%%% A 135 line code for topology optimization with same size elements, 3D version. Vittorio Latorre Jan. 2019 %%%
function [xPhys,c,loop]=tosse3d(nelx,nely,nelz,volfrac,mu)
%% USER-DEFINED LOOP PARAMETERS &  MATERIAL PROPERTIES
maxloop = 50;     % Maximum number of iterations
E0 = 1;           % Young's modulus of solid material
Emin = 1e-9;      % Young's modulus of void-like material
nu = 0.3;         % Poisson's ratio
%% USER-DEFINED LOAD DOFs
[il,jl,kl] = meshgrid(nelx, 0, 0:nelz);                 % Coordinates
loadnid = kl*(nelx+1)*(nely+1)+il*(nely+1)+(nely+1-jl); % Node IDs
loaddof = 3*loadnid(:) - 1;                             % DOFs
%% USER-DEFINED SUPPORT FIXED DOFs
[iif,jf,kf] = meshgrid(0,0:nely,0:nelz);                  % Coordinates
fixednid = kf*(nelx+1)*(nely+1)+iif*(nely+1)+(nely+1-jf); % Node IDs
fixeddof = [3*fixednid(:); 3*fixednid(:)-1; 3*fixednid(:)-2]; % DOFs
%% PREPARE FINITE ELEMENT ANALYSIS
nele = nelx*nely*nelz;
ndof = 3*(nelx+1)*(nely+1)*(nelz+1);
F = sparse(loaddof,1,-1,ndof,1);
U = zeros(ndof,1);
freedofs = setdiff(1:ndof,fixeddof);
KE = lk_H8(nu);
nodegrd = reshape(1:(nely+1)*(nelx+1),nely+1,nelx+1);
nodeids = reshape(nodegrd(1:end-1,1:end-1),nely*nelx,1);
nodeidz = 0:(nely+1)*(nelx+1):(nelz-1)*(nely+1)*(nelx+1);
nodeids = repmat(nodeids,size(nodeidz))+repmat(nodeidz,size(nodeids));
edofVec = 3*nodeids(:)+1;
edofMat = repmat(edofVec,1,24)+ ...
    repmat([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]],nele,1);
iK = reshape(kron(edofMat,ones(24,1))',24*24*nele,1);
jK = reshape(kron(edofMat,ones(1,24))',24*24*nele,1);
%% INITIALIZE ITERATION
vgam=1;
loop = 0;
change = 1;
xPhys = ones(nely,nelx,nelz)*vgam;
%% START ITERATION
while change > 0 && loop < maxloop
    loop = loop+1;
    vgam = max(volfrac,vgam*mu);
    %% FE-ANALYSIS
    sK = reshape(KE(:)*(Emin+xPhys(:)'.*(E0-Emin)),24*24*nele,1);
    K = sparse(iK,jK,sK); 
    K = (K+K')/2;
    U(freedofs,:) = K(freedofs,freedofs)\F(freedofs,:);
    %% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
    ce = (xPhys(:)+Emin)*E0.*(sum((U(edofMat)*KE).*U(edofMat),2));
    c = sum((Emin+ce*(1-Emin/E0)));
    %% SOLVE THE KNAPSACK PROBLEM
    [~,I]=sort(ce,1,'descend');
    xnew=zeros(nelx*nely,1);
    xnew(I(1:floor(vgam*nelx*nely*nelz)))=1;
    change = max(abs(xnew(:)-xPhys(:)));
    xPhys=reshape(xnew,[nely,nelx,nelz]);
    %% PRINT RESULTS
    fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\n',loop,c,mean(xPhys(:)),change);
end
%% PLOT DENSITIES
clf; display_3D(xPhys);
TimeMinute=toc/(60);
title(['TOSSE3D:',' Vc=',num2str((volfrac)),', nex= ',num2str(nelx),  ', ney=',num2str(abs(nely)),...
