%%%%%%%%%% 3D FEM with brick element %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [U]=FEM_Beam(nx,ny,nz,ke_all)
N = 3*(nx+1)*(ny+1)*(nz+1);
% K = sparse(N, N);
nele=nx*ny*nz;
si=zeros(1,nele*24^2);
sj=zeros(1,nele*24^2);
sv=zeros(1,nele*24^2);

for elx = 1:nx
    for ely = 1:ny
        for elz = 1:nz
%             n1 = (nz+1)*(ny+1)*elx + (nz+1)*(ely-1) + elz;
%             n2 = n1 - (nz+1)*(ny+1);
            n2 = (nz+1)*(ny+1)*elx + (nz+1)*(ely-1) + elz;
            n1 = n2-(nz+1)*(ny+1);
            n3 = n1 + (nz+1);
            n4 = n2 + (nz+1);
            n5 = n1 + 1;
            n6 = n2 + 1;
            n7 = n3 + 1;
            n8 = n4 + 1;
            edof = [3*n1-2; 3*n1-1; 3*n1;
                    3*n2-2; 3*n2-1; 3*n2;
                    3*n3-2; 3*n3-1; 3*n3;
                    3*n4-2; 3*n4-1; 3*n4;
                    3*n5-2; 3*n5-1; 3*n5;
                    3*n6-2; 3*n6-1; 3*n6;
                    3*n7-2; 3*n7-1; 3*n7;
                    3*n8-2; 3*n8-1; 3*n8];
            ne=(elx-1)*ny*nz+(ely-1)*nz+elz;
            si((ne-1)*24^2+1:ne*24^2)=kron(ones(1,24),edof.');
            sj((ne-1)*24^2+1:ne*24^2)=kron(edof.',ones(1,24));
            ke=ke_all(:,:,elz,ely,elx);
            sv((ne-1)*24^2+1:ne*24^2)=ke(:);
%             K(edof,edof) = K(edof,edof) + ke_all(:,:,elz,ely,elx);
        end
    end
end
K = sparse(si,sj,sv,N,N);

loadnodes=nx*(ny+1)*(nz+1)+1:nz+1:(nx+1)*(ny+1)*(nz+1)-nz;
loaddofs = loadnodes(:).*3;
F = zeros(N,1); F(loaddofs) = -1;
fixeddofs = [1:3*(ny+1)*(nz+1)];
alldofs     = [1:N];
freedofs    = setdiff(alldofs,fixeddofs);
U = zeros(N,1);
U(freedofs,:) = K(freedofs,freedofs) \ F(freedofs,:);   
end