I was thinking about multiplication of two singularity functions. It is possible and it is mathematically significant. We can implement this too in Sympy. Similarly with powers.
I need your suggestions. Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Wed, Mar 16, 2016 at 9:41 PM, SAMPAD SAHA <[email protected]> wrote: > Yah , You are right . A software having good documentations about all the > functionality is preffered more over the others by the users. I will be > spending a good amount of time in preparing the documentation citing plenty > of examples and tutorials. > > Here > <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions> > is > link to my proposal. I have almost added all the things which we have > disscussed. I still need to add the example and many more "TODO"s are left. > I am working on those. > > > Suggestions are welcomed. > > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 16, 2016 at 6:18 AM, Jason Moore <[email protected]> wrote: > >> Looks good. I think you should have plenty of examples in the docs. >> People tend to use software more if the docs are top notch. So plenty of >> examples and tutorials will really help. >> >> >> Jason >> moorepants.info >> +01 530-601-9791 >> >> On Tue, Mar 15, 2016 at 5:25 PM, SAMPAD SAHA <[email protected]> >> wrote: >> >>> You are right. *delta_function.py *needs to be improved. I will to be >>> using only* DiracDelta* and *Heaviside *for generating almost all the >>> Singularity Functions. >>> >>> I was also thinking to complete this project in four phases: >>> >>> 1. Improving existiing Functions. >>> 2. Creating Singularity Functions module >>> 3. Creating beam Module >>> 4. Documentation >>> >>> >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore <[email protected]> >>> wrote: >>> >>>> https://www.python.org/dev/peps/pep-0008/ >>>> >>>> I think you will need a pure singularity function module and then you >>>> will need a beam module that utlizes the singularity function module. You >>>> will also likely need to improve the discontinuous functions that are >>>> already in sympy. There are at least three layers to this in my eyes. >>>> >>>> >>>> Jason >>>> moorepants.info >>>> +01 530-601-9791 >>>> >>>> On Tue, Mar 15, 2016 at 5:07 PM, SAMPAD SAHA <[email protected]> >>>> wrote: >>>> >>>>> Jason >>>>> >>>>> Pardon please. I couldn't get you by "You will need to follow PEP8 >>>>> for the method and class names". >>>>> >>>>> and yah, i also felt that it would be better if i use the input and >>>>> output values of the example problem done by hand. >>>>> >>>>> So , what do you suggest, Would it be better if we create a different >>>>> module ,other than the singularity function module, for solving beam >>>>> problems? That module would import the singularity function module for >>>>> using them. >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> Regards >>>>> Sampad Kumar Saha >>>>> Mathematics and Computing >>>>> I.I.T. Kharagpur >>>>> >>>>> On Wed, Mar 16, 2016 at 5:22 AM, Jason Moore <[email protected]> >>>>> wrote: >>>>> >>>>>> I think it is a good start. You will need to follow PEP8 for the >>>>>> method and class names. But I just want to see desired functionality. The >>>>>> more you can think up, the better. I would suggest doing a beam problem >>>>>> by >>>>>> hand and then translating that to a desired API. You can mock up what you >>>>>> think the inputs and outputs should be for that example problem. >>>>>> >>>>>> >>>>>> Jason >>>>>> moorepants.info >>>>>> +01 530-601-9791 >>>>>> >>>>>> On Tue, Mar 15, 2016 at 4:46 PM, SAMPAD SAHA <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> Ok Jason, >>>>>>> >>>>>>> And what about the API I have posted just before the earlier post? >>>>>>> >>>>>>> Any suggestions >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> Regards >>>>>>> Sampad Kumar Saha >>>>>>> Mathematics and Computing >>>>>>> I.I.T. Kharagpur >>>>>>> >>>>>>> On