As simple as demonstrated !

Prova funzione.sm (7kb) downloaded 30 time(s).

Thanks to both, but I'm dealing with a more complex case:
Forum example.sm (49kb) downloaded 28 time(s).

As you can see, I know the solution of the system from a textbook example made with Mathcad: the single variable equation works well (apart the fact I've to input a very short range of solution...), but for the system of two eqn there is an errorro referring to a matrix...

Can anyone help me?
Thanks in advance.

PS: I know Jean doesn't like the unit usage, but it's very useful for making more general spreadsheets!

It is a know issues/beahvior of Unknowns; I have plans to improve it although isn't easy to provide something generic and reliable.



Italian code NTC2018 probably, it allows to use different diagrams.

No, I'm not obliged to use the parabola-rectangle diagramma for the ULS.



Thanks. I can remote units before defining the functions, but what are the subscript-related issues?



Yes, the Italian code is very similar to Eurocodes, also for the design of structures made with material other than concrete.

Old school. See AlgLib 3.1x.

Edited by user 16 May 2020 17:08:14(UTC)  | Reason: Not specified

I think maxima Solve() can't handle functions containing conditional statements. Using boolean expressions won't help, as these aren't translated to maxima.

Hi Alvaro, thanks for the unit_step() hint. Generally, charfun() is a more general approach to convert boolean expressions to 0 and 1. However, symbolic integration in maxima can't handle charfun(), whereas the unit_step() function is handled. See feature request SS-99.
.
Some testing shows that Solve() (maxima's solve()) doesn't handle step functions well. Perhaps there are some options or special packages to improve this, but it doesn't work out of the box. Handling of integrals with abs() and sign() is enabled by loading the package abs_integrate, which is done by default in the plugin, see the session log in the printout.

Here is an overview of integration of piecewise continuous functions (from the interactive handbook). Some of these are handled symbolically by maxima, some of them are returned unchanged and then handled by poor man's non-adaptive SMath numeric integrator.

For now, the sign() and abs() approaches work.


Section math piecewise.sm (31kb) downloaded 16 time(s).

I do not well understand your suggestions... There are 3 double integrals with a functions of 3 variables.
However I compared the results of the previous design with those from a simple domain discretization (using the known solution), in a way to detect some input errors: no errors but the solver still does not work.

Forum discretization example.sm (124kb) downloaded 20 time(s).
Forum example w-o units_4.sm (80kb) downloaded 13 time(s)..

https://en.smath.com/for...t1775p2_AlgLib-3-1x.aspx : I see the solver deals also with 3 variables...

Any other suggested solver?

Edited by user 26 May 2020 13:20:44(UTC)  | Reason: Not specified

Hello SteelCat,

Could you please tell me what are the equations you want to solve (as I sincerely don't know about the Jacobian procedure and the AlgLib solver).




Nint = ?;
Mxint = ?;
Myint = ?;


I will give it a try, I understand that you are dealing with biaxial bending of a concrete column.. as I am working on my interaction volume these weeks, I think I could help you.

By the way, I am proceeding with the shoelace Gauss formula to obtain the compression volume of concrete (a discrete approach, not a continuous double-integral approach) and also with the R diagram for concrete (not P-R).

But I will try to find a solution for your equations (staying continuous).

Regards,

Alvaro

Forum example w-o units_4-BIS.sm (81kb) downloaded 17 time(s).

It seems that the issue was due to the Jacob() function: I defined manually the Jacobian matrix, but Smath still do not show me the result...