I am having a big confusion over this. There is no *integrate()* method defined in *DiracDelta* and* Heaviside. *But still how can this happen.
In [ ] : DiracDelta(x).integrate() Out [ ] : Heaviside(x) In [ ] : Heaviside(x).integrate() Out [ ] : x*Heaviside(x) I feel like this should raise error as *AttributeError: 'DiracDelta' object has no attribute 'integrate'.* Please explain how this is happenning. Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Wed, Mar 23, 2016 at 4:48 AM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > > Here is my proposal. > > https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha:-Singularity-Functions > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 23, 2016 at 4:08 AM, SAMPAD SAHA <sampadsa...@gmail.com> > wrote: > >> Thanks Jason, I have made some changes. Can you please review those? I >> have also added some comments along with yours. >> >> I didn't get you in this comment. Can you please elaborate it? >> "*Comment from Jason: You will need to make sure everything is backwards >> compatible. See the wiki for our policy.*" >> >> >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Tue, Mar 22, 2016 at 8:53 PM, Jason Moore <moorepa...@gmail.com> >> wrote: >> >>> The example you show doesn't seem to reflect what we may actually see >>> when using this for beams. I'd suggest picking a simple beam problem and >>> showing what all of your code will look like. You did that pretty well for >>> the later examples, but this one with the random polynomials wasn't that >>> clear. >>> >>> >>> Jason >>> moorepants.info >>> +01 530-601-9791 >>> >>> On Tue, Mar 22, 2016 at 7:43 AM, SAMPAD SAHA <sampadsa...@gmail.com> >>> wrote: >>> >>>> Thank You Jason. I will put it. >>>> >>>> I have a doubt about this comment in my proposal : >>>> >>>> *"Comment from Jason: It would be more informative to show what a beam >>>> equation would look like in Piecewise form. This is a little abstract." * >>>> >>>> Can you explain it a little more? >>>> >>>> I have also added some comment next to yours, I am still working on >>>> some of your comments. >>>> >>>> Regards >>>> Sampad Kumar Saha >>>> Mathematics and Computing >>>> I.I.T. Kharagpur >>>> >>>> On Tue, Mar 22, 2016 at 8:08 PM, Jason Moore <moorepa...@gmail.com> >>>> wrote: >>>> >>>>> Sounds good, just put it in your proposal. >>>>> >>>>> >>>>> Jason >>>>> moorepants.info >>>>> +01 530-601-9791 >>>>> >>>>> On Tue, Mar 22, 2016 at 7:32 AM, SAMPAD SAHA <sampadsa...@gmail.com> >>>>> wrote: >>>>> >>>>>> I will start coding along with community bonding. I will spend 3-4 >>>>>> hours extra in the last week of the community bonding period in order to >>>>>> achieve the proposed target in my proposal. I will have no problem >>>>>> managing >>>>>> with those extra hours since I will be having Summer break at that time >>>>>> and >>>>>> along with that I have no other commitments. And I will also have fun >>>>>> working those extra hours. >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> Regards >>>>>> Sampad Kumar Saha >>>>>> Mathematics and Computing >>>>>> I.I.T. Kharagpur >>>>>> >>>>>> On Tue, Mar 22, 2016 at 4:13 AM, Jason Moore <moorepa...@gmail.com> >>>>>> wrote: >>>>>> >>>>>>> No need to cancel your vacation. Just give a plan for how you will >>>>>>> make up the days. >>>>>>> >>>>>>> >>>>>>> Jason >>>>>>> moorepants.info >>>>>>> +01 530-601-9791 >>>>>>> >>>>>>> On Mon, Mar 21, 2016 at 2:52 PM, SAMPAD SAHA <sampadsa...@gmail.com> >>>>>>> wrote: >>>>>>> >>>>>>>> Thank You Jason for the suggestions in my proposal. I will work on >>>>>>>> those and let you know as soon as possible. >>>>>>>> >>>>>>>> I have mentioned in my proposal about the days of the vacation and >>>>>>>> how can I compensate the work. If this vacation raises any problem, I >>>>>>>> can >>>>>>>> cancel it . That will not be a problem for me. I don't want to let >>>>>>>> anything >>>>>>>> ruin the progess of the project as this Summer of Code will become an >>>>>>>> integral part of all my learning throughout the summer. >>>>>>>> >>>>>>>> ---------------- >>>>>>>> Regards >>>>>>>> Sampad >>>>>>>> >>>>>>>> >>>>>>>> Regards >>>>>>>> Sampad Kumar Saha >>>>>>>> Mathematics and Computing >>>>>>>> I.I.T. Kharagpur >>>>>>>> >>>>>>>> On Tue, Mar 22, 2016 at 2:33 AM, Jason Moore <moorepa...