T(i,j) = 293.15;
else
T(i,j) = 1/4*(2*T(i+1,j)+T(i,j-1)+T(i,j+1)+qB1*dx*dy/lamedaEW(i+1,j)/2);
end
end
i = ni;
for j=2:nj-1
if(j>bT1(1))&&(j<=bT1(2))
T(i,j) = 293.15;
else
T(i,j) = 1/4*(2*T(i-1,j)+T(i,j-1)+T(i,j+1)+qB1*dx*dy/lamedaEW(i,j)/2);
end
end
j = 1;
for i=2:ni-1
if (i>=bT0(1))&&(i<=bT0(2))
T(i,j) = 293.15;
else
T(i,j) = 1/4*(2*T(i,j+1)+T(i-1,j)+T(i+1,j)+qB1*dx*dy/lamedaNS(i,j+1)/2);
end
end
j = nj;
for i=2:ni-1
if (i>=bT1(1))&&(i<=bT1(2))
T(i,j) = 293.15;
else
T(i,j) = 1/4*(2*T(i,j-1)+T(i-1,j)+T(i+1,j)+qB1*dx*dy/lamedaNS(i,j)/2);
end
end
%% 四个角点处理
T(1,1) = 1/2*(T(2,1)+T(1,2)+qB1*dy*dx/lamedaEW(i+1,j)/4);
T(ni,1) = 1/2*(T(ni-1,1)+T(ni,2)+qB1*dy*dx/lamedaEW(i,j)/4);
T(1,nj) = 1/2*(T(2,nj)+T(1,nj-1)+qB1*dy*dx/lamedaEW(i+1,j)/4);
T(ni,nj) = 1/2*(T(ni-1,nj)+T(ni,nj-1)+qB1*dy*dx/lamedaEW(i,j)/4);
counter = counter + 1;
end
time = time + dt;
end
敏度求解
function dc = calcdc(ni,nj,ei,ej,Dy,Dx,lameda0,T,theta,p)
Elameda=lameda0*theta.^p;
Ap(1:nj,1:nj) = 0;
lamedaEW(1:ni+1,1:nj)=0;
lamedaNS(1:ni,1:nj+1)=0;
for i=1:ni+1
for j = 1:nj
if j == 1
lamedaEW(i,j) = Elameda(i,j+1);
elseif j==nj
lamedaEW(i,j) = Elameda(i,j);
else
lamedaEW(i,j) = (Elameda(i,j)+Elameda(i,j+1))*0.5;
end
end
end
for j=1:nj+1
for i = 1:ni
if i == 1
lamedaNS(i,j) = Elameda(i+1,j);
elseif i==ni
lamedaNS(i,j) = Elameda(i,j);
else
lamedaNS(i,j) = (Elameda(i,j)+Elameda(i+1,j))*0.5;
end
end
end
%+++++++++++++++++++++++++++++++++++
for i=1:ni+1
for j=1:nj
kh(i,j) = lamedaEW(i,j);
Ah(i,j)=kh(i,j)*Dy/Dx;
end
end
for j=1:nj+1
for i=1:ni
kv(i,j) = lamedaNS(i,j);
Av(i,j)=kv(i,j)*Dx/Dy;
end
end
for i=1:ni
for j=1:nj
Ap(i,j) = Ah(i,j)+Ah(i+1,j)+Av(i,j)+Av(i,j+1);
end
end
dk = p*(theta.^(p-1))*lameda0;
dc = zeros(ei,ej);
%% 目标函数倒数求解(边界是否要单独处理)
for i=2:ei-1
for j=2:ej-1
KK = [Ap(i-1,j-1) -Ah(i,j-1) 0 -Av(i-1,j)
-Ah(i,j-1) Ap(i,j-1) -Av(i,j) 0
0 -Av(i,j) Ap(i,j) -Ah(i,j)
-Av(i-1,j) 0 -Ah(i,j) Ap(i-1,j)];
dKK = dk(i,j)*[1 -1/2 0 -1/2
-1/2 1 -1/2 0
0 -1/2 1 -1/2
-1/2 0 -1/2 1];
TT =[T(i-1,j-1),T(i,j-1),T(i,j),T(i-1,j)]';
Lameda = -(1/4*ones(1,4)/KK)';
%dc(i,j) = Lameda'*dKK*TT;
dc(i,j) = TT'*dKK*TT;
end
end
MMA程序更新设计变量
function [xnew]=MMA1(nelx,nely,x,volfrac,dc)
xlow=0.001; xhigh=1;
L=x-0.1*(xhigh-xlow)*ones(nelx,nely);
high=(x-L).^2.*-dc./(xlow-L).^2;
low=(x-L).^2.*-dc./(xhigh-L).^2;
l2 = min(min(high));
l1 = max(max(low));
for i=1:50
lmid = 0.5*(l2+l1);
xnew=max(xlow,min(xhigh,L+abs(x-L).*sqrt(-dc./lmid)));
if sum(sum(xnew)) - volfrac*nelx*nely > 0;
l2 = lmid;
else
l1 = lmid;
end
end
过滤函数
function dfnew=SensitivityFilter(Ex,Ey,ei,ej,r,df,theta)
dfnew(1:ei,1:ej)=0;
for i=2:ei-1
for j=2:ej-1
sum1 = 0;
sum2 = 0;
temp1=0;
temp2=0;
for i2=2:ei-1
for j2=2:ej-1
if (((Ex(i2)-Ex(i))^2+(Ey(j2)-Ey(j))^2)参考文献
《Topology optimization using the finite volume method》
《Topology Optimization Using the SIMP Method for Multiobjective Conductive Problems》