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. For more options, visit https://groups.google.com/d/optout.
