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48 lines
1.2 KiB
48 lines
1.2 KiB
2 years ago
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clear
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close all
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format compact
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set(groot,'defaulttextinterpreter','latex');
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set(groot, 'defaultAxesTickLabelInterpreter','latex');
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set(groot, 'defaultLegendInterpreter','latex');
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cantilever_beam_data;
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x = positions(1, :)';
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y = positions(2, :)';
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u = displacement(:, 1);
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v = displacement(:, 2);
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sxx = stress(:, 1);
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syy = stress(:, 2);
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sxy = stress(:, 3);
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mises = sqrt(sxx.^2 - sxx.*syy + syy.^2 + 3*sxy.^2);
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f = 1e5;
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scatter(x+f*u, y+f*v, 15, mises/1000, 'filled');
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title('Von Mises stress and deflection of catilever beam.');
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daspect([1 1 1])
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xlabel('$x$')
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ylabel('$y$')
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xlim([-1, 31])
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ylim([-5, 5])
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c = colorbar;
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title(c, 'kPa');
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caxis([0, inf])
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colormap jet
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grid on
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box on
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% Analytical solution
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I = D^3 / 12;
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asxx = I.^(-1).*P.*x.*y;
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asyy = zeros(size(x));
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asxy = (1/2).*I.^(-1).*P.*((1/4).*D.^2+(-1).*y.^2);
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au = (1/24).*E.^(-1).*I.^(-1).*P.*y.*(3.*D.^2.*(1+nu)-...
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4.*(3.*L.^2+(-3).*x.^2+(2+nu).*y.^2));
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av = (-1/24).*E.^(-1).*I.^(-1).*P.*(3.*D.^2.*(1+nu).*(L+(-1).*x)+...
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4.*(2.*L.^3+(-3).*L.^2.*x+x.^3+3.*nu.*x.*y.^2));
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errInfDispl = norm([au-u; av-v], inf) / norm([au av], inf)
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errInfStress = norm([asxx - sxx, asyy - syy, asxy - sxy], inf) / norm([sxx syy sxy], inf)
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