Hi Aaron, Pardon Please. I am bit confused. Are you taking about the "*Piecewise Representation*" that I have mentioned in Phase I ?
Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Fri, Mar 25, 2016 at 12:00 AM, Aaron Meurer <[email protected]> wrote: > You should call the method _eval_rewrite_Piecewise. Then you can call it > with expr.rewrite(Piecewise). The advantage here is that this will > automatically work even if it's a subexpression of some larger expression. > > Aaron Meurer > > On Fri, Mar 18, 2016 at 9:37 PM, Jason Moore <[email protected]> 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 <[email protected]> >> 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 <[email protected]> >>> 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 <[email protected]> >>>> 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 <[email protected]> >>>>> 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 <[email protected]> >>>>>> 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 <[email protected]> >>>>>>> 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 < >>>>>>> [email protected]> 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 <[email protected]> >>>>>>> wrote: >>>>>>> > Add the constants when you integrate in your beam class. >>>>>>> > >>>>>>> > >>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA <[email protected]> >>>>>>> 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 <[email protected]> >>>>>>> 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 <[email protected]> >>>>>>> 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 < >>>>>>> [email protected]> 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 < >>>>>>> [email protected]> 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 < >>>>>>> [email protected]> 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 < >>>>>>> [email protected]> 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 < >>>>>>> [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 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: >>>>>>> >> > • 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 < >>>>>>> [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. 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 [email protected]. >>>>>>> >> > > >> To post to this group, send email to >>>>>>> [email protected]. >>>>>>> >> > > >> 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 >>>>>>> . >>>>>>> >> > > > >>>>>>> >> > > > -- >>>>>>> >> > > > 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 [email protected]. >>>>>>> >> > > > To post to this group, send email to [email protected] >>>>>>> . >>>>>>> >> > > > 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/1795A385-4AEA-44FD-BEE8-8115D53DA14B%40gmail.com >>>>>>> . >>>>>>> >> > > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > > >>>>>>> >> > > -- >>>>>>> >> > > 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 [email protected]. >>>>>>> >> > > To post to this group, send email to [email protected]. >>>>>>> >> > > 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/CAKgW%3D6JiW6zhx%3DcTahjcugKaR3jOTrYOnFJWYRr-%2BNiS-2zcLQ%40mail.gmail.com >>>>>>> . >>>>>>> >> > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > > >>>>>>> >> > > >>>>>>> >> > > -- >>>>>>> >> > > 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 [email protected]. >>>>>>> >> > > To post to this group, send email to [email protected]. >>>>>>> >> > > 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/CANzav4HrH7YbrOm4%3D9s2%2BHevCnCv4vz1RbuU%2BZWwLWLnCZpbcw%40mail.gmail.com >>>>>>> . >>>>>>> >> > > >>>>>>> >> > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > > >>>>>>> >> > > >>>>>>> >> > > -- >>>>>>> >> > > 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 [email protected]. >>>>>>> >> > > To post to this group, send email to [email protected]. >>>>>>> >> > > 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/CAKgW%3D6KrEOoZ-CvGJ_HTBVSpTLVkW6geUfvXdP8GAiBNO4y8qQ%40mail.gmail.com >>>>>>> . >>>>>>> >> > > >>>>>>> >> > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > > >>>>>>> >> > > >>>>>>> >> > > -- >>>>>>> >> > > 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 [email protected]. >>>>>>> >> > > To post to this group, send email to [email protected]. >>>>>>> >> > > 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/CANzav4EeosCsLaP55dwMpKxOxBkGhW6ZAkeCQiSvQnXtieU6PQ%40mail.gmail.com >>>>>>> . >>>>>>> >> > > >>>>>>> >> > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > > >>>>>>> >> > > >>>>>>> >> > > -- >>>>>>> >> > > 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 [email protected]. >>>>>>> >> > > To post to this group, send email to [email protected]. >>>>>>> >> > > 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/CAP7f1AjHOvGfvxRfOTy2RhRm3YnNc_eJ9OpjBOain6iK15chMA%40mail.gmail.com >>>>>>> . >>>>>>> >> > > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> > >>>>>>> >> > -- >>>>>>> >> > 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 [email protected]. >>>>>>> >> > To post to this group, send email to [email protected]. >>>>>>> >> > 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/B66DECFB-0205-41DC-A09D-342BBDF6FAC4%40gmail.com >>>>>>> . >>>>>>> >> > For more options, visit https://groups.google.com/d/optout. >>>>>>> >> >>>>>>> >> >>>>>>> > >>>>>>> > >>>>>>> >>>>>>> >>>>>> >>>>> >>>> >>> >> -- >> 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 [email protected]. >> To post to this group, send email to [email protected]. >> 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/CAP7f1AiuP1c2LxKte0%3DEV3BYAb-TYEi1wDBfNXg4E5YV1e64Aw%40mail.gmail.com >> <https://groups.google.com/d/msgid/sympy/CAP7f1AiuP1c2LxKte0%3DEV3BYAb-TYEi1wDBfNXg4E5YV1e64Aw%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> >> For more options, visit https://groups.google.com/d/optout. >> > > -- 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 [email protected]. To post to this group, send email to [email protected]. 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/CANzav4Gxk5jRChZwTDiRfD0F%2ByMjAHcgJgN6WnLJD9LSmyKiqA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
