That FEA problem used to drive me mad
It happened to me a countless number of times.
I had just finished to set up my FEA model and run the analysis and I knew more or less what range of stresses I wanted to find.
I was waiting for the results to confirm that…
BUT…As you know there is always a factor between le results you expect and what you actually get… that’s normal in FEA.
…but why was the error so big???
I was looking at the maximum Von Mises Stress and I realized the average values inside the model were more or less OK, but I was just getting a small red point that was changing everything.
Inside this red area, the “normal” von mises stresses were 3 or 4 times the expected value and it clearly indicated that there was a big problem in my model…
So what did I do?
Of course, I started to search on the Internet! :)
And I found I was not alone to have such a problem… in fact, this problem was very common.
It was a singularity.
A “SINGULARITY” !!
This word sounds like coming right from Star Trek…
Do you know what is a singularity?
You see the image below?
Well…a singularity is basically the same… but inside your FE model!
Now I knew what it was…a singularity… but I still knew nothing.
The very famous physicist Richard Feynman said something I always remember:
“Even if you know the name of a bird in hundred languages, you still know nothing about the bird.”
So I decided to learn more about singularities and by what they were caused.
But, maybe before I explain that, you are wondering why singularities are such a pain in your model??
After all…I didn’t discuss that
Why is a single singularity in your model such a pain?
Well, singularities are causing many problems, but the major ones are:
– They cause an accuracy problem inside your model near the singularity.
– They cause a problem of visualization of your results by extending the range of the color inside your legend.
Those 2 problems are very painful…and that’s why I was wondering what ultimately causes singularities.
What causes a singularity
At first, I searched the answer on the Internet, but I couldn’t find it.
(I always thought that all the answers were available on the Internet for free, but that’s really not true)
Finally, I had to ask someone more expert than me about this topic to understand finally what was the major cause of singularities.
And it was …boundary conditions!
I didn’t want to believe it at first, but when I modified a bit the boundary conditions of my model, I discovered that the singularity vanished immediately.
Who knew that boundary conditions had such an impact…
Since then, I made a lot and a lot of progress (this situation I described happened 6 years ago when I just started to use FEA seriously)
I understood that there are a lot of ways to tackle singularity problems and also to set up boundary conditions so you will never get singularities…but that really took a lot of time to understand and a lot of efforts.
Maybe I’ll do some short course about it to explain all that in real details to you. That will save you a lot of time for sure.
Ok, it’s already late here… I’ll write more in a next article.
Just tell me:
Would you like to learn more about this topic?
Let me know by writing a comment
Yes my friend,Boundary conditions playing a major role to evolve Singularity…. Best u can check results with inertia relief and compare with contained BCs.
Thank you for your post! I would like to know in dept on this topic. I believe there would be other factors that cause the singularity, and what should be the appropriate approach when the singularity can’t be removed in the process of analysis. Thank you once again!
It would be amazing if you write another article about this topic! Singularities always drive me mad!
Hi Helena, Sure, I plan to write more in depth about it!
Actually singularity arises due to free node or free edge.means one of the diagonal value or bandwidth becomes zero.
the free nodes and edges are vrey simple to remove，but sometimes the stress of some location are very bigger than other location, which is not for stress concentration. how to tackle this issues？
Hi. Actually when there is no proper and sufficient constraint in the model there will be an internal mechanism developed internally. It’s either because of insufficient constraint which you have applied or if the model has free edges I.e some where in your model it has no node to node connectivity
You are right Amit, that’s a part of the answer. I will work on a more detailed answer and post more. Be sure to follow the blog!
Actually singularity arises due to free node or free edge.means one of the diagonal value or bandwidth becomes zero.if any boundary condition arises there will be pivot ratio error u think.
the free nodes and edges are vrey simple to remove，but sometimes the stress of some location are very bigger than other location, which is not for stress concentration. how to tackle this issues？
Amit, I think you you are referring to a case of singular matrix due to insufficient boundary condition, here the singularity referes to the caSe when stress at a point is infinite due to the geometry viz. sharp corners or edges
Thanks for your post on these topic. So many times I came across to singularity & difficult to justify it. Boundary conditions play effective role in FEA. But still singularity is problem in some cases. ASME has given some guidelines to tackle such type of max. stress (peak stress) at localized region. But still it can not apply or justify for all cases.
I would appreciate if you will share an more detail article on these.
hi，what is ASME and how it guide to tackle singularity？
Yes. I would be happy to have dept knowledge about the singularity problem.
Thank you for your post! I really enjoy reading your blog.
I would be more than happy if you had shared more of your knowledge regarding this topic :)
I would definitely like to learn more about this topic.
Thank you for your post. I would like to know in depth on this topic.
Hi Cyprien,
Thanks you for all the knowledge sharing in your blog, it is very useful.
I would like to know more about how your mesh can give you singularities.
Cheers,
Marcelo
Yes,
I would like learn about the singularity because its learning stage for me,
How to over come this singularity..?how to identify the singularity …?
Thank you for your post! I would like to know in depth on this topic. In general,l believe there would be other factors that cause the singularity, and what should be the appropriate approach to remove singularity in the process of analysis.
I am re-reading this post after mire than a year after its publication, but still there is no another article about singularities.
I hope Cyprian will return to this topic once again.
Hello Sir,
It would be really helpful if you could explain about it.
Best Regards,
Hi Mr.Cyprien
Can you please write a blog on theories of failure with real time examples.
Thanks in advance…
Yes sir of course! I want to know how to overcome singularity errors with an example.
Thank you very much! For another wonderful article.
Definitely, I would like to know more.
Just to clarify my self I thought singularity at sharp edges are inevitable, however, you have mentioned that can be corrected, so you are basically saying an in T junction stress rise at junction can be corrected with boundary condition?
I view a singularity in a boundary condition well for understand this kind of mesh defect, is a small zone about 1/1000 of boundary condition and I suppose the poisson factor in a super rigid condition and the external free boundary makes a gradient normal and shear stresss, modifying the principal stress direction and creating a huge VonMises stresss, you can try make disappear with a fillet o really you can ignore it and spect that the plastic zone be appear and auto correct the analysis design.