# Solving constraint equations [Term Paper, HELP ]

1. Dec 6, 2004

### skjalff

Solving constraint equations [Term Paper, HELP plz]

Hi, I am new here. I'm not sure if this fits in calculus&analysis forum, but i figured its not really simple math so, please move it into approprieate area if deemed necessary...

I am doing materials selection analysis and my constraint equations came down to:

Yield strength constraint
Mass constraint
Deflection constraint

310000>25/(3.14*X*(X+2*Y))
3.3>.45*3.14*ρ*X*(X+2*Y)
0.002>(15*.09)/(12*220000000*X*(X+2*Y)*(((X+Y)^2)+(Y^2)))

where X is wall thickness of a hollow cyllinder and Y is its inner radius. All other constants are evaluated for simplicity. Basically I need to find the ranges for X and Y that satisfy all three conditions..

I plotted all 3 equations as surfaces equating them to Z, and got the general picture of behaviors, but now I need to cap the Z-values of each surface by the constraint values and look at the X-Y plane in 2D to find the required range... I have no idea what software would do this part and if i knew, HOW would i get it to do it...

ANY HELP IS GREATLY APPRECIATED!!! I am not stuck on this method, itd be kinda nice to get the result graphically, but at this point ANY method you would suggest would do just fine! My deadline is in a day, so I am really in a crunch here!!!

thanks in appreciation,

Eugene

Last edited: Dec 6, 2004
2. Dec 6, 2004

### Tide

Why would you complicate matters by going to three dimensions? Plot them in 2D cartesian coordinates.

Many programs will plot implicit equations and some will plot implicit inequalities (MuPAD for example).

3. Dec 6, 2004

### skjalff

I'm sorry, I'm too slow right now.. How do you plot a function of three variables in two dimensions? All I need really is to plot them in two dimensions, but in such a way that only X and Y values that yield a value lower than the constraint are plotted... How do I do that?? I am downloading MuPAD currently if that would help (I have never worked with it though)

thanks,

Eugene

4. Dec 6, 2004

### skjalff

Tide! Thanks so much man, you reply was EXACTLY what I needed, just a new perspective, I cracked this like 20 minutes after I read what you wrote!! You frigging saved me man )))))

Eugene