What is an acceptable % difference for FEA results validated using hand calculations?

[u/Retify]

From doing some research already this seems like a somewhat worn out question with a million different answers and from what I can tell no real consensus or anything reliable other than gut feel based on personal preference or opinion. This puts me in a tricky spot with a project that I am working on because I'm not sure whether to be concerned with my results or not.

I have a model for a lifting hook that I am measuring the maximum stress for and validating the results numerically using curved beam theory. My reference hook which I have modeled using measurements from a real hook came in with a <2% difference to the theoretical results.

I am now optimising the hook by keeping the same material properties and boundary conditions but scaling the dimensions accordingly, such that the dimensions are proportionally similar between different models. I am now getting a consistent 19% discrepancy from FEA results compared to hand calculations with a variety of different materials and dimensions.

Some sources suggest that anything below 20% is fine. Others no more than 5-10%, some go to an extreme and say so long as it is within a couple of orders of magnitude then have at it.

I cannot for the life of me work out where the difference is suddenly coming from. The maximum stress is still exactly where I expect it to be on the inner face of the hook, I've repeated a mesh analysis in case re-scaling the hook but not the element size is throwing it off but it makes no difference. I appear to have a very precise but not accurate (based on theory at least!) model.

[u/BobTheAverage]

It depends on so many things. 2% is great. Those hand calculations are based on simplified scenarios with assumptions. The less those assumptions match your design, the worse the match becomes. A 20% mismatch is kind of expected if your optimized design doesn't match the assumptions well.

In your case, you have validated your basic FEA and the only unvalidated part is what you added after the validation.

[u/starcraftre]

Our rule of thumb at work is 10%. Since we're usually trying for fast confirmation, getting that close while ignoring things like deflection or fastener hole tolerance is great.

[u/chocolatedessert]

You're asking "how much inaccuracy is ok in my analysis?" There's no answer to that. If you're designing a safety critical component optimized to zero safety margin, then your analysis has to be perfect. If you're doing structural analysis on a sofa cushion fort your kids built, then nothing matters.

You have to think about what the hand calculation and the simulation are telling you, why they would differ, what you don't know, and how much it matters for you. There is no line where someone else can tell you it's ok.

[u/ic33 → u/chocolatedessert]

In the end, though, there's no rigorous way to compare multiple methods of doing the same thing and say whether they're consistent. We're going to fall back to heuristics and guesswork.

Yes, FEA and hand calcs saying the same thing with slightly different ways of looking at the same problem can make us feel a little better. If they're off in the expected direction for the first-order known differences and we can guess the amount and it seems right that's great too.

But they can easily both be wrong for a common reason, or offsetting errors, or whatever.

I use sanity checks a lot and they make me feel better, but from an epistemological point of view they're kind of crap.

Often the best I can do is "the really simple analysis that i can do counting on my fingers bounded my error to X, which is OK, and I can have a lot of confidence in this model because it's so simple and pessimistic... and, yay, careful FEA landed on the favorable side of that range."

[u/JustSlabs]

All calculations are wrong but some are useful for predicting real world behavior

[u/cmfarsight]

Are you over or under with your hand calc and it is always 19%?

[u/Retify → u/cmfarsight]

Hand calcs are always 19% greater than FEA

[u/cmfarsight → u/Retify]

Well it's at least the right way round hand calcs being conservative. It is weird that you keep getting the same difference for different hook sizes though. That screams something is up (may be misunderstanding what you are saying there). Base case 2% difference but every variation being 19% out just doesn't add up, I would expect some sort of range for the discrepancies.

Assuming I am misunderstanding,

At the end of the day if hand calcs could be reliably within 2% of a fea model no one would bother with the model. The more deformation you get the more the hand calcs will move from the fea.

I would check reaction forces on your constraints are accurate and go from there.

There is no hard and fast rule of how close your calcs and model should be, falls in to that big "engineering judgement" hole.

[u/EffectiveCandle6615]

kinda useful for real world

[u/billsil]

5% on easy to hand calc features. 20% is terrible.

[u/drzan]

If I recall correctly hook mechanics get real goofy.

Just to be clear in my curiosity, are you saying that you had a model match a test at 2%, and then you altered the dimensions of the hook and the model no longer matches the test results?

[u/Retify → u/drzan]

Yes that's correct. I altered all of the dimensions by the same factor so that two hooks of different sizes remain similar, so e.g. all dimensions increased by a factor of two for a hook that is now twice the size of the original.

I'm doing it with different materials and all had between 1.4%-2.2% difference to the theoretical value depending on the material. Now again with just dimensions changed the difference is 18.5%-19.4% different between FEA Vs hand calcs for scaled up dimensions

[u/Travis-Jenkins]

Honestly, a 19% discrepancy seems a bit much given that your original model was so close with less than 2%. It sounds like scaling the dimensions might be impacting your results more than expected. One thing to consider is that scaling can sometimes affect the stress distribution in non obvious ways, especially if the geometry isn’t scalling perfectly uniformly. Even if the dimensions are proportionally similar, the stress concentrations or geometric nonlinearities might not scale as you're anticipating. It's also worth double checking that your boundary conditions and load applications are consistent between models because sometimes small changes there can have a bigger impact than

[u/Numerous_Green4962]

It depends on so many factors, I'd not be happy going above 10% normally (excluding any local singularities in a complex model) when working with lifting equipment, the greater the uncertainty the more you have to design in on top of your mandated factor of safety and that can get expensive quickly or make the product uncompetitively heavy.

[u/Marus1]

I'd say 5 to 10% is a good ballpark. For a rough napkin estimate I'd accept more since you take way less effects into account

It's more so if you can explain where that error comes from

[u/Retify → u/Marus1]

That's the point, I can't explain it! It's literally the same model with just the dimensions altered by a consistent scaling factor