visualization friday, 9/6/2002. hedgehog method matlab functions plot example x = 0:pi/100:2*pi; y =...
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![Page 1: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/1.jpg)
Visualization
Friday, 9/6/2002
![Page 2: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/2.jpg)
Hedgehog Method
€
σ xx σxy
σ yx σyy
⎡
⎣ ⎢ ⎤
⎦ ⎥ =1 2
2 1⎡
⎣ ⎢ ⎤
⎦ ⎥
![Page 3: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/3.jpg)
MATLAB functions
plot
Example
x = 0:pi/100:2*pi;y = sin(x);plot(x,y)
![Page 4: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/4.jpg)
Bean-Bag Method
€
σ11 σ12 σ13
σ21 σ 22 σ 23
σ31 σ 32 σ 33
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥ =
1 2 3
2 2 −1
3 −1 1
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
![Page 5: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/5.jpg)
MATLAB functions
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)
meshgridmesh
![Page 6: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/6.jpg)
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) = … … ; endendmesh(x,y,z)
![Page 7: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/7.jpg)
Hole Problem
€
σr =σ0 1−a2 r2( )
σθ =σ0 1+a2 r2( )
![Page 8: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/8.jpg)
Stress Field
Radial stress
Tangential stress
![Page 9: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/9.jpg)
Cymbals
![Page 10: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/10.jpg)
Stress Field Around Crack Tip
€
τzx=τzy =0
€
σzx ≈0Thin plate
€
σy =K
2πrcos
θ2
1+sinθ2
sin3θ2
⎛ ⎝
⎞ ⎠
€
σx =K
2πrcos
θ2
1−sinθ2
sin3θ2
⎛ ⎝
⎞ ⎠
€
τxy=K
2πrsin
θ2
cosθ2
cos3θ2
![Page 11: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/11.jpg)
Von Mises’ Yield Criterion
€
σe =2
2(σx−σy)
2 +(σy−σz)2 +(σz−σx)
2 +6(τxy2 +τyz
2 +τzx2 )2
[ ]1/ 2
Perfect plasticity
€
σe =σys, if σ e >σ ys
![Page 12: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/12.jpg)
Crack Tip Stress Field
![Page 13: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/13.jpg)
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.
![Page 14: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/14.jpg)
Dislocation Emissions
![Page 15: Visualization Friday, 9/6/2002. Hedgehog Method MATLAB functions plot Example x = 0:pi/100:2*pi; y = sin(x); plot(x,y)](https://reader035.vdocuments.site/reader035/viewer/2022062619/5515d5bc550346cf6f8b4832/html5/thumbnails/15.jpg)