FEA gives an approximate solution? Why?? 2

[9865395996]

I have learned, heard,experienced that finite element analysis gives only an approximate solution .

Just i need to know that what are all the factors that leads to this approximation??

How can we improve the efficiency of FEA to the highest?

 

[Twoballcane]

Yes I agree. At Preliminary Design Reviews, I don't take FEA at face value until the Analyst can walk me thru the hand calcs just so I know we are going in the right direction. FEA should always come with an appendix of hand calc’s or previous like test data to back it up. The poster made it sound like FEA is not accepted at all.



Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[KevinDeSmet]

I don't know about hand calcs, aren't they privy to the same assumptions problem FE is? I suppose they're simply better documented and that's never a bad thing. I just find it hard to do hand calculations because it's pretty alien to me, I guess to most people it would kind of be the other way around.

Certified SolidWorks Professional

 

[IFRs]

FEA for some types of elements is simply solving a system of simultaneous equations that equate deflections and rotations at nodes that belong to more than one elements. You could do it by hand if you had the time. It's not magic. At one time, I took a small structure of maybe 50 members, solved for all the forces by hand using simultaneous equations (OK - matrix manipulations) and then repeated it using FEA. No surprise, the answers were the same. It is vital that engineers understand what FEA is and what it is not, what its weakness and strengths are and how important the problem definition and assumptions are. Exactness of the solution suggests that you are concerned with the precision of the answer. In reality, more than one or two decimal places is excessive.

 

[ThomasH]

Interesting discussion. A few thoughts.

I would say that there are two types of approximations in FEM analysis.

The first type appies specifically to FEM and it is the difference between FEM and an exact analytical solution. Say that you have a simply supported beam. Most structural engineers would hopefully agree that the midspan moment from a uniform load is M = q L^2 / 8.
That is an analytical exact solution. Similars solutions exist for other structure types. There are analytical solutions for beams, frames, plates etcetera etcetera and those are often the solutions we aim for with our simulations. They are also the solutions that the FEM vendors use for verification purposes.

However, FEM is by definition approximate. For example, the deformations are assumed to be described by the base functions for the element. We make assumptions with the mathematics (weak formulations etc) and hopefully those assumptions are "good enuogh" for the results to be meaningful.
So the approximations are based om a numerical solution of an differential equation. The exact solution is sometimes impossible to find so we test the software with examples that have known solutions. Often these solutions are the analytical solutions.

The second part of approximations are not limited to FEM analysis but applies for all structural analysis. A simply supported beam with a uniform och concentrated load, a concentrated load implies a infinitely small loading area, anybody seen something like that?
Fixed (or free) support conditions don't exist in the real world, everything is flexible to some degree. Material models are usually approximations of reality and so on. Static and linear in a dynamic and nonlinear world means simplifications. And all these simplifications is something that the engineer needs to quantify so the FEM-software can do the number crunshing. FEM can handle huge amounts of data but it has to be told how to handle them.

As for the quality of the final analysis. I would say that the limitations is very seldom in the FEM approximations. FEM is an approximation, yes definitely, but compared to the other approxomations in structural analysis FEM is not the big issue.

Regards

Thomas

 

[Twoballcane]

“I just find it hard to do hand calculations because it's pretty alien to me, I guess to most people it would kind of be the other way around.”

Well, you need two points to make a straight line. Having the two points such as hand calcs and FEA or similar test data and FEA, this will indicate that the FEA is going in the right direction. Also, when I say hand calcs, I’m implying the math and physics of engineering theory using a combination of algebra and calculus not the matrix calculations of each node programmed in FEA. In my opinion, if one do’s not understand the engineering theory and cannot do the hand calcs associated with it, the FEA is almost meaningless.



Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[GregLocock]

I disagree.

Someone models a structure in FEA and gets a result, whether it is frequency or stiffness or whatever. Someone else test the structure in the real world and gets good correlation.

Neither person has had to understand FEA theory.

Neither person has performed a hand calc.

If they successfully do this repeatedly they have demonstrated good FEA modelling techniques.

Oh, and just in case you were wondering, I've been running FEA models for 32 years and testing real world structures for 31 years, and I've never cracked an FEA theory book in my life. And my models correlate, oh yes. Admittedly I am pretty good at hand calcs.

Cheers

Greg Locock


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[inline6]

Greg, the chances are if you know theory behind engineering/physics etc you will probably use better modelling techniques than someone that does not..........

 

[IceBreakerSours]

GregLocock:

I agree - for the most part. The exception is, for example, when you need a material model that is NOT provided in the library of the software package you are using. In such a case you will not only need strong modeling skills but also have a good grasp of FEA theory. User defined elements are an extreme example.

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[Twoballcane]

GregLocock,
I’m not sure where you disagree with me? However, my statement agrees with you and as stated in my last post that if you have past test data (i.e. measured frequency, deflections, G loads…etc) and it correlates to the FEA, then the FEA is going in the right directions and trust worthy. The alternative is if you don’t have past test data, then you will have to do some hand calcs to make sure the FEA is doing what you think it should be doing. But, if a decision has to be made and one only has FEA results and nothing to compare it to is a dangerous road to travel.

A point on FEA results, if person who is deciphering it does not understand engineering theory then it is useless to that person. For example, if the results are in Von Mises stress (or max principle stress) one would have to understand the failure theories to make a determination. If a modal analysis is done and the Fn is found, one would have to understand shock and random vibration theories to come to a conclusion of what the design can handle in stress/deflection and/or damping methods to reduce amplification/transmissibility…and so on.

Also, I tip my hat to you, in the past ten years I do know you have prowess in your engineering skills.




Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[GregLocock]

" In my opinion, if one do’s not understand the engineering theory and cannot do the hand calcs associated with it, the FEA is almost meaningless."

The logical 'and' there implies both are prerequisites, I gave an example where neither need apply yet the results could be superior to those commonly attained. I strongly suspect that of all the FEAs that are run in this world fewer than 10% have any meaningful correlated basis.

Cheers

Greg Locock


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