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SImulation Mechanical Pm & Pm+b

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Message 1 of 5
travis.potier
566 Views, 4 Replies

SImulation Mechanical Pm & Pm+b

I am working with Simulation Mechanical 2015. I am running models using non-linear material models, so I don't have the option to use the built-in stress linearization feature. I created my own excel spreadsheet that linearizes the stresses and calculates Pm and Pm+b stresses from the stress values pulled from the results page.

 

I have confirmed the following:

  • My spreadsheet correctly and accurately transforms the global stress tensor to the local stress tensor
  • It also correctly calculates the membrane stress when using the maximum shear stress theory

I'm attempting to use the methodology as per the link below (from Autodesk)

 

https://knowledge.autodesk.com/support/simulation-mechanical/learn-explore/caas/CloudHelp/cloudhelp/...

 

Where things fall apart is the bending portion. In equations 13, 14, and 15, I interpret the "T" value to be the distance from the center of the SCL to the node. Is this correct? If not, what value does the "T" represent?

 

In equations 19, 21, and 24, what exactly does the term (2T/t) represent? I interpreted this to be in line with my above comment: the bending stresses are multiplied by 2*(the distance from the center of the SCL to the node)/(the length of the SCL). If this is not correct, can someone please explain the (2T/t) term? 

 

Something goes wrong in my spreadsheet in the bending stress because I've compared its results to a model using the build in stress linearization feature and the Pm+b stresses do not match using either M.S.S. or von Mises.

 

Also, in all text books and literature I've ever use, when calculation the von Mises equivalent stress, the squares of the differences are divided by 2, but in equations 27 and 28, the 1/2 term is not present. Also, when using the form shown in the link, the von Mises value differs drastically from the MSS value (that I confirmed with the built in feature), however when the 1/2 term is applied, it provides a result that makes a lot more sense. Can someone confirm if equations 27 and 28 are incorrect?

 

Thanks in advance.

 

4 REPLIES 4
Message 2 of 5
AstroJohnPE
in reply to: travis.potier

Hi Travis,

 

I agree with your conclusions.

 

  • "T" is the distance from the center of the SCL. It should be positive in one direction (toward the "last point") and negative in the other.
  • The bending stress S at some distance T from the center of the SCL is proportional to the maximum bending stress and the ratio of the distances, or S= Smax*T/(0.5t) = Smax*2*T/t, where t is the length of the SCL.
  • The equations [27] and [28] for the von Mises stress are missing the factor 0.5.

 

My only thought is that maybe there is a problem with the calculation of the principal stress, which is not given in the documentation. That's a solution to a cubic equation, right? (Or is it a solution to a matrix?) You should be able to confirm your calculation using any node and results in the Results environment. In other words, you do not need to use the Stress Linearization to confirm your calculation of the principal stress.

 

Keep in mind that the result at a node that is shared by multiple elements might have a different stress value due to each element. It is probably better if you turn the smoothing off when checking the values in the Results environment with the calculations from your spreadsheet.

Message 3 of 5
travis.potier
in reply to: AstroJohnPE

Hi John,

 

Thanks for the response. My spreadsheet uses the stress invariants to calculate the principal stresses (derived from matrix operations). I've confirmed the principal stress calculations within my spreadsheet using a couple of different methods, one being the use of Excels goal-seek function to solve the cubic equation of the principal stresses. So, I'm confident in that portion of the spreadsheet. 

 

Something I didn't ask in my original post regarding equations 19, 21, 24 from Autodesk's website is the Node 1 and Node 2 reference. Am I correct in thinking that Node 1 would be the node at one end of the SCL and Node 2 would be the node on the opposite end? I'm made some changes per this and your comments and get results much closer to the built in feature, but not as exact as the Pm stress results. 

 

I've uploaded my spreadsheet if you'd like to take a peak at it. There is a lot of unused data on the sheet (I keep everything as I troubleshoot and then once I'm comfortable and confident in the spreadsheet I'll remove the unnecessary information).

 

I'm going to run some more comparison tests, and if all of my results are as close as these are, I'll assume it's likely computation round-off error and move forward. 

 

Travis

Message 4 of 5
John_Holtz
in reply to: travis.potier

Hi Travis.

 

Yes, nodes 1 and 2 are at the ends of the SCL, per the diagram on this page: Define Points and Perpendicular Direction. One thing that is missing from that diagram is that the origin is half way between the end points, or at a distance of t/2 (where t is the total length).

 

I have not used stress linearization for a while. I will take a look to refresh my memory.



John Holtz, P.E.

Global Product Support
Autodesk, Inc.


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Message 5 of 5
travis.potier
in reply to: John_Holtz

John,

 

I've gotten it figured out. Had a misplaced term and implemented everything in your comments. I'm now getting reliable results out of my spreadsheet when compared to the built in stress linearization feature. I thank you for taking the time to make the comments.

 

Travis

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