topic Re: Can I use Polyroots in a in a loop ? in Mathcad

Can I use Polyroots in a in a loop ?

remslie — Thu, 03 May 2018 14:30:32 GMT

Hi, I am wishing to solve a Hertzian contact problem for sub-surface stresses for multiple points in order to plot contours. The solution routine uses Polyroots to extract the maximum root for use in the calculation and works fine for a single point. Is it possible to automate the

Re: Can I use Polyroots in a in a loop ?

StuartBruff — Fri, 29 Apr 2016 09:19:23 GMT

Ross Emslie wrote:

Hi, I am wishing to solve a Hertzian contact problem for sub-surface stresses for multiple points in order to plot contours. The solution routine uses Polyroots to extract the maximum root for use in the calculation and works fine for a single point. Is it possible to automate the process in a loop for variable x, y and z using Polyroots? I tried a couple of attempts but get errors.

I'm not sure you need to use the symbolic processor as you already know the form of the polynomial. You should be able to wrap the S1S equations up into a function like this ...

which you can then call as part of a loop (program or range variable)

Stuart

Re: Can I use Polyroots in a in a loop ?

-MFra- — Fri, 29 Apr 2016 10:37:56 GMT

What do you think about my solution?

Re: Can I use Polyroots in a in a loop ?

remslie — Sun, 01 May 2016 13:37:21 GMT

Stuart, Thanks for looking into my problem.

I have tried splicing your routine into the program and assigned a range variable to z (ultimately I would like to vary all x, y and z) but running into difficulty with extracting the maximum root for each iteration z. My function f(x1,y1,z1) now has complex roots and includes all roots. So I need to extract the max root for each iteration and use this as s1s in subsequent equations. The current max(f(x1,y1,z1)) only gives a single value and not the multiple values for the range variable z1?

Cheers

Ross

Re: Can I use Polyroots in a in a loop ?

remslie — Sun, 01 May 2016 13:45:18 GMT

FM, I can see where you are going with this enhancement. Your programming skills are a level above mine. I have tried reproducing your routine but something basic is missing.I think there are some errors in the definition of deltax, deltay and deltaz but that does not seem to be the reason for the undefined variable ? Perhaps you could send your version of the mathcad sheet.

Thanks

Ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Mon, 02 May 2016 13:35:48 GMT

In my file goes all "smoothly". You have incorrectly written the name of the rootsdistr routine.

Bye

Re: Can I use Polyroots in a in a loop ?

remslie — Mon, 02 May 2016 23:01:34 GMT

FM, That leaves me a bit red faced with embarrassment! Thanks for the correction to a simple error. I will include this routine in the progarm. thanks for your help.

Ross

Re: Can I use Polyroots in a in a loop ?

remslie — Sun, 08 May 2016 10:56:22 GMT

FM, I have incorporated your suggested routine into my calculation and now get results for a 3D grid which is just what I wanted. Brilliant!! However, I am having difficulty plotting contours for a specific X-Z or Y-Z plane. Do you have any ideas on how to assign the 3D x,y,z coordinates to a 2D plane subset of the results so the contours can be plotted? Any assistance would be appreciated.

Cheers

ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Mon, 09 May 2016 16:10:43 GMT

Hi Ross. Since it is not clear what do you want to plot, for now, I can advise you to read the mathcad guide on 3D graphics and of which I am attaching a photo.

Greetings

F. M.

Re: Can I use Polyroots in a in a loop ?

remslie — Tue, 10 May 2016 08:16:55 GMT

FM,

In Rev3 above I have a 3D matrix of all computed stress values (called Testroot), which is essentially the stress values distributed through a 3D solid rectangle with geometric coordinates (x1,y1,z1). I now wish to plot the stress results in contour from for a plane cut through this solid say the plane (1.0,y1,z1). The examples showing how to plot contours of data in the Mathcad tutorials use range variables for a predefined function e.g. f(xsubi,ysubi). My results matrix has no asssociativity to the geometry co-ordinates. Is there an easy way of extracting the data for a 2D plane from the 3D matrix of results and plotting this as a contour?

Thanks

Ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Tue, 10 May 2016 11:43:22 GMT

Hello Ross, it's ok so?