@gmail.com> >>>>>>>> wrote: >>>>>>>> >>>>>>>>> I've put some comments in your proposal. >>>>>>>>> >>>>>>>>> >>>>>>>>> Jason >>>>>>>>> moorepants.info >>>>>>>>> +01 530-601-9791 >>>>>>>>> >>>>>>>>> On Sat, Mar 19, 2016 at 10:58 AM, SAMPAD SAHA < >>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> Jason, >>>>>>>>>> >>>>>>>>>> Actually I have misunderstood earlier. >>>>>>>>>> >>>>>>>>>> I have updated my proposal here >>>>>>>>>> <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions> >>>>>>>>>> . >>>>>>>>>> Can you please review it and suggest me to improve it. >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Regards >>>>>>>>>> Sampad Kumar Saha >>>>>>>>>> Mathematics and Computing >>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>> >>>>>>>>>> On Sat, Mar 19, 2016 at 9:14 PM, Jason Moore < >>>>>>>>>> moorepa...@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> I don't think we should do "a hack". If we follow the patterns >>>>>>>>>>> in the integration code, we should leave the constants of >>>>>>>>>>> integration off. >>>>>>>>>>> But in the Beam classes you can have them manage the constants of >>>>>>>>>>> integration. What you show above looks fine. >>>>>>>>>>> >>>>>>>>>>> I didn't mean to use dsolve in any way. I just meant to have a >>>>>>>>>>> look at that code because they include constants of integration >>>>>>>>>>> when you >>>>>>>>>>> solve the ode. You can also set the boundary conditions in the >>>>>>>>>>> constructor. >>>>>>>>>>> It can give you ideas of how to design your api. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Jason >>>>>>>>>>> moorepants.info >>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>> >>>>>>>>>>> On Sat, Mar 19, 2016 at 8:27 AM, SAMPAD SAHA < >>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> Jason, >>>>>>>>>>>> >>>>>>>>>>>> I went through the ode package. I felt that it would be >>>>>>>>>>>> difficult to use boundary condition to solve for the constants of >>>>>>>>>>>> integration using the exisiting *dsolve() *method. It seems >>>>>>>>>>>> that it is still under development. >>>>>>>>>>>> >>>>>>>>>>>> So I thought of implementing that functionality explicitly for >>>>>>>>>>>> solving beam problems. >>>>>>>>>>>> >>>>>>>>>>>> I would be taking Boundary conditions as input as: >>>>>>>>>>>> >>>>>>>>>>>> *bcs = Beam.BoundaryCondition( {f(0) : 5, f.diff(0) : 4 } )* >>>>>>>>>>>> and so on. >>>>>>>>>>>> >>>>>>>>>>>> If nothing is provided then *f(0) != 0 , f.diff(0) = 0 *or >>>>>>>>>>>> something like this would be assumed. >>>>>>>>>>>> >>>>>>>>>>>> Depending on this boundary condition I would add the required >>>>>>>>>>>> constants by myself while finding the slope and deflection >>>>>>>>>>>> function and >>>>>>>>>>>> output the value by solving for those constants. >>>>>>>>>>>> >>>>>>>>>>>> By this way, the hack would be easier. What do you suggests? >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Regards >>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>> >>>>>>>>>>>> On Sat, Mar 19, 2016 at 7:17 AM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> Yah, you are right . We should not have the name simplify() as >>>>>>>>>>>>> a method since it have already created some issues in #7716 >>>>>>>>>>>>> <https://github.com/sympy/sympy/issues/7716> and #8798 >>>>>>>>>>>>> <https://github.com/sympy/sympy/issues/8798>. So i will keep >>>>>>>>>>>>> it as *to_piecewise()* . it would be fine then. >>>>>>>>>>>>> >>>>>>>>>>>>> As you suggested I will be look at ode package for this >>>>>>>>>>>>> constant of integration thing. >>>>>>>>>>>>> >>>>>>>>>>>>> Thank You... >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Regards >>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>> >>>>>>>>>>>>> On Sat, Mar 19, 2016 at 7:07 AM, Jason Moore < >>>>>>>>>>>>> moorepa...@gmail.com> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> Simplification means something very specific in SymPy, see >>>>>>>>>>>>>> the simplify() function. I think you need to choose a different >>>>>>>>>>>>>> method name >>>>>>>>>>>>>> for converting to piecewise continuous. Maybe: .to_piecewise()? >>>>>>>>>>>>>> >>>>>>>>>>>>>> You will need to implement some method for dealing with the >>>>>>>>>>>>>> constants of integration and boundary conditions. Maybe you >>>>>>>>>>>>>> should have a >>>>>>>>>>>>>> look at the ordinary differential equations package in SymPy to >>>>>>>>>>>>>> get some >>>>>>>>>>>>>> ideas about that. >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Jason >>>>>>>>>>>>>> moorepants.info >>>>>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 4:04 PM, SAMPAD SAHA < >>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>>> Thank You Jason for the appreciation. