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AATaylor1-Visitor
1-Visitor
September 9, 2019
Solved

Direct Integration Problem - MathCAD

  • September 9, 2019
  • 3 replies
  • 6965 views

Hello All,

 

I am having a bit of trouble with direct integration on the attached sheet. I have a data set provided in Excel format which I have converted to matrix/vector form and then to function form using cubic spline interpolation. Unfortunately I am having trouble integrating the resulting function in x and am receiving a "This calculation does not converge to a solution" error message.

 

I have tried changing TOL to ridiculous values like 1E-50, with no luck.

 

Any assistance would be greatly appreciated.

 

Many thanks and kind regards

Best answer by AlanStevens

utot works ok as it is for me!

 

The uvol integral works by using an overbar.

 

See attached.

 

Alan

 

NB I removed the ridiculously low value of TOL.

 

3 replies

D
DJF16-Pearl
16-Pearl
September 9, 2019

I'm not sure what the problem is, but a b-spline works (at least in prime).

 

2019-09-09_8-54-41.png

    A
    AATaylor1-VisitorAuthor
    1-Visitor
    September 9, 2019
    Hi Alex, Thanks for the response, much appreciated, although Cspline appears to be working now

    Cheers
    A
    AlanStevens19-TanzaniteAnswer
    19-Tanzanite
    September 9, 2019

    utot works ok as it is for me!

     

    The uvol integral works by using an overbar.

     

    See attached.

     

    Alan

     

    NB I removed the ridiculously low value of TOL.

     

      A
      AATaylor1-VisitorAuthor
      1-Visitor
      September 9, 2019
      Hi Alan,

      Iā€™m not sure what has happened but it now works for me too! Annoyingly I wasted about 2 hours fiddling with the sheet without any obvious remedy before giving up and posting here...

      Thanks for the overbar vectorisation tip - I had missed that detail from the online help example!

      Cheers
      L
      LucMeekes23-Emerald IV
      23-Emerald IV
      September 9, 2019

      Without seeing your worksheet...

      Why do you think that creating a spline from a data vector and integrating along that spline would give you a better (more accurate?) result than just summing all data points?

      A spline is no more than a nice curve along your data points and, unless there is other/prior knowledge about the system that creates the data points, you cannot add accuracy by creating a spline.

       

      Assuming that Alan solved the problem, and you now know the result of integration: compare that with simply adding up the data points. Then decide if creating the spline is worth all the trouble...

       

      Success!
      Luc

        A
        AATaylor1-VisitorAuthor
        1-Visitor
        September 9, 2019
        Hi Luc,

        Iā€™m not sure what you mean by summing all the data points? Surely just adding the stress values would not be the same as calculating the area? Are you referring to a summation of trapezoidal areas? I have done a crude method of that in the worksheet.

        The basic answer to your question is that the method I used is the easiest way I know to find the area under a curve in mathcad.

        If you know a different way using the vectors directly Iā€™d love to know!

        Cheers
        W
        Werner_E25-Diamond I
        25-Diamond I
        September 9, 2019

        You are wondering why in Alan's sheet the integral utot works now for you? The reason is that he disabled your TOL setting and so the default TOL=10^-3 is valid now.

        Setting the value of TOL to lower values (10^-4 or lower, as you did) increases the chance of the integral NOT converging!

        Your approach with U.vol works without vectorization if you use an undefined variable (quickplot) or a range as argument:

        B1.png

        As to the trapezoid rule - here is an approach using your raw data:

        B2.png

        Worksheet in MC15 format attached.

         

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