## FEA verification with hand calculations

## FEA verification with hand calculations

(OP)

Hi,

many people advise to do hand calculations in order to verify FEA results at least approximately. Some even say that they always do these hand calculations. However, I Wonder how it is possible to do such calculations. I know that in static solid mechanics constructions can be simplified to basic elements: beams, bars, frames, trusses, plates, curved beams etc. But it's only possible in case of fairly simple shapes.

Also in other fields (for example buckling, modal analysis) there are some equations that allow hand calculations for specific problems.

But how to do these calculations for example in fluid dynamics ? Even square channel flow would be hard to evaluate. I doubt anyone uses Navier-Stokes equations in such cases.

And as an example of something hard to verify with hand calculations (going back to static stress analysis) can you say how to calculate this (obly the way to do it, without any numbers of course):

https://4437c3e4-a-62cb3a1a-s-sites.googlegroups.c...

or this:

https://keislerautomation.com/products/nanb-miata-...

and this:

http://pelecollins.com/f3-drag-racer/f3-fea/

P.S. From what I know it's not possible to use FEM in hand calculations of anything more complicated than simple bar or couple of beams so I guess it's not the way people do it.

many people advise to do hand calculations in order to verify FEA results at least approximately. Some even say that they always do these hand calculations. However, I Wonder how it is possible to do such calculations. I know that in static solid mechanics constructions can be simplified to basic elements: beams, bars, frames, trusses, plates, curved beams etc. But it's only possible in case of fairly simple shapes.

Also in other fields (for example buckling, modal analysis) there are some equations that allow hand calculations for specific problems.

But how to do these calculations for example in fluid dynamics ? Even square channel flow would be hard to evaluate. I doubt anyone uses Navier-Stokes equations in such cases.

And as an example of something hard to verify with hand calculations (going back to static stress analysis) can you say how to calculate this (obly the way to do it, without any numbers of course):

https://4437c3e4-a-62cb3a1a-s-sites.googlegroups.c...

or this:

https://keislerautomation.com/products/nanb-miata-...

and this:

http://pelecollins.com/f3-drag-racer/f3-fea/

P.S. From what I know it's not possible to use FEM in hand calculations of anything more complicated than simple bar or couple of beams so I guess it's not the way people do it.

## RE: FEA verification with hand calculations

This shows that you understand the mechanics and behavior, that you can model the important aspects parts properly (and the I/O is proper), and that you are prepared to create a useful model of the actual part. You might discover something unanticipated, at which point you resolve this on the verification model(s). It also gives someone else the opportunity to check your models and identify if the simpler models are good choices to represent the behavior (this can uncover a root lack of understanding of the mechanics, which is relatively common). Once the simpler models check out, you increase the confidence that your actual FEM model is done properly (since it should just be an augmented version of the verification models).

Brian

www.espcomposites.com

## RE: FEA verification with hand calculations

## RE: FEA verification with hand calculations

2. Once a sufficient mechanics background and its appropriate use for various actual problems is established (usually over several years), there are many effective (and creative) test models that can be developed. These will be specific to the structure you are solving and the aspects which you want to validate. If you can't think of how to create these, there is a good chance that you have not mastered step 1.

3. Ideally, to minimize the chance of GIGO, the actual FEM should only be done by someone who has mastered steps 1 and 2. In the real world, this often does not occur, especially in today's engineering culture. Some learn all 3 simultaneously (not too bad), but some mostly skip 1 and 2. In turn, FEM has often associated with poor results and GIGO.

Brian

www.espcomposites.com

## RE: FEA verification with hand calculations

But there were no practical examples of how to calculate various structures. It's the biggest problem of universities (at least in my country) but also books as all of them (again - at least in my country) only show simple examples without any real constructions.

So what I need is to examine as many meaningful examples of FEA hand calculations as possible.That's why I am asking you to provide me with some examples and tell me how to solve these models I attached at first. By hand calculations of course. I will be very grateful for such help.## RE: FEA verification with hand calculations

When such solutions are not available, then you divide and (hopefully) conquer by reducing the number of nonlinearities and abstracting the problem down to something that has a known solution (such as solutions involving rods/beams/shells/ .. or benchmarks). Once you have some confidence, only then do you begin to consider swimming in the deep. In this case, you can gain additional confidence by comparing with codes that are different than the one you are using, preferably that does not use the same mathematical framework as your code (FEA vs FD, as an example).

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## RE: FEA verification with hand calculations

Student BEFollowing examples explain what I would do for hand calculation of some complex problems in structural analysis.

1)In a pressure vessel stress analysis with all sorts of complexity I would check whether my hoop and longitudinal(PD/2t, PD/4t) stresses in continuous section are matching with the FEA result. For thermal analysis, I would check for the thermal expansions(LαΔT)matching with FEA deflections.

2)In a problem of Front Lower Control Arms of link you provided- my abstract problem would be to calculate the stress/deflection by hand calculations of L beam with section equivalent to component section with all three end points allowed/restricted as per actual DOF's and load at appropriate points.