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Yah, that *Simplify * method would convert into continous >>>>>>>>>>>>>>> piecewise. Like this :- >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> In [ ] : F = singularityFunc(x, 0, 1) + >>>>>>>>>>>>>>> singularityFunc(x, 3, 2) >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> In [ ] : F >>>>>>>>>>>>>>> Out [ ] : >>>>>>>>>>>>>>> 2 >>>>>>>>>>>>>>> <x> + <x - 3> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> In [ ] : F.simplify() >>>>>>>>>>>>>>> Out [ ] : >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> 0 for x < 0 >>>>>>>>>>>>>>> x for 0 <= x < 3 >>>>>>>>>>>>>>> x + (x-3)^2 for x >= 3 >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> As you have suggested earlier, I have solved some examples >>>>>>>>>>>>>>> by hand and then tried to implement a desired api. From that I >>>>>>>>>>>>>>> came to this >>>>>>>>>>>>>>> conclusion that if we implement Addition, Substraction, >>>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity Functions >>>>>>>>>>>>>>> then we can >>>>>>>>>>>>>>> successfully solve out the beam problems. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> But i got doubt while implementing the boundary constants. I >>>>>>>>>>>>>>> mean to say that sympy dont gives constant of integration while >>>>>>>>>>>>>>> doing >>>>>>>>>>>>>>> indefinite integration. We can take boundary conditions as >>>>>>>>>>>>>>> input from users >>>>>>>>>>>>>>> that is not a problem, but we cant use it since there will be >>>>>>>>>>>>>>> no constant >>>>>>>>>>>>>>> of integration. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On Sat, Mar 19, 2016 at 4:07 AM, Jason Moore < >>>>>>>>>>>>>>> moorepa...@gmail.com> wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Sounds like a good start. How about a method to convert to >>>>>>>>>>>>>>>> continuous piecewise? >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Like I said earlier, you should pick some examples that you >>>>>>>>>>>>>>>> want the software to be able to solve and then implement >>>>>>>>>>>>>>>> methods and >>>>>>>>>>>>>>>> functionality based on those examples. It's hard to think of >>>>>>>>>>>>>>>> all the needed >>>>>>>>>>>>>>>> functionality and API without motivating examples first. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Jason >>>>>>>>>>>>>>>> moorepants.info >>>>>>>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 10:27 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Jason, >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> I have thought of implementing Addition, Substraction, >>>>>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity >>>>>>>>>>>>>>>>> Functions. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> What are the other functionalities we should implement? >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:16 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Yah you are correct. Differentiation of heaviside and >>>>>>>>>>>>>>>>>> diracdelta also exists. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> It was my mistake. Thanks for rectifying me. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Regards >>>>>>>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:02 PM, Tim Lahey < >>>>>>>>>>>>>>>>>> tim.la...@gmail.com> wrote: >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> For differentiation you’re missing a case, >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> if n = 0 or n = -1 >>>>>>>>>>>>>>>>>>> return Singularity(x, a, n-1) >>>>>>>>>>>>>>>>>>> else if n < -1 >>>>>>>>>>>>>>>>>>> return error >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> In other words, you can still differentiate for the n = >>>>>>>>>>>>>>>>>>> 0 and n = -1 cases. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Cheers, >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Tim. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> > On Mar 18, 2016, at 10:22 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > And what about the pseudocode of integration and >>>>>>>>>>>>>>>>>>> differentiation i have posted earlier , is it alright? >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > Regards >>>>>>>>>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:51 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> > Thanks Tim, >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > It is really a nice and effective solution. >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > Regards >>>>>>>>>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:46 PM, Tim Lahey < >>>>>>>>>>>>>>>>>>> tim.la...