%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2020-10-29 15:04:15
 % @LastEditTime: 2021-03-13 16:40:38
%--------------------------

% FE-ANALYSIS
function [Ue, sigma] = microFEAsimp(nelx, nely, iK, jK, d1, d2, d3, d4, ...
                        ufixed, wfixed, xPhys, KE0, KE1)

    % if nargin>13
    %     % 1-mat
    %     sK = reshape(KE0(:) * (Emin + xPhys(:)' * (E0 - Emin)), 64 * nelx * nely, 1);
    % else

    % 2-mat
    sK = zeros(64, nelx*nely);
    for i = 1:nelx
        for j = 1:nely       
            ele = j + (i-1)*nely;
            if xPhys(ele)==1
                sK(:, ele) = KE1(:);
            else
                sK(:, ele) = KE0(:);
            end
        end
    end
    sK = sK(:);
    % end


    K = sparse(iK, jK, sK); 
    K = (K + K') / 2;

    Kr = [K(d2, d2), K(d2, d3) + K(d2, d4);
        K(d3, d2) + K(d4, d2), K(d3, d3) + K(d3, d4) + K(d4, d3) + K(d4, d4)];
    Ue(d1, :) = ufixed;
    Ue([d2, d3], :) = Kr \ (-[K(d2, d1); K(d3, d1) + K(d4, d1)] * ufixed - ...
        [K(d2, d4); K(d3, d4) + K(d4, d4)] * wfixed);
    Ue(d4, :) = Ue(d3, :) + wfixed;       

    R = K*Ue;
    lxx = ((2*nelx*(nely+1)+1):2:2*(nelx+1)*(nely+1));
    lyy = (2:2*(nely+1):2*(nelx+1)*(nely+1));
    lxy = ((2*nelx*(nely+1)+2):2:2*(nelx+1)*(nely+1));
    sigma = [sum(R(lxx))/nely;sum(R(lyy))/nelx;sum(R(lxy))/nely];
    
%     % test
%     [cx,cy] = meshgrid((0:nelx)/nelx, (0:nely)/nely);
%     for j = 1:3
%         figure;       
%         coorx = reshape(Ue(1:2:end,j),nely+1,nelx+1) + cx;
%         coory = reshape(Ue(2:2:end,j),nely+1,nelx+1) + flipud(cy);
%         scatter(coorx(:),coory(:)); hold on;
%     end
end