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FEA gives an approximate solution? Why??
2

FEA gives an approximate solution? Why??

FEA gives an approximate solution? Why??

(OP)
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?

RE: FEA gives an approximate solution? Why??

Hello!,
In fact, FEA is an approximate method of simulation using the computer, but the good part is that everything is in your hand to make your results to be accurate or not. It depends of many factors: accuracy in the material properties used, if loadings & boundary conditions prescribed in your FE model are correct, if meshing approach used is reasonable or not based in the finite elements used in your model, also if the mesh density is coarsed or refined, if the solution type used is reasonable or not, etc.. Please note everything in real life is nonlinear, dynamic & transient, but is up to you to make your assumptions, in your hands is the admissible error of your solution.

In summary, yes, FEA is an approximate method, but is THE method, the best we have today, if your learn to use it in a professional way you will see that is great, impressing ...

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: http://www.iberisa.com
Blog de FEMAP & NX Nastran: http://iberisa.wordpress.com/

RE: FEA gives an approximate solution? Why??

I hate to burst your bubble, but EVERYTHING in analysis is an APPROXIMATION. You assume that all your bolts are identically loaded and strained, you assume that your materials are homogeneous and yield at the values specified, etc.

The fact of the matter is that no EXACT solution can be had, even for the abstraction of reality that is your "model." FEA is the closest thing to being a solution that you can possibly have, for all problems beyond the trivial ones.

TTFN
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RE: FEA gives an approximate solution? Why??

.. factors that leads to this approximation??

Approximations occur at several levels:

a/ mathematical model of the physical problem
b/ discretization
c/ applied loading, boundary conditions, interactions
d/ material model (isotropic/anisotropic .. linear elastic/hyperelastic .. )
e/ analysis (static/dynamic/viscoelastic,..)
f/ perhaps, the least worrisome (in overwhelming majority of cases) numerical approximation

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

I assume you are a beginner, and if so, I would grab a decent book, Bathe's for example, watch his online video lectures on linear finite element analysis first - available on YouTube, solve a bunch of simple problems for which analytical solutions are known.

Best.

RE: FEA gives an approximate solution? Why??

I agree with IRstuff. To add, FEA is just an interface tool between management and analysis. You should be doing hand calculations to understand what you are analyzing and then use FEA to confirm and show pretty pictures to management and the uninitiated. I suggest that you truly understand the math and physics that goes with the analysis. FEA is garbage in garbage out. If you are unfamiliar with the math and theories of what you are analyzing, please (PLEASE) hire a person who does (Structural/Mechanical Engineer). Also, hand calculations and FEA will either get you 80% there or total failure. Analysis altogether is just your best guess. Actual testing of the device is your final and accurate answer.

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

RE: FEA gives an approximate solution? Why??

firstly what is the "real" solution? IMO it is impossible to know. Physical testing to verify FE models also has its own problems with regard to accuracy.........

RE: FEA gives an approximate solution? Why??

sorry in advance, but ...

"truth ? you can't handle the truth ..."

i'd start with a basic text book on FEA; very quickly you'll see the approximations being made and solutions to minimise the error.

RE: FEA gives an approximate solution? Why??

Just note :

(1) Quadrilateral elements, other 2D/3D elements are approximation of the problem and the result depend of the meshing quality and refinement.

(2) For strucural engineer, the 2D/3D beam element is exact at node location (displacement and end forces). Exact means it give the exact same output than by hand calculation of the bernouilli beam solution.

RE: FEA gives an approximate solution? Why??

PicoStruc said:

"For strucural engineer, the 2D/3D beam element is exact at node location (displacement and end forces). Exact means it give the exact same output than by hand calculation of the bernouilli beam solution. "

Which may be true, but of course, Bernoulli Beam theory is only an approximation to the real world!

http://julianh72.blogspot.com

RE: FEA gives an approximate solution? Why??

picostruc - don't be quick to categorize....SEs are far more advanced than just 2D and 3D beams.....We've been known to use plates and shells and knives and forks and tension/compression elements, brick elements, all kinds of spring elements and on and on...

Regards,
Qshake
pipe
Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

RE: FEA gives an approximate solution? Why??

Can anyone define the exact solution? Even reality is very seldom repeatable, and thus the exact solution is hard to define. As engineers, we are responsible for defining the solution to a problem that will fulfill the requirements. I think asking what is the exact solution is the wrong question. Rather: Will this solve the problem? I have never encountered a problem that can not be soved with approximate solutions. But then we can always discuss: How close do we have to be? Hove reliable are the answers? Have I used adequate factors of safety?

RE: FEA gives an approximate solution? Why??

Analysis in general should be the search of minimums and maximums i.e. the minimum plate thickness to carry the maximum load and then add margin by factor of safety. Thus you’re looking for ranges of possibilities rather than exact solutions. You’re trying to make the best mathematical guess you can before you build and go to test. By doing the analysis and knowing the ranges, you will know the weak points of the design before going to test. With this knowledge, you can come up with a better test procedure to monitor the week points. The advantage is you can correlate the analysis and test data and for the next round you will get closer to guessing the measured physical phenomenon (deflection, strain, frequency, temperature…etc.). However, theories like stress, fatigue, PE and KE energy, heat rate…etc are still mathematical guesses with measured test data.

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

RE: FEA gives an approximate solution? Why??

Postjhardy1... Of course but generally when we are taking about the approximation/Exactitude of FEM... It's in comparison to best known model... not reality

Qshake... For sure we use other elements are used to by structural engineeers... see slab & shear wall design, stair design, custom built girder, etc.... What I meant is that beam are generally more used by structural engineer that any other kind of enginner.

RE: FEA gives an approximate solution? Why??

When FEA is world wide an acceptable method of analysis then I don't think we can conclude something by discussing it why it is approximate.

IR

RE: FEA gives an approximate solution? Why??

Ummm where is FEA not accepted?

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

RE: FEA gives an approximate solution? Why??

Nonlinearer:

One of the take home messages, for a beginner or even an intermediate level FEA person, is that: If you are not aware of the assumptions, you are playing with a time bomb.

RE: FEA gives an approximate solution? Why??

IceBreakerSours... It worse than that !

One word... Ignorance !

> the bomb is already exploded... The problem is that you aren't aware of his existance yet !

Read that : http://opinionator.blogs.nytimes.com/2010/06/20/the-anosognosics-dilemma-1/

RE: FEA gives an approximate solution? Why??

[bigsmile] I stand corrected!

RE: FEA gives an approximate solution? Why??

"Ummm where is FEA not accepted? "
> often FE results are not accepted by the FAA until the model is correlated to test data

RE: FEA gives an approximate solution? Why??

"often FE results are not accepted by the FAA until the model is correlated to test data "

rightly so, there are two many morons out there doing FEA..........it's scary.

RE: FEA gives an approximate solution? Why??

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”

RE: FEA gives an approximate solution? Why??

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

RE: FEA gives an approximate solution? Why??

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.

RE: FEA gives an approximate solution? Why??

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

RE: FEA gives an approximate solution? Why??

“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”

RE: FEA gives an approximate solution? Why??

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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RE: FEA gives an approximate solution? Why??

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

RE: FEA gives an approximate solution? Why??

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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RE: FEA gives an approximate solution? Why??

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”

RE: FEA gives an approximate solution? Why??

" 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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