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> > Add the constants when you integrate in your beam >>>>>>>>>>>>>>>>>>> class. >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> > >>>>>>>>>>>>>>>>>>> >> Thanks TIm, >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Integration and Differentiation are really very >>>>>>>>>>>>>>>>>>> straight forward that is why i am thinking to add diff and >>>>>>>>>>>>>>>>>>> integrate method >>>>>>>>>>>>>>>>>>> to the Singularity function class itself. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> For integrate the pseuesocode will be :- >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> if(n<0) >>>>>>>>>>>>>>>>>>> >> return SingularityFunction(x , a, n+1) >>>>>>>>>>>>>>>>>>> >> else >>>>>>>>>>>>>>>>>>> >> return (1/n+1 * SingularityFunction(x , a, n+1)) >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Similarly for differentiation: >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> if (n>0) >>>>>>>>>>>>>>>>>>> >> return n * SingularityFunction(x , a, n - 1) >>>>>>>>>>>>>>>>>>> >> else >>>>>>>>>>>>>>>>>>> >> Error message >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> My doubt regarding Boundary condition was actually >>>>>>>>>>>>>>>>>>> was that since sympy don't provide constant of integration >>>>>>>>>>>>>>>>>>> while performing >>>>>>>>>>>>>>>>>>> indefinite integration on any expression, how to use the >>>>>>>>>>>>>>>>>>> boundary >>>>>>>>>>>>>>>>>>> conditions to find the exact values of constant of >>>>>>>>>>>>>>>>>>> integration? >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Regards >>>>>>>>>>>>>>>>>>> >> Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> >> Mathematics and Computing >>>>>>>>>>>>>>>>>>> >> I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> On Fri, Mar 18, 2016 at 6:09 PM, Tim Lahey < >>>>>>>>>>>>>>>>>>> tim.la...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> Hi, >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Do you know the integration and differentiation rules >>>>>>>>>>>>>>>>>>> for singularity functions? They’re pretty straightforward. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> As for boundary conditions, the beam will have >>>>>>>>>>>>>>>>>>> supports (or a free end) at each end of the beam and as >>>>>>>>>>>>>>>>>>> part of the beam >>>>>>>>>>>>>>>>>>> creation each end type is specified. Each type corresponds >>>>>>>>>>>>>>>>>>> to a specific >>>>>>>>>>>>>>>>>>> set of conditions on that end (either at x=0 or x=L). You >>>>>>>>>>>>>>>>>>> substitute those >>>>>>>>>>>>>>>>>>> conditions in the appropriate equation and solve for the >>>>>>>>>>>>>>>>>>> integration >>>>>>>>>>>>>>>>>>> constant as necessary. All of the conditions should be in >>>>>>>>>>>>>>>>>>> any decent >>>>>>>>>>>>>>>>>>> mechanics of deformable solids text book. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> You’ll want to do sums of forces and moments as well >>>>>>>>>>>>>>>>>>> to solve for reaction forces as well. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> The only trick is making sure you don’t double count >>>>>>>>>>>>>>>>>>> things. If you have a step function due to a reaction force >>>>>>>>>>>>>>>>>>> at the start of >>>>>>>>>>>>>>>>>>> the beam and assume it’s zero at x=0 (effectively the limit >>>>>>>>>>>>>>>>>>> at x=0^-) you >>>>>>>>>>>>>>>>>>> can get a non-zero integration constant that can be double >>>>>>>>>>>>>>>>>>> counting that >>>>>>>>>>>>>>>>>>> reaction since at x=0^+ that reaction force is non-zero. >>>>>>>>>>>>>>>>>>> Note that you can >>>>>>>>>>>>>>>>>>> get a non-zero integration constant (even when including >>>>>>>>>>>>>>>>>>> reaction forces in >>>>>>>>>>>>>>>>>>> the loading function) for shear and moment equations if you >>>>>>>>>>>>>>>>>>> have >>>>>>>>>>>>>>>>>>> non-polynomial loads (e.g., sine and cosine). You’ll also >>>>>>>>>>>>>>>>>>> have to think >>>>>>>>>>>>>>>>>>> about the other end as well. I leave it up to you to reason >>>>>>>>>>>>>>>>>>> that out. Make >>>>>>>>>>>>>>>>>>> sure you completely document how you’ve implemented it for >>>>>>>>>>>>>>>>>>> the user (and >>>>>>>>>>>>>>>>>>> why). >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Beam coordinate systems must start at the left end >>>>>>>>>>>>>>>>>>> and increase to the right. The definition of the >>>>>>>>>>>>>>>>>>> singularity functions >>>>>>>>>>>>>>>>>>> require this. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> I hope this helps. