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Visualization. Friday, 9/6/2002. Hedgehog Method. MATLAB functions. plot. Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y). Bean-Bag Method. MATLAB functions. meshgrid mesh. Examples: [x,y]=meshgrid(-10:10,-10:10); [r,theta]=meshgrid(0:5:10,0:pi/20:pi); z=sqrt(x.^2+y.^2);

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**Visualization**Friday, 9/6/2002**MATLAB functions**plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)**MATLAB functions**meshgrid mesh Examples: [x,y]=meshgrid(-10:10,-10:10); [r,theta]=meshgrid(0:5:10,0:pi/20:pi); z=sqrt(x.^2+y.^2); mesh(x,y,z)**Sphere Scanning**theta = linspace(0,2*pi,ntheta); phi = linspace(0,pi,nphi); [x,y] = meshgrid( theta, phi ); for i=1:nphi for j=1:ntheta n = [ sin(phi(i))*cos(theta(j)), ... sin(phi(i))*sin(theta(j)), ... cos(phi(i)) ]'; x(i,j) = … … ; y(i,j) = … … ; z(i,j) = … … ; end end mesh(x,y,z)**Stress Field**Tangential stress Radial stress**Stress Field Around Crack Tip**Thin plate**Von Mises’ Yield Criterion**Perfect plasticity**Mountain Stream**A mountain stream comes trickling in the sunlight down the hill, And gathers volume until it has strength to run the mill; It happily continues then, upon its useful way, Turns other mills still further down, until it joins the bay.

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