Wed, Mar 16, 2016 at 5:10 AM, Jason Moore <[email protected]> >>>>>>> wrote: >>>>>>> >>>>>>>> The file locations and method class names are just fine details >>>>>>>> that can be worked out later. They are generally not important for your >>>>>>>> proposal. Just focus on describing what the future modules should do. >>>>>>>> >>>>>>>> >>>>>>>> Jason >>>>>>>> moorepants.info >>>>>>>> +01 530-601-9791 >>>>>>>> >>>>>>>> On Tue, Mar 15, 2016 at 4:36 PM, SAMPAD SAHA <[email protected] >>>>>>>> > wrote: >>>>>>>> >>>>>>>>> Hi Jason, >>>>>>>>> >>>>>>>>> As I am thinking to create a another module for solving especially >>>>>>>>> beam problems (suppose *beambending.py) *, what will be its file >>>>>>>>> location? >>>>>>>>> Similarly for Singularity Functions (suppose >>>>>>>>> singularity_function.py), What will be its location? >>>>>>>>> >>>>>>>>> And what about the names of methods and classes, Can I give any >>>>>>>>> name or we will be discussing it at the time of developing them? >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> --------------------- >>>>>>>>> Regards, >>>>>>>>> Sampad >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> Regards >>>>>>>>> Sampad Kumar Saha >>>>>>>>> Mathematics and Computing >>>>>>>>> I.I.T. Kharagpur >>>>>>>>> >>>>>>>>> On Wed, Mar 16, 2016 at 3:56 AM, SAMPAD SAHA < >>>>>>>>> [email protected]> wrote: >>>>>>>>> >>>>>>>>>> Thank You Tim and Jason for your suggestions and clearing my >>>>>>>>>> doubts. >>>>>>>>>> >>>>>>>>>> We can also have an another module for solving beam problems. As >>>>>>>>>> Jason Have suggested earlier. >>>>>>>>>> >>>>>>>>>> Some of its classes would be Beam, DistributedLoad, PointLoad, >>>>>>>>>> Moment. >>>>>>>>>> >>>>>>>>>> We can have the API as:- >>>>>>>>>> >>>>>>>>>> from sympy import >>>>>>>>>> SingularityFunction,Beam,DistributedLoad,PointLoad,Moment >>>>>>>>>> b = Beam(length = 1, E = 1.87, I = 12) >>>>>>>>>> Load1 = DistrubutedLoad(start=l/2, end=l, value= 50) >>>>>>>>>> Load2 = PointLoad(location=l/3, value=60) >>>>>>>>>> Load3 = Moment(locaton = 1, value = 40, anticlockwise = True) >>>>>>>>>> b.apply(Load1,Load2,Load3) >>>>>>>>>> b.loadDistribution # Outputs the loading function in the form >>>>>>>>>> of singularity function >>>>>>>>>> b.shearForce # Outputs the Shear Force Function >>>>>>>>>> b.bendingMoment # Outputs the bending Moment Function >>>>>>>>>> b.slope # Outputs the Slope Function >>>>>>>>>> b.deflection # Outputs the deflection Function >>>>>>>>>> >>>>>>>>>> b.plotLoadDistribution # Outputs the plot of load Distribution >>>>>>>>>> Curve >>>>>>>>>> b.plotBendingMoment # Outputs the plot of Bending Moment >>>>>>>>>> Curve >>>>>>>>>> b.plotDeflection # Outputs the plot of Deflection Curve >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Regards >>>>>>>>>> Sampad Kumar Saha >>>>>>>>>> Mathematics and Computing >>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>> >>>>>>>>>> On Wed, Mar 16, 2016 at 2:45 AM, Tim Lahey <[email protected]> >>>>>>>>>> wrote: >>>>>>>>>> >>>>>>>>>>> I agree. One should start directly from the loading function >>>>>>>>>>> q(x). The general steps are: >>>>>>>>>>> >>>>>>>>>>> 1. Start with the loading function q(x) >>>>>>>>>>> 2. Integrate to get the shear function V(x). >>>>>>>>>>> 3. Integrate again to get the bending moment function M(x). >>>>>>>>>>> 4. Integrate to get the slope function E*I*v’(x). >>>>>>>>>>> 5. Integrate to get the displacement function E*I*v(x). >>>>>>>>>>> >>>>>>>>>>> Note that the singularity functions can be multiplied by >>>>>>>>>>> arbitrary functions of x as well. This allows for varied loads and >>>>>>>>>>> cases >>>>>>>>>>> where E and I vary too. To be strictly correct one should include >>>>>>>>>>> the >>>>>>>>>>> integration constants as well and then solve for the reaction >>>>>>>>>>> forces and >>>>>>>>>>> the constants. >>>>>>>>>>> >>>>>>>>>>> You’ll need to carefully consider how you handle evaluating at >>>>>>>>>>> transition