Smbolic calculation with one (or more) variables unresolved?

[ClaudioPedrazzi]

Hi everyone,

I do not often use symbolic calculation, and I have already tried the keyword "explicit" but I don't seem to get it right.

How can I obtain a symbolic result without the numerical substitution of a variable?

I have attached a practical example (a stripped version of a worksheet where I am trying to use the Rayleigh Distribution to compute the fatigue cumulative usage factors caused by a random narrow-band Gaussian vibration on a part, given the rms stress and the number of cycles).

But the question is general. Mathcad substitutes the values of the variables he knows.  Sometimes it is not desirable.  How do I reach this?

Thanks for every hint

Best regards

Claudio

[ValeryOchkov]

One try

[ClaudioPedrazzi]

Thanks Valery,

but the 100000 is exactly what I would like not to see.

[Fred_Kohlhepp]

Mathcad symbolics will not substitute for n unassigned variable:

Write the function definitions without assigning the variable values, ignore the red circle protests of the numeric processor.  If the variable is assigned, you get numbers:

[ClaudioPedrazzi]

Hi Fred,

thanks, that seems to work but ...

In my case not really pretty.  And I do wish to have my variables defined in my worksheet.  Well, this could be solved just using different names.

Look what happens with your proposed solution (I just deactivated the definitions).

Possibly I am asking too much.  For the human behind the screen it would be better if the magenta crossed parts just disappeared.  The first integral results in 1, and the second in nrms.

I was hoping in some kind of keywords telling Mathcad "please consider the following as parameters: nrms, sigma0, and so on.

[MJG]

The portion you X-ed out in magenta is only 0 if sigma.rms is less than infinity.  See my post below.

[MJG · Accepted solution]

How about this?

[MJG]

Also, in case you're not aware, you can "hide keywords" to get this:

[ClaudioPedrazzi]

yes I wasn't aware ... thanks again.

[MJG]

FYI - "hide keywords" can be found in the right-click menu.

[ClaudioPedrazzi]

Wow

thanks.  Well for an engineer the root mean square of the stress amplitude should well be finite ;-).

Thanks, it was not clear to me how to use the "assume" and "simplify" keywords.

[MJG]

After posting, I actually realized that "simplify" was not necessary in this case.  You only need to use the "assume" keyword.

[LucMeekes]

You don't even need the assume keyword. The magic (if any) is in making sure the symbolic processor does not know the value of certain variables.

I think that you should just judisiously undefine variables, using the construct:

<variable> := <variable>

And you should be able to re/abuse sigma.rms instead of sigma.0.

Then you might get (my additions are in red):

Luc

[LucMeekes]

Correction,

For the first problem, you can do without sigma.0 and without sigma.rms, but then you need to make sure the symbolic processor understands that sigma is not dominant (so it is less than infinite)

Luc

[ClaudioPedrazzi]

Thanks a lot to all of you, Fred, Marc, Luc and Valery.  This was a good lesson in Symbolic 101!!

Regards

Claudio