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. 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