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What are the methods for assessing accuracy of FEM models?

That is, to guide the development of a FEM model, and finally for assessing its reliability, what kinds of practices are used?

Sometimes it might be impossible to compare a model to a real-world scenario, because such scenario may not exist.

What does one do in such situation?

mavavilj
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  • You need to be more specific and citing example(s) for your claim "Sometimes it might be impossible to compare a model to a real-world scenario, because such scenario may not exist." – r13 Jun 14 '22 at 11:15
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    If you don’t have a real-world scenario then compare to a theoretical one. – Solar Mike Jun 14 '22 at 11:16
  • @r13 Ehh, isn't this quite evident that one might try modelling scenarios that one hasn't observed or cannot observe, but one speculates about their possibility. I.e. one models for the unseen risks (an earthquake, for example, or a misuse of equipment). – mavavilj Jun 14 '22 at 11:17
  • @SolarMike Then what's "accuracy" in that context? – mavavilj Jun 14 '22 at 11:19
  • As a practical example, consider if one wished to design a USB stick and a USB port that are very durable. Then how is one going to model all the possible types of forces that are applied to them? Still, USB equipment does break, so have they been tested enough? – mavavilj Jun 14 '22 at 11:20
  • 1%, 5%, 10% or 50% your assumption. – Solar Mike Jun 14 '22 at 11:21
  • Per your usb example, are you considering normal use or abuse? – Solar Mike Jun 14 '22 at 11:25
  • @SolarMike Consider designing a stick and a port that you want to last min. 10 years with 95-99% of the possible use cases. Now, how does one connect FEM analysis and real-world testing in this case for example? – mavavilj Jun 14 '22 at 12:04
  • If this is too simple example, then consider some other example, and then how would one know a proper "validation scheme" for it. – mavavilj Jun 14 '22 at 12:11
  • Am I looking at this question too simply? There must be verification techniques for FEM analysis, in general. If so, what are they? If not, then FEM analysis products are nothing more than black boxes & how & why should we trust a black box as if it's an oracle that can't be questioned or criticized? – Fred Jun 14 '22 at 12:37
  • I don't see that an impossible task, though can be tedious, and your smart selection of loading cases that are considered critical. – r13 Jun 14 '22 at 13:37
  • Are you just looking for mesh (and consequently loading) refinement? showing convergence and increased distance from unrealistic approximations can show your model is closer to valid. However, you must model to the appropriate theory- physics models are dependent on scale after all. – Abel Jun 15 '22 at 01:11
  • On FEM being black boxes, they often are, and so one should not trust. People make mistakes in loading and meshing, and when they do not share their model it makes for it fearsome black box like statistics. The difference is that instead of having to go collect your own data, you can often generate your own FEM, loaded and meshed "correctly" with your knowledge of the scenario. – Abel Jun 18 '22 at 18:20

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Usually the best way would be to start with a simple problem which has a solution --analytically or experimentally-- and validate the FEM results against the analytical solution or the experimental data.

Then move on to something more complex, and usually experimental validation is required.

Most FEM software have simple benchmark cases that if you go through the documentation you can find.

NMech
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You are conflating two different things:

  1. Proof that your mathematical model is an accurate enough description of physical reality
  2. Proof that your numerical model is an accurate enough description of the mathematical model

For the first, you run physical validation experiments (using a design of experiments to cover a large enough range of possibilities) and compare the collected data with numerical simulation results. These numerical simulations can be as complex as needed and may include physics + chemistry.

For the second, you find analytical solutions or numerical solutions that are of high degree of accuracy and compare your numerical results. Ideally, your numerical method must be an accurate representation of the mathematical model and that is what most commercial codes do to get certified (for nuclear plant design, for example).

Whether the mathematical model is good enough is a different ball game and is typically determined via both new theory and experiment developments.

Biswajit Banerjee
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