points, especially the beam boundaries. >>>>>>>>>>> >>>>>>>>>>> Cheers, >>>>>>>>>>> >>>>>>>>>>> Tim. >>>>>>>>>>> >>>>>>>>>>> > On Mar 15, 2016, at 4:53 PM, Jason Moore <[email protected]> >>>>>>>>>>> wrote: >>>>>>>>>>> > >>>>>>>>>>> > I think you'd want the user to input the loads on the beam as >>>>>>>>>>> singularity functions or some higher level abstraction. If you >>>>>>>>>>> require them >>>>>>>>>>> to manually compute the bending moment then you are defeating the >>>>>>>>>>> purpose >>>>>>>>>>> of having a CAS do it for you. >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > Jason >>>>>>>>>>> > moorepants.info >>>>>>>>>>> > +01 530-601-9791 >>>>>>>>>>> > >>>>>>>>>>> > On Sun, Mar 13, 2016 at 2:25 PM, SAMPAD SAHA < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> > Hi Jason, >>>>>>>>>>> > >>>>>>>>>>> > I have a confusion regarding the user inputs for the beam >>>>>>>>>>> problems. >>>>>>>>>>> > >>>>>>>>>>> > I think that we should take only the Bending Moment Function >>>>>>>>>>> (in the form of singularity functions) and the boundary conditions >>>>>>>>>>> as >>>>>>>>>>> inputs. >>>>>>>>>>> > >>>>>>>>>>> > I mean to say that generally in a given beam bending problem, >>>>>>>>>>> a diagram of a beam and distributed loads are provided. So it is not >>>>>>>>>>> possible to get these data as an user input. Rather we can expect >>>>>>>>>>> that the >>>>>>>>>>> user would formulate the bending moment function, in the form of >>>>>>>>>>> Singularity function, and then provide that function as an input for >>>>>>>>>>> getting the elastic curve equation. >>>>>>>>>>> > >>>>>>>>>>> > Note:- Values of E , I , Boundary Conditions are also >>>>>>>>>>> expected as an input. >>>>>>>>>>> > >>>>>>>>>>> > I need your suggestions. >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > ----------------- >>>>>>>>>>> > Regards, >>>>>>>>>>> > Sampad >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > Regards >>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>> > >>>>>>>>>>> > On Sat, Mar 12, 2016 at 11:50 AM, Aaron Meurer < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> > It should give (-1)**n*f^(n)(0) (that is, (-1)**n*diff(f(x), >>>>>>>>>>> x, n).subs(x, 0)), if I remember the formula correctly. >>>>>>>>>>> > >>>>>>>>>>> > Aaron Meurer >>>>>>>>>>> > >>>>>>>>>>> > On Fri, Mar 11, 2016 at 9:00 AM, SAMPAD SAHA < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> > Hi Aaron, >>>>>>>>>>> > >>>>>>>>>>> > I have a doubt . >>>>>>>>>>> > >>>>>>>>>>> > Do we want: >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > integrate(f(x)*DiracDelta(x, n), (x, -oo, oo)) would output as >>>>>>>>>>> > >>>>>>>>>>> > <image.png> >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > Regards >>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>> > >>>>>>>>>>> > On Wed, Mar 9, 2016 at 3:11 AM, Aaron Meurer < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> > DiracDelta(x, k) gives the k-th derivative of DiracDelta(x) >>>>>>>>>>> (or you >>>>>>>>>>> > can write DiracDelta(x).diff(x, k)). >>>>>>>>>>> > >>>>>>>>>>> > It does look like the delta integrate routines could be >>>>>>>>>>> improved here, though: >>>>>>>>>>> > >>>>>>>>>>> > In [2]: integrate(f(x)*DiracDelta(x), (x, -oo, oo)) >>>>>>>>>>> > Out[2]: f(0) >>>>>>>>>>> > >>>>>>>>>>> > In [3]: integrate(f(x)*DiracDelta(x, 1), (x, -oo, oo)) >>>>>>>>>>> > Out[3]: >>>>>>>>>>> > ∞ >>>>>>>>>>> > ⌠ >>>>>>>>>>> > ⎮ f(x)⋅DiracDelta(x, 1) dx >>>>>>>>>>> > ⌡ >>>>>>>>>>> > -∞ >>>>>>>>>>> > >>>>>>>>>>> > Since the integration rules for derivatives of delta functions >>>>>>>>>>> are >>>>>>>>>>> > simple extensions of the rules for the delta function itself, >>>>>>>>>>> this is >>>>>>>>>>> > probably not difficult to fix. >>>>>>>>>>> > >>>>>>>>>>> > Aaron Meurer >>>>>>>>>>> > >>>>>>>>>>> > On Mon, Feb 29, 2016 at 3:39 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. 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