function compliance_after_threshold()
load top3d_case2_p1.mat
xx = xPhys>=0.33;
xx = max(xx,1e-3);

xPhys = xx;

nelx=60;
nely=20;
nelz=1;

E0 = 1;           % Young's modulus of solid material
Emin = 1e-3;      % Young's modulus of void-like material
nu = 0.33;         % 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

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);

sK = reshape(KE(:)*(Emin+xPhys(:)'.^penal*(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 = reshape(sum((U(edofMat)*KE).*U(edofMat),2),[nely,nelx,nelz]);
    compliance = (Emin+xPhys.^penal*(E0-Emin)).*ce;

set(gcf,'position',[100 650 300 300])
cc = squeeze(compliance(:,:,1));
colormap(1-gray); 
imagesc(cc); 
axis equal; axis tight; axis off;
disp(sum(sum(compliance)))
end

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