SAW-FEM-MATLAB/codes/gaussQuadrature.m at main · Duane245/SAW-FEM-MATLAB · GitHub

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function [weights,locations] = gaussQuadrature(option)
% Gauss quadrature for 2D elements
% option 'third' (3x3)
% option 'complete' (2x2)
% option 'reduced'  (1x1)
% locations: Gauss point locations
% weights: Gauss point weights

switch option
    case 'third'
        locations = [-0.774596669241483 -0.774596669241483;
                      0.                -0.774596669241483;
                      0.774596669241483 -0.774596669241483;
                     -0.774596669241483  0.;
                      0.                 0.;
                      0.774596669241483  0.;
                     -0.774596669241483  0.774596669241483;
                      0.                 0.774596669241483;
                      0.774596669241483  0.774596669241483];
        weights = [0.555555555555556*0.555555555555556;
                   0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556;
                   0.888888888888889*0.555555555555556;
                   0.888888888888889*0.888888888888889;
                   0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556;
                   0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556];

    case 'complete'
        locations = [ -0.577350269189626 -0.577350269189626;
                       0.577350269189626 -0.577350269189626;
                       0.577350269189626  0.577350269189626;
                      -0.577350269189626  0.577350269189626];
        weights = [1;1;1;1];

    case 'reduced'
        locations = [0 0];
        weights = 4;
    case 'Q1'
        p = -1/sqrt(3);
        q =  1/sqrt(3);
        locations = [p, p, p;                       % Integration points. Gauss quadrature, weight = 1
            p, p, q;
            p, q, p;
            p, q, q;
            q, p, p;
            q, p, q;
            q, q, p;
            q, q, q];

        weights = [1;1;1;1;1;1;1;1];
    case 'H20'
        locations = [-0.774596669241483, -0.774596669241483, -0.774596669241483;
            0.000000000000000, -0.774596669241483, -0.774596669241483;
            0.774596669241483, -0.774596669241483, -0.774596669241483;
            -0.774596669241483, 0.000000000000000, -0.774596669241483;
            0.000000000000000, 0.000000000000000, -0.774596669241483;
            0.774596669241483, 0.000000000000000, -0.774596669241483;
            -0.774596669241483, 0.774596669241483, -0.774596669241483;
            0.000000000000000, 0.774596669241483, -0.774596669241483;
            0.774596669241483, 0.774596669241483, -0.774596669241483;

            -0.774596669241483, -0.774596669241483, 0.000000000000000;
            0.000000000000000, -0.774596669241483, 0.000000000000000;
            0.774596669241483, -0.774596669241483, 0.000000000000000;
            -0.774596669241483, 0.000000000000000, 0.000000000000000;
            0.000000000000000, 0.000000000000000, 0.000000000000000;
            0.774596669241483, 0.000000000000000, 0.000000000000000;
            -0.774596669241483, 0.774596669241483, 0.000000000000000;
            0.000000000000000, 0.774596669241483, 0.000000000000000;
            0.774596669241483, 0.774596669241483, 0.000000000000000;

            -0.774596669241483, -0.774596669241483, 0.774596669241483;
            0.000000000000000, -0.774596669241483, 0.774596669241483;
            0.774596669241483, -0.774596669241483, 0.774596669241483;
            -0.774596669241483, 0.000000000000000, 0.774596669241483;
            0.000000000000000, 0.000000000000000, 0.774596669241483;
            0.774596669241483, 0.000000000000000, 0.774596669241483;
            -0.774596669241483, 0.774596669241483, 0.774596669241483;
            0.000000000000000, 0.774596669241483, 0.774596669241483;
            0.774596669241483, 0.774596669241483, 0.774596669241483];

        weights = [0.555555555555556*0.555555555555556*0.555555555555556;
                   0.888888888888889*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.888888888888889*0.555555555555556;
                   0.888888888888889*0.888888888888889*0.555555555555556;
                   0.555555555555556*0.888888888888889*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.888888888888889*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.888888888888889;
                   0.888888888888889*0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556*0.888888888888889;
                   0.555555555555556*0.888888888888889*0.888888888888889;
                   0.888888888888889*0.888888888888889*0.888888888888889;
                   0.555555555555556*0.888888888888889*0.888888888888889;
                   0.555555555555556*0.555555555555556*0.888888888888889;
                   0.888888888888889*0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556*0.888888888888889;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.888888888888889*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.888888888888889*0.555555555555556;
                   0.888888888888889*0.888888888888889*0.555555555555556;
                   0.555555555555556*0.888888888888889*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556;
                   0.888888888888889*0.555555555555556*0.555555555555556;
                   0.555555555555556*0.555555555555556*0.555555555555556];
end

end  % end function gaussQuadrature