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Cheers, >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> Tim. >>>>>>>>>>>>>>>>>>> >> >>>>>>>>>>>>>>>>>>> >> > On Mar 18, 2016, at 8:17 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > I am also confused about implementing the boundary >>>>>>>>>>>>>>>>>>> conditions for getting the deflection curve. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Any suggestions on how to implement it. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 5:36 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> > Yah, you are right multiplication of singularity >>>>>>>>>>>>>>>>>>> functions are not needed for solving beam problems. >>>>>>>>>>>>>>>>>>> Mathematically, it is >>>>>>>>>>>>>>>>>>> also not used that much. So lets leave this multiplication >>>>>>>>>>>>>>>>>>> and powers part. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > I was thinking about the integrate and diff >>>>>>>>>>>>>>>>>>> methods. I feel that we should define instance methods diff >>>>>>>>>>>>>>>>>>> and integrate >>>>>>>>>>>>>>>>>>> in the singularity function module which would internally >>>>>>>>>>>>>>>>>>> use the existing >>>>>>>>>>>>>>>>>>> diff and integrate function for Differentiation and >>>>>>>>>>>>>>>>>>> Integration >>>>>>>>>>>>>>>>>>> respectively. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > I need your suggestions. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 3:14 AM, Jason Moore < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> > I think you need to override the operators. I'm not >>>>>>>>>>>>>>>>>>> sure if multiplying singularity functions is needed (at >>>>>>>>>>>>>>>>>>> least for beam >>>>>>>>>>>>>>>>>>> problems), even if it is mathematically correct, you don't >>>>>>>>>>>>>>>>>>> have to >>>>>>>>>>>>>>>>>>> implement it. If it is easy to implement then, sure, do so. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Jason >>>>>>>>>>>>>>>>>>> >> > moorepants.info >>>>>>>>>>>>>>>>>>> >> > +01 530-601-9791 >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > On Thu, Mar 17, 2016 at 1:34 PM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Jason, >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > For implementing Additon , Multiplication Do we >>>>>>>>>>>>>>>>>>> need to over ride __mul__ , __add__ these methods inside >>>>>>>>>>>>>>>>>>> the class >>>>>>>>>>>>>>>>>>> SingularityFunction or we can just use simplify for getting >>>>>>>>>>>>>>>>>>> the results. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > I am really confused. >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 1:59 AM, SAMPAD SAHA < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 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 < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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: >>>>>>>>>>>>>>>>>>> >> > • Improving existiing Functions. >>>>>>>>>>>>>>>>>>> >> > • Creating Singularity Functions module >>>>>>>>>>>>>>>>>>> >> > • Creating beam Module >>>>>>>>>>>>>>>>>>> >> > • Documentation >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > Regards >>>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>>>>>>>>> >> > >>>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> tim.la...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> asmeu...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> asmeu...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> tim.la...@gmail.com> 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 < >>>>>>>>>>>>>>>>>>> sampadsa...@gmail.com> 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 >>>>>>>>>>>>>>>>>>> >> > > >> >>>>>>>>>>>>>>>>>>> >> > > >> -- >>>>>>>>>>>>>>>>>>> >> > > >> You received this message because you are >>>>>>>>>>>>>>>>>>> subscribed to the Google Groups "sympy" group. >>>>>>>>>>>>>>>>>>> >> > > >> To unsubscribe from this group and stop >>>>>>>>>>>>>>>>>>> receiving emails from it, send an email to >>>>>>>>>>>>>>>>>>> sympy+unsubscr...@googlegroups.com. >>>>>>>>>>>>>>>>>>> >> > > >> To post to this group, send email to >>>>>>>>>>>>>>>>>>> sympy@googlegroups.com. >>>>>>>>>>>>>>>>>>> >> > > >> Visit this group at >>>>>>>>>>>>>>>>>>> https://groups.google.com/group/sympy. >>>>>>>>>>>>>>>>>>> >> > > >> To view this discussion on the web visit >>>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/7cbe2101-fd59-484b-9e25-f563636d6366%40googlegroups.com >>>>>>>>>>>>>>>>>>> . >>>>>>>>>>>>>>>>>>> >> > > >> For more options, visit >>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout. >>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>> >> > > > -- 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