    ', nez=',num2str(abs(nelz)),', C=',num2str(c),', It=',num2str(loop),', TM=',num2str(TimeMinute)]);  
 xlabel(['nelx= ',num2str(nelx),' nely= ',num2str(abs(nely)),' nelz= ',num2str(abs(nelz))]);  
end
% === GENERATE ELEMENT STIFFNESS MATRIX ===
function [KE] = lk_H8(nu)
A = [32 6 -8 6 -6 4 3 -6 -10 3 -3 -3 -4 -8;
    -48 0 0 -24 24 0 0 0 12 -12 0 12 12 12];
k = 1/144*A'*[1; nu];
K1 = [k(1) k(2) k(2) k(3) k(5) k(5);
    k(2) k(1) k(2) k(4) k(6) k(7);
    k(2) k(2) k(1) k(4) k(7) k(6);
    k(3) k(4) k(4) k(1) k(8) k(8);
    k(5) k(6) k(7) k(8) k(1) k(2);
    k(5) k(7) k(6) k(8) k(2) k(1)];
K2 = [k(9)  k(8)  k(12) k(6)  k(4)  k(7);
    k(8)  k(9)  k(12) k(5)  k(3)  k(5);
    k(10) k(10) k(13) k(7)  k(4)  k(6);
    k(6)  k(5)  k(11) k(9)  k(2)  k(10);
    k(4)  k(3)  k(5)  k(2)  k(9)  k(12)
    k(11) k(4)  k(6)  k(12) k(10) k(13)];
K3 = [k(6)  k(7)  k(4)  k(9)  k(12) k(8);
    k(7)  k(6)  k(4)  k(10) k(13) k(10);
    k(5)  k(5)  k(3)  k(8)  k(12) k(9);
    k(9)  k(10) k(2)  k(6)  k(11) k(5);
    k(12) k(13) k(10) k(11) k(6)  k(4);
    k(2)  k(12) k(9)  k(4)  k(5)  k(3)];
K4 = [k(14) k(11) k(11) k(13) k(10) k(10);
    k(11) k(14) k(11) k(12) k(9)  k(8);
    k(11) k(11) k(14) k(12) k(8)  k(9);
    k(13) k(12) k(12) k(14) k(7)  k(7);
    k(10) k(9)  k(8)  k(7)  k(14) k(11);
    k(10) k(8)  k(9)  k(7)  k(11) k(14)];
K5 = [k(1) k(2)  k(8)  k(3) k(5)  k(4);
    k(2) k(1)  k(8)  k(4) k(6)  k(11);
    k(8) k(8)  k(1)  k(5) k(11) k(6);
    k(3) k(4)  k(5)  k(1) k(8)  k(2);
    k(5) k(6)  k(11) k(8) k(1)  k(8);
    k(4) k(11) k(6)  k(2) k(8)  k(1)];
K6 = [k(14) k(11) k(7)  k(13) k(10) k(12);
    k(11) k(14) k(7)  k(12) k(9)  k(2);
    k(7)  k(7)  k(14) k(10) k(2)  k(9);
    k(13) k(12) k(10) k(14) k(7)  k(11);
    k(10) k(9)  k(2)  k(7)  k(14) k(7);
    k(12) k(2)  k(9)  k(11) k(7)  k(14)];
KE = 1/((nu+1)*(1-2*nu))*...
    [ K1  K2  K3  K4;
    K2'  K5  K6  K3';
    K3' K6  K5' K2';
    K4  K3  K2  K1'];
end
% === DISPLAY 3D TOPOLOGY (ISO-VIEW) ===
function display_3D(rho)
[nely,nelx,nelz] = size(rho);
hx = 1; hy = 1; hz = 1;            % User-defined unit element size
face = [1 2 3 4; 2 6 7 3; 4 3 7 8; 1 5 8 4; 1 2 6 5; 5 6 7 8];
set(gcf,'Name','ISO display','NumberTitle','off');
for k = 1:nelz
    z = (k-1)*hz;
    for i = 1:nelx
        x = (i-1)*hx;
        for j = 1:nely
            y = nely*hy - (j-1)*hy;
            if (rho(j,i,k) > 0.5)  % User-defined display density threshold
                vert = [x y z; x y-hx z; x+hx y-hx z; x+hx y z; x y z+hx;x y-hx z+hx; x+hx y-hx z+hx;x+hx y z+hx];
                vert(:,[2 3]) = vert(:,[3 2]); vert(:,2,:) = -vert(:,2,:);
                patch('Faces',face,'Vertices',vert,'FaceColor',[0.2+0.8*(1-rho(j,i,k)),0.2+0.8*(1-rho(j,i,k)),0.2+0.8*(1-rho(j,i,k))]);
                hold on;
            end
        end
    end
end
axis equal; axis tight; axis off; box on; view([30,30]); pause(1e-6);
end
%%%This code is partially based on the code reported in:          %%%
%%%"An efficient 3D topology optimization code written in Matlab" %%%
%%%By Kai Liu and Andres Tovar.                                   %%%