Download presentation

Presentation is loading. Please wait.

Published byAvery Schmitt Modified over 3 years ago

1
Stress Matrix Visualization Wednesday, 9/4/2002

2
Stress Vector

3
Proof

4
Normal Stress If n is a row vector, normal_stress = (sigma*n)*n If n is a column vector, normal_stress = (sigma*n)*n Mathematical Expression MATLAB Expression

5
Shear Stress If all vectors expressed as row vectors, t = (sigma*n) shear_stress = t - (t*n)*n If all vectors expressed as column vectors, t = sigma*n shear_stress = t - (t*n)*n Mathematical Expression MATLAB Expression

6
Stress Visualization Method

7
Stress Visualization

8
Principal Direction [Vectors, Principal] = eig (stress)

9
Non-symmetric Square Matrix

10
Eigenvector Demonstration http://www.math.ucla.edu/~baker/java/hoefer/Eigendemo.htm

11
MATLAB code S=[1,2;2,1] n=50; hold on axis square S0=sqrt(sum(sum(S.^2))); axis([-S0*2,S0*2,-S0*2,S0*2]) theta = linspace( 0, pi*2, n ); plot(S0*cos(theta),S0*sin(theta),'r-'); for i=1:n t = theta(i); x0 = S0*cos(t); y0 = S0*sin(t); x1 = x0 + S(1,1)*cos(t) + S(1,2)*sin(t); y1 = y0 + S(2,1)*cos(t) + S(2,2)*sin(t); plot([x0,x1],[y0,y1]) end

12
Normal Stress Visualization Method

13
3D Stress State

14
MATLAB functions axis xlabel, ylabel, zlabel hold Plot linspace meshgrid mesh

Similar presentations

OK

ENGR-25_Plot_Model-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical.

ENGR-25_Plot_Model-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on internal structure of cpu Ppt on energy cogeneration definition Ppt on media advertising Ppt on online banking project in java Doc convert to ppt online templates Ppt on male reproductive system of human Ppt on carburetor diagram Ppt on world war 2 Ppt on praying together Ppt on my dream company google