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); 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 mesh(x,y,z)

Hole Problem

Stress Field Tangential stress Radial stress

Cymbals

Stress Field Around Crack Tip Thin plate

Von Mises’ Yield Criterion Perfect plasticity

Crack Tip Stress Field

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.

Dislocation Emissions