Pressure Vessel Analysis with Matlab | Propulsion Workgroup | Forum

- I have done some stress calculations for pressure vessels with Matlab. These calculations are for vessels that are not closed at the ends, as a result, there is no longitudinal stress. I haven't yet used the thin wall approximation equation, rather, I have been using other equations for tangential (hoop) and radial stress. In a pressure vessel, the stresses have a distribution throughout the thickness of the cylinder. In the wave, there were files that were attached. They are also in Dropbox.

http://dl.dropbox.com/u/295234…..linder.png

- If the thickness is about 1/20 of the radius, then the approximation can be used since the tangential stress is much larger than the radial stress:

(theta_t)_av=p*r_i/t

(theta_t)_max=p(d_i+t)/(2*t)

- The picture below are the equations I used in Matlab for the analysis.

http://dl.dropbox.com/u/295234…..ations.png

- The first analysis I have done with Matlab plots the distribution of stress for varying thickness throughout the thickness for both radial and tangential stress for a given inside pressure, outside pressure, inside radius and thickness range.

- The values I used were:

p_i=1000000; % Inside pressure (Pa)

p_o=101325; % Outside pressure (Pa)

r_i=0.3; % Inside radius (m)

t_min=0.001; % Minimum thickness (m)

t_max=0.1; % Maximum thickness (m)

- The resulting plots for tangential stress and radial stress are below as well as the Matlab file

Tangential Stress: http://dl.dropbox.com/u/295234…..Stress.png

Radial Stress: http://dl.dropbox.com/u/295234…..Stress.png

Matlab File:http://dl.dropbox.com/u/2952347/Pressure_Vessel/Pressure_Vessel_with_Given_Pressures/Pressure_Vessel_with_given_pressures.m

- Hopefully this is comprehensible. The inside radius is fixed at 0.3m. At the left corner in the tangential plot it can be seen that the thickness is 0.001m and the stress is plotted throughout the radius of the cylinder from 0.3m to 0.301m. At the right, the stress is plotted throughout the radius of a cylinder with inside radius 0.3m and outside radius 0.3m+0.1m=0.4m. The same logic is used for the for the plot with radial stress. One thing to note with the radial stress is that the values are negative, meaning the stress is in compression.

- These plots can provide insight on the reactions to pressure vessels, such as, at what point is the thickness impractical because it is no longer providing strength, rather it is just adding to the mass. The files can be altered so that they will apply more to our model. This was only a start. I will continue with more analysis (what is the plural form of analysis? Somebody help me out) as well.

- Feel free to correct/modify this.

I am a little bit confused since the density doesn't affect the stress involved. I can create a new analysis though. What would you like to see? density vs mass vs inside radius at given thickness and height?

Post edited 12:14 pm – November 17, 2009 by rpulkrabek

What we are after is the material's yield strength. From here, we will be able to determine how much stress the material can handle before it plastically deforms, meaning, before it has permanent deformation. There are many things we can do to determine the most suited material, but basically, we need to find one that has a the highest yield strength to density ratio. We can make a type of scatter plot with each point being a seperate material. There is software that is meant for this type of stuff. What I used in University was some software called Granta (http://www.grantadesign.com/pr…..ucts/ces/). I don't have access to it anymore, but maybe there is some sort of free database somewhere for us to use.