All the posts by fellow members tells same thing. It's difficult to find solution by exact hand calculation of FEA problem. One has to abstract the actual problem to simplified problem

where one knows the solution beforehandas for examples above. Then you need to have confidence that yes these results seem appropriate. This confidence comes with experience. Right after school, you can not( and are not expected to) become a expert in field. Also note its easy to check selected no of parameters that we can calculate with formula to validate FEA results rather than finding comprehensive formula that can find solution to the problem.Roark's Formulas for Stress and Strain-This book can help you find formulas for different structural problems and conditions to validate your FEA results. You can also use different Engineering handbooks to find specific formula for hand calculations for validating the FEA results.

## RE: FEA verification with hand calculations

## RE: FEA verification with hand calculations

Depending on your application you might also find experimental data in the literature. This can be a good source for validation of CFD work.

## RE: FEA verification with hand calculations

But there were no practical examples of how to calculate various structures. It's the biggest problem of universities (at least in my country) but also books as all of them (again - at least in my country) only show simple examples without any real constructions.

So what I need is to examine as many meaningful examples of FEA hand calculations as possible. That's why I am asking you to provide me with some examples and tell me how to solve these models I attached at first. By hand calculations of course. I will be very grateful for such help."

This is nothing new. The whole skill in engineering is seeing how to simplify a structure down to elements you can analyze. School is meant to teach you these simple elements, but that depends on how well you learnt them.

I think others have already said this but i'll chime in ...

step away from the FEA, it will seduce you with pretty pictures and scare you with (maybe) some (hidden) truths.

start with simple structures (trusses, beams, bolt groups, etc) ... yes (possibly) boring stuff, but stuff you will nonetheless need.

then start to approach FEA ... approach it as you would a mad bull or a rabid dog (ie carefully) it will turn on you,

but learn the foundation material and then you may become a "model-whisperer",

able to tame this savage beast, and bend it to your will.

but i wax poetic ...

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

## RE: FEA verification with hand calculations

What about thermal analysis (not thermal stress, only temperature calculation) ? How would you verify that ? I guess that nobody uses Fourier’s PDE for verification ?

## RE: FEA verification with hand calculations

can you bounce your modelling off standard text books ?

how difficult to test ??

is there an existing design with known performance that you can model ??

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

## RE: FEA verification with hand calculations

I will give you an example (Easter-related one) - let's say that we want to check how long it will take to cook an egg. We assume that egg is in fact a spherical body and consists of only one material with known thermal properties. We apply temperature (98°C) to the outer surface of that sphere and want to know the time when the temperature inside reaches 50°C. Is it even possible to do it with hand calculations ?

## RE: FEA verification with hand calculations

q_r=-k*A*dT_r/dr

A=4*pi*r^2

dT_r/dt=....

even if that is intractable as an integral (looks doable to me) it is very easy to formulate as a numerical problem and solve it in matlab or excel or python or pretty much any programming language I have ever seen.

as to flow in channels

Prof. White summarized the solution for Poiseuille Flow for non-circular ducts on Chapter (1991 edition).

Viscous Fluid Flow (McGraw-Hill Mechanical Engineering) 3rd Edition

by Frank M. White (Author)

It seems to me you aren't trying very hard to find hand worked examples, any older textbooks or papers will of necessity either have test results or calculus based equations, or both.

Cheers

Greg Locock

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## RE: FEA verification with hand calculations

IMHO that is a really bad way to learn FEA. I'd start with theory, but who has time for that. So start with simple problems you can solve by hand.

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

## RE: FEA verification with hand calculations

Running these simple problems can be a great aid in self-teaching, to see how the software can be used for classes of problems that you are unfamiliar with. Once you understand how to model and interpret a simple "classical" problem, you can "stretch your wings" and apply the methods to your own "real world" problems.

If you can't access your software's verification and benchmark manuals, see if your library can access the NAFEMS Benchmark manuals. For example,

"Selected FE Benchmarks in Structural & Thermal Analysis"will probably have an example that you can apply to your "cooking an egg" problem.http://julianh72.blogspot.com

## RE: FEA verification with hand calculations

Also, (this is how I felt when I was starting out), I think the expectation was that hand calculations are 'quick', i.e. you can quickly get a result in 1/2 an hour or something, whereas in reality you could spend hours/potentially days validating something done in an CAE program.

It's all experience though - you're not going to get this quickly, you need a lot of examples. There aren't sets of crazy equations to calculate stresses in complex brackets that you aren't aware of yet - really, you just start by looking at something, thinking "Well, this looks kind of like a beam, can I calculate the stress like a beam?" and go from there. Your answer most likely won't line up, that's when you start asking questions (to colleagues, teachers, etc) to work out what you might be missing,

Finally, get a copy of a book like Roarks Formulas for Stress and Strain - 90% of the time you should be able to simplify something down to one of the cases in that book.

## RE: FEA verification with hand calculations

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## RE: FEA verification with hand calculations

I guess this topic should be in Frequently Asked Questions(FAQ). Besides there are lot of posts on this topic on eng-tips forums. After reading various posts on forums and bit of reading articles on net, I am compiling books which can help FEA engineers to validate their analysis results by abstract problem formulas. Since this can be lengthy discussion, I have started new thread.

thread727-437411: Book List: For validating FE analysis/CFD Analysis results

## RE: FEA verification with hand calculations

## RE: FEA verification with hand calculations

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

## RE: FEA verification with hand calculations

Hand calc's is a basic check you don't have any unit errors, wrong constraints etc.