Bye

Re: Can I use Polyroots in a in a loop ?

remslie — Tue, 10 May 2016 21:58:19 GMT

FM, Surprisingly simple! Many thanks for your assistance. Cheers ross

Re: Can I use Polyroots in a in a loop ?

remslie — Mon, 30 May 2016 22:58:59 GMT

FM,

I am continuing to have difficulty obtaining correct answers for the three level nested loop. I believe the syntax I am using is incorrect. In the attached Example 3a sheet, I have bypassed the polyroots result I am attempting to calculate and simply sending the x1 increment to the output matrix (see XRoot). I am also doing this for y1 and z1 in separate calculations (YRoot and ZRoot).For each of the x1, y1 and z1 increments there should only be three different values(i.e. Nx=Ny=Nz=3). This is correct for x1 but not correct for y1 and z1. There are 7 different values of y1 in YRoot and 19 different values of z1 in ZRoot.

Can you advise where the problem lies.

Many Thanks Ross

Re: Can I use Polyroots in a in a loop ?

remslie — Tue, 31 May 2016 09:31:21 GMT

FM,

I located an error in the loop in Example 3a sheet above which was incrementing x1, y1, z1 from the previous value in addition to the increment Deltax1 etc. this has been corrected in example sheet 3b attached. My understanding is that each of the 3x3 matricies should have alll elements the same for x1, y1 & z1. Can you advise how I can ensure that there will be 3x3x3=27 unique elements in the 3D Nx-Ny-Nz matrix.

Any ideas how to correct this?

Cheers

Ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Tue, 31 May 2016 12:47:28 GMT

Hi E. R., I realize that my little program is unsatisfactory. I'm trying to reinterpret your problem. A point P moves in a lattice going from one plane to another and in each point must calculate a particular property at that same point. I wrote this little program that does what I said. The result is rather strange.

I have considered the modulo of each root since in pairs they can be complex conjugates.

Perhaps it is more acceptable my previous version, of course, after eliminating some mistakes.

Re: Can I use Polyroots in a in a loop ?

remslie — Wed, 01 Jun 2016 08:19:25 GMT

FM,

This is a baffling problem. I have included your "ESDU first part" program on the same sheet as the original equations to derive the Polyroots from my "Example 1" sheet and the program values do not correlate with the matrix values from your program. The maximum root for the example (x,y,z) = (1.0,0.5,0.2) equals 0.07287. I have also calculated several other points using this manual method and included the results in an Excel table in the attached sheet. The 3x3x3 matrix output for the example in the attached sheet should include the result for (x,y,z) = (1.0,0.5,0.2) equals 0.07287. But this value does not appear anywhere in the program results??? This seems to indicate that the nested loop is still not computing the correct or expected results.

Many thanks for your continued assistsance.

Cheers

Ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Wed, 01 Jun 2016 14:41:59 GMT

Dear Mr. RE, I would like to know what values can take the integer constants Nx, Ny, Nz.

Also, if you could enlighten me, wanting to know more, at least all that leads to the polynomial equation used.

I attached the revised version 4 with some modest results.

With best regards

Re: Can I use Polyroots in a in a loop ?

remslie — Thu, 02 Jun 2016 07:40:43 GMT

FM,

Your revised program in version 4 now calculates the correct value for the first point in the calculation being (x,y,z) = (0,0,0.1) = 0.00278. . However, all other points seem to deviate from what is expected and grow in magnitude.

The Nx, Ny and Nz integer values represent the number of points along each axis within the 3D lattice that stresses are to be calculated. The calculation routine is not valid for the surface (z=0) but is valid for z>0 (i.e. below the surface of contact- see diagram for orientation of axes at the head of the sheet).The maximum root for the example (x,y,z) = (1.0,0.5,0.2) equals 0.07287 is a value given in the technical paper as a worked example and the manual method computes this value correctly. The nested loops certainly count correctly but do not seem to increment correctly. I have attached an extract from the technical paper providing the methodology and equations. The worked example is at the end of this extract. I trust this assists.

Regards,

Ross

Re: Can I use Polyroots in a in a loop ?

remslie — Thu, 02 Jun 2016 08:33:09 GMT

FM,

Your question about Nx,Ny,Nz prompted a review and the deltax, deltay and delta z need to have the denominator reduced by one i.e. Nx-1, Ny-1 and Nz-1. This now gives three correct results as shown in attached sheet. It still seems the increments are not being computed correctly??

Regards,

Ross

Re: Can I use Polyroots in a in a loop ?

-MFra- — Thu, 02 Jun 2016 10:37:13 GMT

Hi, RE,

I made some changes and compared the result with the solution provided by the posted document, which already provides the formula for calculating the maximum root at a point P (x, y, z) , so there would be no need to use polyroots. Given that the increments are made at the end of each loop, you have to replace Nx-1, Ny-1, Nz-1 with Nx, Ny, Nz in the two programs, as follows:

Yours sincerely.