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# FEA verification with hand calculations3

## 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):

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

You don't need to verify the actual model. But you can do simple verification models (various ones) that capture the responses of interest for the actual model (deflection, stress, natural frequency, nonlinearity, etc.). These would use the same type of element(s) and be as similar to the actual model as possible, but in a form that can be cross checked 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).

### RE: FEA verification with hand calculations

(OP)
Thanks for your reply. It sounds like a good idea to create simplified models for verification reasons. But what I wonder is how to do any hand calculations for cases more complicated than for example cantilever beam bending. I've heard that it's a good idea to use Free Body Diagrams for that but I'm looking for examples and other methods of hand calculations in FEM verification.

### RE: FEA verification with hand calculations

1. First, you should have a very solid understanding of classical solutions (without the use of FEM). Without this, there is significant chance of GIGO (garbage in, garbage out). The unfortunate reality is that it is common to go to step 3 for various reasons (simpler to learn FEM than good classical analysis, pressure from management, desire to produce pictures, no mentor to assist in developing classical skillset, limited time, simply unaware that their skillset is not sufficient, etc.).

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.

### RE: FEA verification with hand calculations

(OP)
The problem is that my university only taught me how to solve typical tasks of strength of materials calculations. Like bending of beams, torsion of bars etc. I also had a subject called "fundamentals of machine design" where we were calculating weldments, threaded connections and similar problems.

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

There are several solutions in elasticity/fluids/fluid-structure interaction/structure-thermal interaction/EM/EM-structure interaction/.. .. .. that code developers try to compare their numerical solutions against. These are usually referred to as benchmarks. There are researchers whose primary area of interest is to come up with such benchmark problems and their solutions. For instance, Hertz was a giant in a variety of areas and he provided a classic solution for contact. These benchmarks can vary from simple cantilever beam bending solutions in elasticity to complex multiphysics analytical solutions (though these are hard to come by, for good reason).

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 BE

Following 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 beforehand as 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

(OP)
Thank you very much. And how would you check results from CFD simulation ? For example flow in square channel or curved one.

### RE: FEA verification with hand calculations

There are entire chapters in fluid mechanics textbooks dedicated to internal (pipe/duct) flow, external flow and open channel flow. I would start there.

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

"The problem is that my university only taught me how to solve typical tasks of strength of materials calculations. Like bending of beams, torsion of bars etc. I also had a subject called "fundamentals of machine design" where we were calculating weldments, threaded connections and similar problems.

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 ...

### RE: FEA verification with hand calculations

(OP)
I will try to look for some examples but I doubt there are any useful equations for square channel flow.

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

my previous comments intended for stress FEA, but possibly applicable to other fields. the basic question is "how confident are you that your model is telling the truth ?

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 ??

### RE: FEA verification with hand calculations

(OP)
Most calculations I perform are made for problems that do not come from real designs. I learn FEA at my university creating my own examples. So it's hard to verify them otherwise than using 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

Never done it but that's uniaxial heat flux with a varying cross section

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

"I learn FEA at my university creating my own examples."

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.

### RE: FEA verification with hand calculations

Most (all?) reputable commercial FEA software will include references to industry-standard benchmarks and verification problems. Some of these are aimed at verifying that the software does indeed converge to the relevant "classical solution" when appropriate element properties and boundary conditions are applied, while others test the stability of the software and element formulations to converge when used in non-ideal meshes, such as high aspect ratio elements, small included corner angles, etc.

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.

### RE: FEA verification with hand calculations

I wonder if there is some confusion between calling them 'hand calculations' and the intent of telling someone 'do some hand calculations' - I mean, the example regarding the egg would be terrible to do on paper, but could be put into a spreadsheet in a couple of hours. No one (well, probably no one) is expecting a fully worked by hand calculation if you can put it in a spreadsheet, as long as you can explain how the spreadsheet works, and how it matches the model.

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

Fellow Members

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

(OP)
Thank you very much for all the replies. I am really glad that it's possible to get such a complex help on this forum. I will start from expanding my knowledge in terms of typical cases like beams or bars. Roark's book will be helpful for sure. However I am still looking for some examples of how to simplify real structures to these basic cases. If you know any good resources for that it will be nice if you let me know.

### RE: FEA verification with hand calculations

"how to simplify real structures to these basic cases" ... years, and years, of experience with successes and failures.

### RE: FEA verification with hand calculations

I usually check reaction forces, and that displacements are in the correct order of magnitude. This can be verified with hand calc's; free body diagram, displacement of a similar size but "simple" part. Also compare with handbook data for fillet stresses and measurements, if you have such data. If your part is constrained in a statically indeterminate manner, i.e. over constrained, you need to consider to include more of the structure in the analysis, include contacts etc. Sometimes the load history is not known, is such cases, strain gauge measurements are valuable.

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

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