Download presentation

Presentation is loading. Please wait.

Published byAvery Schmitt Modified over 4 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

Introduction to MATLAB for Biomedical Engineering BME 1008 Introduction to Biomedical Engineering FIU, Spring 2015 Lesson 2: Element-wise vs. matrix operations.

Introduction to MATLAB for Biomedical Engineering BME 1008 Introduction to Biomedical Engineering FIU, Spring 2015 Lesson 2: Element-wise vs. matrix operations.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google