## How should I answer what is the error of my FEM calculation?

## How should I answer what is the error of my FEM calculation?

(OP)

Hi guys,

Once somebody asked me a question: what is the error of your calculation?

How should I answer?

-I know error depends on elements: beam elements are most precise, shell elements are medium and solid elements are giving biggest error in calculation.

-For sure error depends on mesh quality.

-When I simplyfy my model - use shells instead of solids I also might lose some accuracy.

-I ommit here all the job regarding proper loading and fixation - lets assume it is all correct.

Can I give a number that describes the error? Then I will be able to say Fem calc error is 5% or so.

What is your opinion?

Best regards,

Wnuczko

Once somebody asked me a question: what is the error of your calculation?

How should I answer?

-I know error depends on elements: beam elements are most precise, shell elements are medium and solid elements are giving biggest error in calculation.

-For sure error depends on mesh quality.

-When I simplyfy my model - use shells instead of solids I also might lose some accuracy.

-I ommit here all the job regarding proper loading and fixation - lets assume it is all correct.

Can I give a number that describes the error? Then I will be able to say Fem calc error is 5% or so.

What is your opinion?

Best regards,

Wnuczko

## RE: How should I answer what is the error of my FEM calculation?

sounds like an interview question i had once ... "what's important in designing for fatigue ?" ... "umm, everything ?"

another day in paradise, or is paradise one day closer ?

## RE: How should I answer what is the error of my FEM calculation?

what is the error of your calculation?

My answer would depend very much on who is asking.

But just to point out two things in your post:

"beam elements are most precise, shell elements are medium and solid elements are giving biggest error in calculation."

"use shells instead of solids I also might lose some accuracy."

Those two statements don't add up if I understand you correct.

Also, the choice of element type depends on the application. There is, in my opinion, no specific element that is always "the best". Modelling soil with beams is probably not a good idea and neither is modelling a steel frame with solid elements. The key is the application after that you select the most suitable element.

And if somebody asked me for a typical percent error in FEM. Well, could lead to a loooong discussion depending om the mood and, again, who is asking. It's a bit like, how long is a piece of string of you want to be rude .

Thomas

## RE: How should I answer what is the error of my FEM calculation?

True that element type must be suitable for particular geometry.

Regarding "beam elements are most precise, shell elements are medium and solid elements are giving biggest error in calculation." I have heard that 1-D elements definition fits the best in the solution matrix. With 2-D and 3-D elements, in their definition there are some assumptions to make it possible to solve the matrix equation. But i'm not an expert - possible I'm completely wrong.

Regarding "use shells instead of solids I also might lose some accuracy." I mean for example I-beam 500mm after midsurfacing is not 500mm high but less. Is this 100% compensated by applying thickness?

My doubt is for example if a factor exist that I can compare result from 2 different mesh quality meshed on the same geometry.

Maybe it could be related to model convergence?

Kind regards,

Wnuczko

## RE: How should I answer what is the error of my FEM calculation?

2D elements are best suited to 2D structures, like large membranes/webs.

3D elements are best suited to 3D structures, like machined fittings.

you minimise error by convergence studies.

another day in paradise, or is paradise one day closer ?

## RE: How should I answer what is the error of my FEM calculation?

As far as I know there are theoretically exact element formulations for line elements but not for any 2D or 3D elements. But I would not say that it is a choice between "exact" and "really bad". The elements I am familiar with are usually very good, even if they are not "exact" in a strict sense. When it comes to sources for error I don't think element formulations are a major source. Provided you know their limitations.

When it comes the the mesh quality you can check it with convergence studies. Other sources for error are boundary conditions like loads and constraints.

Regarding your beam. I have made models and tests like that. In Femap, just check the "Double Sided Contour" Box in the Postprocessing meny. If you have "Element-Thickness/Cross Section" active you should be able so see a stress variation through the thickness for a 2D element. When I have checked results like that in the past the difference between hand calculation and simplified FEM models the error was usually small (<1%) if things were ok. The "real" analysis was usually not possible to do "by hand", hence FEM.

Thomas

## RE: How should I answer what is the error of my FEM calculation?

Remember: any FEM MUST be verified, otherwise it is useless to anyone.

Remember: FEM result is only 3% job done, rest 97 % is still engineering work...

However, nowadays looks that 97% of the job is skipping in a regular manner...

Looks like the one questioning you knows more that you think.

How your FEM account for material anisotropy, thermal treatment, grain size and shape, sensitivity on stress concentration, sensitivity on mean stress, residual stress, chemical treatment, coating, ...

You cannot just skip all of these.

## RE: How should I answer what is the error of my FEM calculation?

Seems any solver can not tell me what is the error since there is no way measure such thing. You receive results and you can't compare it with anything..

Thank you Guys.

## RE: How should I answer what is the error of my FEM calculation?

If you are interested in the effect of the mesh quality, study it. Do convergence studies to get some references. It is not very complicated.

As for comparing with "something". If you do an analysis and have absolutly no idea what the results will be. Then you are in trouble.

There is always something to compare it with. Even it it is just a crude hand calculation.

Like NikonF6 says, FEM is a tool. Handled with experience and knowledge a very powerful tool. But to say a certain percent error is typical. That I would say is impossible.

I suggest that you study the background theory. Just to understand the assumptions that FEM is based on.

Good Luck

Thomas

## RE: How should I answer what is the error of my FEM calculation?

The comments are leaning towards the ever-important mantra emphasizing FEA as a tool. I wholeheartedly agree. Just so you have something to work off of: Validity tests like these are common - (NASA, Sikorsky, Lockheed) as they provide some level of assertion purporting the validity of using a Finite Element Model and its output - for technical stress reports, as an example.

The information you can glean from a free-free eigenmode check is usually very informative.

http://ipek.hsr.ch/fileadmin/user_upload/ipek.hsr....

## RE: How should I answer what is the error of my FEM calculation?

The behavior of an FE model will differ from that of the physical system due to uncertainty and error. Uncertainty arises when it is not possible to accurately define an analysis parameter (e.g. loading condition, material parameter etc.). To deal with uncertainty we use experience, safety factors, sensitivity analyses and probabilistic methods.

Error arises due to mathematical idealization [behavioral assumptions (i.e. beam,shell,brick), dimensional assumptions (i.e. 1D, 2D, 3D), geometrical assumptions (i.e. model reduction, symmetry etc.)] and numerical approximation (spatial and temporal discretisation etc.). The magnitude of the error is determined by your understanding of the physical problem and your experience with the tools/capabilities/limitations of the FEA package. Error cannot be quantified precisely but can be estimated by performing sensitivity studies. Thorough validation is required to bound uncertainty and reduce the estimated error to an acceptable level so that FEA results can be reported with confidence.

This is worth a read.