Hi,
Singularity functions are just Dirac deltas, Heaviside functions, and
polynomials multiplying a Heaviside function with an offset. I seriously wrote
something to do it in less than an hour. The Maple code to do it is,
sFunc := proc(n,a)
if (n = -1) then
return diff(Heaviside(x-a),x);
else
if (n = -2) then
return diff(Heaviside(x-a),x$2);
else
return (x-a)^n*Heaviside(x-a);
end if;
end if;
end proc:
So, one just calls sFunc(n,a) where n is the power of singularity function and
a is the offset from x=0. It’s worked for every problem I’ve tried (which is
quite a few). Note that this requires good handling of Dirac deltas and
Heaviside functions in the calculus code.
Now that’s just a crude version, if one wants it to look better then it’s a bit
more work, but not a lot.
Cheers,
Tim.
> On Feb 29, 2016, at 11:47 AM, Jason Moore <[email protected]> wrote:
>
> Tim,
>
> I wouldn't say that they are "extremely easy" to implement. If we want a nice
> thorough package that does this, there will be plenty of work for the summer
> for a undergraduate GSoC student. If you'd like to share with us your
> implementation in a form that doesn't require owning Maple to understand it,
> I'm sure it would be helpful.
>
> Thanks,
>
> Jason
>
>
> Jason
> moorepants.info
> +01 530-601-9791
>
> On Mon, Feb 29, 2016 at 12:39 AM, Tim Lahey <[email protected]> wrote:
> Hi,
>
> Singularity functions are actually extremely easy to implement given that we
> have a Dirac delta and Heaviside functions. Assuming that the Dirac delta and
> Heaviside functions properly handle calculus, it’s trivial to wrap them for
> use as singularity functions. The only thing that will need to be added is
> the derivative of the Dirac delta (assuming it’s not already there). I
> implemented singularity functions in Maple in less than an afternoon.
>
> I was a TA for a Mechanics of Deformable Solids course about 11 or 12 times
> and wrote it to help the students (as we have a site license for Maple). I
> also wrote a set of lecture notes on the topic.
>
> Cheers,
>
> Tim.
>
> > On Feb 26, 2016, at 4:29 PM, SAMPAD SAHA <[email protected]> wrote:
> >
> > Hi Jason,
> >
> > Thank you for the explanation. It really helped me.
> >
> > So, basically we want to start it, firstly, by creating a module which
> > would deal with the mathematical operations performed on Singularity
> > Functions. After this whole module is prepared, we would focus on how to
> > use this module for solving beam problems. Am I correct?
> >
> > Can you please explain me in brief that what are the mathematical
> > operations we wanted to implement on that module?
> >
> >
> > On Friday, February 26, 2016 at 4:54:59 PM UTC+5:30, SAMPAD SAHA wrote:
> >
> > Hi,
> >
> > I am Sampad Kumar Saha , an Undergraduate Mathematics and Computing Student
> > at I.I.T. Kharagpur.
> >
> > I have gone through the idea page and I am interested in working on the
> > project named Singularity Function.
> >
> > By going through the Idea, I understood that we want to add a package to
> > Sympy which can be used for for solving beam bending stress and deflection
> > problems using singularity function. Am I correct?
> >
> > We can by this way:-
> > While solving we will be having the moment function as an input which we
> > can arrange in the form of singularity functions and then integrate it
> > twice to get the deflection curve and we can give the plot or the equation
> > obtained of deflection curve as an output.
> >
> > I have gone through some documents available on internet which have brief
> > studies on solving beam bending stress and deflection problems using
> > singularity functions.
> >
> > References:-
> > • Beam Deflection By Discontinuity Functions.
> > • Beam Equation Using Singularity Functions.
> > • Enhanced Student Learning in Engineering Courses with CAS
> > Technology.
> > Since there is just a brief idea given in the idea page, I have a doubt
> > that what are the things other than solving beam bending stress and
> > deflection problems to be implemented in the project?
> >
> > Any type of suggestions are welcome.
> >
> > ==========================================================================================================================================
> > Regards
> > Sampad Kumar Saha
> > Mathematics and Computing
> > I.I.T. Kharagpur
> >
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